├── .DS_Store ├── .gitignore ├── .ipynb_checkpoints ├── DirectProof-checkpoint.ipynb ├── Frameworks for Proofs (P.1 and P.2)-checkpoint.ipynb ├── Jupyter-tutorial-checkpoint.ipynb ├── ProofAnalysis-P3P4-checkpoint.ipynb └── clustering_coefficients-checkpoint.ipynb ├── .vscode └── settings.json ├── Background_for_Euler_and_Hamilton_structures.ipynb ├── Coding from the S8.ipynb ├── Graphs_in_Python_with_networkX.ipynb ├── LICENSE.md ├── MTH225-Fall2021 ├── .DS_Store ├── 225-python.md ├── Information on MTH 225 Final Exam.md ├── assessments │ ├── .DS_Store │ ├── daily-prep │ │ ├── dp-1-1.md │ │ ├── dp-1-2.md │ │ ├── dp-1-3.md │ │ ├── dp-1-4.md │ │ ├── dp-2-1.md │ │ ├── dp-2-2.md │ │ ├── dp-3-2.md │ │ ├── dp-3-3.md │ │ ├── dp-3-4.md │ │ ├── dp-4-1.md │ │ ├── dp-4-5.md │ │ ├── dp-5-1.md │ │ ├── dp-5-6.md │ │ └── dp-5-7.md │ ├── lt-quizzes │ │ ├── f21-last-quiz.pdf │ │ ├── f21-quiz3.pdf │ │ ├── f21-quiz4.pdf │ │ ├── f21-quiz5.pdf │ │ ├── f21-quiz6.pdf │ │ ├── f21-quiz7.pdf │ │ ├── f21-quiz8.pdf │ │ └── lt-miniquiz.pdf │ ├── video-problems.md │ └── weekly-challenge │ │ ├── MTH 225_ Weekly Challege 10.md │ │ ├── MTH 225_ Weekly Challege 6.md │ │ ├── MTH 225_ Weekly Challenge 1.md │ │ ├── MTH 225_ Weekly Challenge 2.md │ │ ├── MTH 225_ Weekly Challenge 3.md │ │ ├── MTH 225_ Weekly Challenge 4.md │ │ ├── MTH 225_ Weekly Challenge 5.md │ │ ├── MTH 225_ Weekly Challenge 7.md │ │ ├── MTH 225_ Weekly Challenge 8.md │ │ ├── MTH 225_ Weekly Challenge 9.md │ │ ├── Numpy tutorial for Weekly Challenge 9.md │ │ ├── wc1.md │ │ ├── wc2.md │ │ ├── wc3.md │ │ ├── wc4.md │ │ ├── wc5.md │ │ └── wc8.md ├── class-outlines │ └── mth225-class-outlines.md ├── course-documentation │ ├── MTH 225 Fall 2021 Learning Targets.md │ ├── MTH 225 Fall 2021 Syllabus.md │ ├── MTH 225 Grade Tracking Checklist Oct update.pdf │ ├── MTH225-F21-syllabus-Oct-31-Update.pdf │ ├── MTH225-F21-syllabus-OctUpdate.pdf │ ├── MTH225-F21-syllabus.pdf │ ├── MTH225-F21-syllabus.tex │ ├── course-map │ ├── crypto-intro.md │ ├── induction.md │ └── specifications.md ├── design-notes │ ├── crypto.md │ ├── mth225-activities-planning.md │ ├── mth225-assessment-planning.md │ ├── mth225-communication-plan.md │ ├── mth225-learning-objectives.md │ ├── mth225-learning-targets.md │ ├── mth225-learning-targets.pdf │ ├── mth225-map.html │ ├── mth225-schedule-draft.md │ ├── mth225-topic-map-other.md │ ├── mth225-topic-map.md │ ├── mth225-video-list.md │ └── syllabus-outline.md └── f21-startup.md ├── MTH225-Fall2023 ├── .DS_Store ├── .vscode │ └── settings.json ├── activities │ ├── .ipynb_checkpoints │ │ ├── Fibonacci-checkpoint.ipynb │ │ └── Untitled-checkpoint.ipynb │ ├── Basic connectives and negating conditional statements.md │ ├── Basic connectives and negating conditional statements.pdf │ ├── Characteristic_root_check.ipynb │ ├── Class activity October 9 Functions.ipynb │ ├── Dots and dividers pair coding.ipynb │ ├── Fibonacci.ipynb │ ├── Induction practice.md │ ├── Induction practice.pdf │ ├── Itertools demo.ipynb │ ├── Quantifying predicates activity.md │ ├── Truth tables and logical equivalence.md │ └── Untitled.ipynb ├── assignments │ ├── .DS_Store │ ├── Mathematican Induction tutorial.md │ ├── aep │ │ ├── .DS_Store │ │ ├── AEP1-mth225-f23.md │ │ ├── AEP1.docx │ │ ├── AEP2-mth225-f23.md │ │ ├── AEP3-mth225-f23.md │ │ ├── AEP4-mth225-f23-PDFversion.pdf │ │ ├── AEP4-mth225-f23.md │ │ ├── AEP5-mth225-f23.md │ │ ├── AEP6-mth225-f23.md │ │ ├── AEP7-mth225-f23.md │ │ ├── AEP8-mth225-f23.md │ │ └── vp352.png │ └── checkpoints │ │ ├── .DS_Store │ │ ├── .ipynb_checkpoints │ │ └── Checkpoint11_solutions-checkpoint.ipynb │ │ ├── .vscode │ │ └── settings.json │ │ ├── Checkpoint 6 solutions.docx │ │ ├── Checkpoint10_solutions.ipynb │ │ ├── Checkpoint11_solutions.ipynb │ │ ├── Checkpoint12_solutions.ipynb │ │ ├── Checkpoint13_solutions.ipynb │ │ ├── Checkpoint4-LT7-solution.md │ │ ├── Checkpoint5-LT7-solution.md │ │ ├── Checkpoint9_solutions.ipynb │ │ ├── Final Checkpoint solutions.ipynb │ │ ├── MTH 225 F23 Checkpoint 1.pdf │ │ ├── MTH 225 F23 Checkpoint 10.md │ │ ├── MTH 225 F23 Checkpoint 10.pdf │ │ ├── MTH 225 F23 Checkpoint 12.pdf │ │ ├── MTH 225 F23 Checkpoint 13.md │ │ ├── MTH 225 F23 Checkpoint 13.pdf │ │ ├── MTH 225 F23 Checkpoint 7.md │ │ ├── MTH 225 F23 Checkpoint 7.pdf │ │ ├── MTH 225 F23 Checkpoint 8.md │ │ ├── MTH 225 F23 Checkpoint 8.pdf │ │ ├── MTH 225 F23 Checkpoint 9.md │ │ ├── MTH 225 F23 Checkpoint 9.pdf │ │ ├── checkpoint1-mth225-f23.md │ │ ├── checkpoint3-mth225-f23.md │ │ ├── checkpoint4-mth225-f23.md │ │ ├── checkpoint5-mth225-f23.md │ │ ├── checkpoint6-mth225-f23.md │ │ ├── counting_flowchart.png │ │ ├── cp6-lt10.png │ │ ├── cp7-lt10.png │ │ ├── cp9-lt10.png │ │ ├── lt10-cp11.png │ │ ├── lt10-cp8-2.png │ │ └── lt10-cp8.png └── course-docs │ ├── MTH 225 F23 Grade tracker.pdf │ ├── MTH 225 Fall 2023 Syllabus static.pdf │ ├── f23-syllabus-draft.md │ ├── mth225-f23-sample-checkpoint.md │ ├── mth225-logo.png │ ├── mth225-syllabus-f23.md │ └── standards-mth225-f23.md ├── MTH225-Spring2022 ├── .DS_Store ├── Mathematical Induction.md ├── build │ ├── Assessment ideation.md │ ├── Class activities ideation.md │ ├── First pass at grading system.md │ ├── Learning Targets.md │ ├── SPEED ROUND.md │ ├── Spr2022-initial-notes.md │ └── Student onboarding.md ├── class-page-sp22.md ├── course-docs │ ├── MTH 225 Spring 2022 Class Page.md │ ├── MTH 225 Spring 2022 Startup Activity.md │ ├── MTH 225 Startup Assignment.md │ ├── MTH 225 Syllabus, Spring 2022.md │ ├── MTH 225_ Python crash course.md │ ├── class-page-sp22.md │ ├── standards-mth225-spr22.md │ ├── startup-mth225-sp22-pdf.pdf │ ├── startup-mth225-sp22.md │ ├── syllabus-mth225-sp22-DOCX.docx │ ├── syllabus-mth225-sp22-HTML.html │ ├── syllabus-mth225-sp22-PDF.pdf │ ├── syllabus-mth225-sp22-PRINT.md │ └── syllabus-mth225-sp22.md ├── final-exam-info.md ├── lt-quizzes │ ├── Learning Target Final Round.md │ ├── Learning Target Quiz 1 Key.md │ ├── Learning Target Quiz 1.md │ ├── Learning Target Quiz 2.md │ ├── Learning Target Quiz 3.md │ ├── Learning Target Quiz 4.md │ ├── Learning Target Quiz 5.md │ ├── Learning Target Quiz 6.md │ ├── Learning Target Quiz 7.md │ ├── Mini-Quiz June 1.md │ ├── Mini-Quiz June 14.md │ ├── Mini-Quiz June 7.md │ ├── Mini-Quiz May 18.md │ ├── Mini-Quiz May 24.md │ ├── lt-q1.md │ └── lt-q2.md ├── prep │ ├── MTH 225 course planning notes.md │ └── Plan for mathematical induction week.md ├── startup-mth225-sp22.md └── syllabus-mth225-sp22.md ├── MTH225-Winter2024 ├── .vscode │ └── settings.json ├── assignments │ ├── .ipynb_checkpoints │ │ └── Untitled-checkpoint.ipynb │ ├── Fall 2023 Checkpoint 2 solutions.pdf │ ├── Fall 2023 MTH 225 Checkpoint 11 solutions.ipynb │ ├── Fall 2023 MTH 225 Checkpoint 11.pdf │ ├── Fall 2023 MTH 225 Checkpoint 2.md │ ├── MTH 225 Winter 2024 Challenge Problems.md │ ├── MTH 225 Winter 2024 final exam guide.md │ ├── challengeproblem4.png │ └── checkpoints │ │ ├── .ipynb_checkpoints │ │ └── Checkpoint1_answers-checkpoint.ipynb │ │ ├── Checkpoint 10 guide.md │ │ ├── Checkpoint 11 guide.md │ │ ├── Checkpoint 2 solutions.md │ │ ├── Checkpoint 3 guide.html │ │ ├── Checkpoint 3 guide.md │ │ ├── Checkpoint 3 guide_files │ │ └── libs │ │ │ ├── bootstrap │ │ │ ├── bootstrap-icons.css │ │ │ ├── bootstrap-icons.woff │ │ │ ├── bootstrap.min.css │ │ │ └── bootstrap.min.js │ │ │ ├── clipboard │ │ │ └── clipboard.min.js │ │ │ └── quarto-html │ │ │ ├── anchor.min.js │ │ │ ├── popper.min.js │ │ │ ├── quarto-syntax-highlighting.css │ │ │ ├── quarto.js │ │ │ ├── tippy.css │ │ │ └── tippy.umd.min.js │ │ ├── Checkpoint 4 Guide.md │ │ ├── Checkpoint 5 Guide.md │ │ ├── Checkpoint 5.5 guide.md │ │ ├── Checkpoint 6 guide.md │ │ ├── Checkpoint 7 guide.md │ │ ├── Checkpoint 8 guide.md │ │ ├── Checkpoint 9 guide.md │ │ ├── Checkpoint1_answers.ipynb │ │ ├── Checkpoint_0_key.ipynb │ │ ├── MTH 225 Checkpoint 7.pdf │ │ ├── Mini Checkpoint S9 and S10 guide.md │ │ ├── Mini Checkpoint week 11 guide.md │ │ └── Practice Checkpoint 3.pdf └── course-docs │ ├── Function review activity solutions.ipynb │ ├── MTH 225 Final Exam Fall 2023 -- Part A.pdf │ ├── MTH 225 Sample Checkpoint.md │ ├── MTH 225 Winter 2024 Syllabus.md │ ├── Practice tips for MTH 225 Skills.md │ ├── Standards for Student Work W24.md │ ├── Syllabus language from F23.md │ ├── feedback_loop.png │ ├── mth225-syllabus-f23.md │ ├── sample_cp_0.png │ └── standards-mth225-f23.md ├── MTH225-Winter2025 ├── .vscode │ └── settings.json ├── How to practice.md ├── assignments │ ├── .vscode │ │ └── settings.json │ ├── AA Exam 1 Solution Guide.md │ ├── AA Exam 1 reattempt 2.md │ ├── AA Exam 2 Solution Guide.md │ ├── AA-HW1-key.md │ ├── AA-HW1.md │ ├── AA-HW2-key.md │ ├── AA-HW2.md │ ├── AA-HW3-key.md │ ├── AA-HW3.md │ ├── AA-HW4.md │ ├── AA-HW5.md │ ├── AA-HW6.md │ ├── AA-HW7.md │ ├── AA-HW8.md │ ├── AA-HW9.md │ ├── Application Analysis April 16 reattempt solutions.md │ ├── Application Analysis Exam 1 MAKEUP VERSION.docx │ ├── Application Analysis Exam 1 Version 2.docx │ ├── Application Analysis Exam 1.docx │ ├── Application Analysis Exam 2 MAKEUP.md │ ├── Application Analysis Exam 2 MAKEUP.pdf │ ├── Application Analysis Exam 2.pdf │ ├── Application:Analysis Exam 2.md │ ├── Core Target Mini Exam.md │ ├── Core Target mini exam solutions.md │ ├── Key for Practice LT exam.md │ ├── Learning Target 10 Do-Over.md │ ├── Learning Target April 14 reassessment solution guide.md │ ├── Learning Target Exam 1 key.md │ ├── Learning Target Exam 1.md │ ├── Learning Target Exam 2 solution guide.md │ ├── Learning Target Exam 3 solution guide.md │ ├── Learning Target Exam 3.md │ ├── Learning Target Exam 4 MAKEUP.md │ ├── Learning Target Exam 4 solution guide.md │ ├── Learning Target Exam 4.md │ ├── Learning Target reassessment April 14.md │ ├── Learning Target reassessment April 18.md │ ├── lt12-exam3.png │ ├── pascal3.png │ └── pascal3.svg └── course-docs │ ├── 225-w25-logo.jpg │ ├── How to work with set builder notation.md │ ├── MTH 225 Winter 2025 Syllabus.md │ ├── Standards for Student Work MTH 225 W25.md │ └── sample_work.jpg ├── MTH325-Fall2022 ├── .DS_Store ├── application-proof-problems │ ├── MTH 325 Fall 2022 Application Problems.md │ ├── MTH 325 Fall 2022 Proof Problems Selected Solutions.md │ ├── MTH 325 Fall 2022 Proof Problems.md │ └── Proof problems.md ├── assessments │ ├── Content Skill Standard Quiz 1.md │ ├── Content Skill Standard Quiz 10.md │ ├── Content Skill Standard Quiz 2.md │ ├── Content Skill Standard Quiz 3.md │ ├── Content Skill Standard Quiz 4.md │ ├── Content Skill Standard Quiz 5.md │ ├── Content Skill Standard Quiz 6.md │ ├── Content Skill Standard Quiz 7.md │ ├── Content Skill Standard Quiz 8.md │ ├── Content Skill Standard Quiz 9.md │ ├── Key for Learning Target quiz 4, 2021-10-22.md │ ├── Key for Learning Target quiz 5, 2021-10-29.md │ ├── Key for Learning Target quiz 9 (Final exam week).md │ ├── Thumbs.db │ ├── app-problem-1-test.ipynb │ ├── app-problem-6-test.ipynb │ ├── css-quiz-final-html.html │ ├── css-quiz-final-word.docx │ ├── css-quiz-final.md │ ├── css-quiz-final.pdf │ ├── css-quiz10.md │ ├── css-quiz6.md │ ├── css-quiz7.md │ ├── css_quiz1.md │ ├── miniquiz-1.md │ ├── miniquiz-1.pdf │ ├── miniquiz-2.md │ ├── miniquiz-2.pdf │ ├── miniquiz1-tree.png │ ├── q-final-dr5.png │ ├── q-final-g4.png │ ├── q-final-g5.png │ ├── q-final-g6.gif │ ├── q-final-t3.png │ ├── q-final-weighted.png │ ├── q10-dr5.png │ ├── q10-g4.png │ ├── q10-g5.png │ ├── q10-g7.png │ ├── quiz10-t3.png │ └── sample-quiz1.md ├── course-documentation │ ├── # Standards for Student Work in MTH 302.md │ ├── 325-f22-course-banner.png │ ├── Instructions for Oral and Video Quizzes in MTH 325.md │ ├── MTH 325 F22 Grade checklist.pdf │ ├── MTH 325 Fall 2022 Syllabus PDF.pdf │ ├── MTH 325 Fall 2022 Syllabus Word.docx │ ├── MTH 325 Syllabus Fall 2022.md │ ├── MTH325-syllabus-F22.md │ ├── Rplot.png │ ├── Specifications for Student Work in MTH 325.md │ ├── Thumbs.db │ ├── css-dec07-chart │ ├── css-dec07-chart.png │ └── dec07-css-tutorial.md ├── design-notes │ ├── 325W17-Banner.png │ ├── Class plans.md │ ├── Course calendar draft.md │ ├── DRAFT MTH 325 F22 syllabus.md │ ├── Lesson level objectives for MTH 325.md │ ├── MTH 325 Course Banner f22.png │ ├── MTH 325 Fall 2022 assessment plan.md │ ├── MTH 325 Fall 2022 content skill standards.md │ ├── MTH 325 W17 Learning Targets.mdown │ ├── MTH 325 initial planning.md │ ├── MTH325W17-syllabus.md │ ├── MTh 325 F22 course grade plan.md │ ├── Random+Graphs+and+Weighted+Graphs+in+networkX.ipynb │ ├── Refinements on Proofs and Applications.md │ ├── Skill Quiz Prototype.md │ ├── Startup activity outline.md │ ├── Taylor Short MTH 325 syllabus.pdf │ └── random_graph.png └── materials │ ├── Composition of a relation with itself.ipynb │ ├── Conditional Statements and Direct Proof.pdf │ ├── Critical analyses of proofs.md │ ├── Critical analyses of proofs.pdf │ ├── Directed graph review activity.md │ ├── Directed graph review activity.pdf │ ├── Directed_graphs.ipynb │ ├── Isomorphism Hamiltonian circuits.md │ ├── MTH 325 Week 4 Practice Exercises.ipynb │ ├── Mathematical Induction.pdf │ ├── Proof by proving the contrapositive.pdf │ ├── Proof setup practice part 2.pdf │ ├── Proof setup practice.md │ ├── Proof setup practice.pdf │ ├── Weighted_graphs_in_networkx.ipynb │ └── conditional-statements-review.md ├── MTH325-Fall2024 ├── Euler_circuit_investigation.ipynb ├── Graph_coloring_in_networkx.ipynb ├── MTH325-F24-Makeup2-Key.ipynb ├── assignments │ ├── MTH 325 F24 Exams │ │ ├── 325final-s5.png │ │ ├── Core-mini-exam-key.md │ │ ├── Exam 3 key_2.jpg │ │ ├── Exam 3 key_3.jpg │ │ ├── Exam 4 makeup partial key.md │ │ ├── MTH 325 Exam 3 old skills.docx │ │ ├── MTH 325 Exam 4 Makeup.pdf │ │ ├── MTH 325 F24 Exam 2 solutions.docx │ │ ├── MTH 325 F24 Exam 4.md │ │ ├── MTH 325 F24 Exam 4.pdf │ │ ├── MTH 325 F24 Second makeup.pdf │ │ ├── MTH 325 Fall 2024 Exam 1 Solutions.docx │ │ ├── MTH 325 Fall 2024 Exam 1 Solutions.pdf │ │ ├── MTH 325 Fall 2024 Exam 1.docx │ │ ├── MTH 325 Fall 2024 Exam 1.pdf │ │ ├── MTH 325 Fall 2024 Exam 2 New Skills.docx │ │ ├── MTH 325 Fall 2024 Exam 2 New Skills.pdf │ │ ├── MTH 325 Fall 2024 Exam 2 Repeat Skills.docx │ │ ├── MTH 325 Fall 2024 Exam 2 Repeat Skills.pdf │ │ ├── MTH 325 Fall 2024 Exam 3 New skills.docx │ │ ├── MTH 325 Fall 2024 Final Exam Key.md │ │ ├── MTH 325 Fall 2024 First makeup exam.docx │ │ ├── MTH 325 Fall 2024 First makeup exam.pdf │ │ ├── MTH 325 Final Exam flowchart.png │ │ ├── MTH 325 Mini Exam.md │ │ ├── MTH 325 Mini Exam.pdf │ │ ├── MTH325-final-core-f24.md │ │ ├── MTH325-final-core-f24.pdf │ │ ├── MTH325-final-noncore-f24.md │ │ ├── MTH325-final-noncore-f24.pdf │ │ ├── Mini Exam on Core Skills.md │ │ ├── exam4-makeup.md │ │ ├── exam4-skill10.png │ │ ├── exam4-skill5.png │ │ ├── exam4-skill7.png │ │ ├── exam4makeup_s10.png │ │ ├── exam4makeup_s4.png │ │ ├── exam4makeup_s6.jpg │ │ ├── exam4makeup_s7.pdf │ │ ├── exam4makeup_s7.png │ │ ├── exam4makeup_s8.png │ │ ├── exam4makeup_s9.png │ │ ├── final-s10.png │ │ ├── final-s11-answer.png │ │ ├── final-s14-answer.png │ │ ├── final-s4.png │ │ ├── final-s6.png │ │ ├── final-s8.png │ │ ├── final-s9.jpg │ │ ├── final-tree.png │ │ ├── makeup-nov25-skill10.png │ │ ├── makeup-nov25-skill5.png │ │ └── mth325-makeup-nov25.md │ ├── North_Ottawa_Dunes.py │ ├── Proof problems F24.md │ └── btree.png └── course-docs │ ├── 325-logo.png │ ├── MTH 325 Fall 2024 syllabus.md │ ├── MTH 325 grade tracker (updated).pdf │ ├── MTH 325 grade tracker.pdf │ ├── Sample Final Exam W24.md │ ├── Sample final take 2.md │ ├── Standards for Student Work W24.md │ ├── Standards for student work.md │ ├── networkX.ipynb │ ├── sample-final-10.png │ ├── sample-final-11.png │ ├── sample-final-12.png │ ├── sample-final-4.png │ ├── sample-final-5g.png │ ├── sample-final-5h.png │ ├── sample-final-7.png │ └── sample-final-8.png ├── README.md ├── Video ├── Module-1 │ ├── Outlines for Module 1 videos.md │ └── Outlines for Module 2 videos.md ├── Video captions │ ├── 1-1 captions EN.srt │ ├── 1-1 captions ES.srt │ ├── 1-2 captions EN.srt │ ├── 1-2 captions ES.srt │ ├── 1-3 captions EN.srt │ ├── 1-3 captions ES.srt │ ├── 1-4 captions EN.srt │ ├── 1-4 captions ES.srt │ ├── 1-5 captions EN.srt │ ├── 1-5 captions ES.srt │ ├── 1-6 captions EN.srt │ ├── 1-6 captions ES.srt │ ├── 1-7 captions EN.srt │ ├── 1-7 captions ES.srt │ ├── 1-8 captions EN.srt │ ├── 1-8 captions ES.srt │ ├── 1-9 captions EN.srt │ ├── 1-9 captions ES.srt │ ├── 2-1 captions EN.srt │ ├── 2-1 captions SP.srt │ ├── 2-10 captions EN.srt │ ├── 2-10 captions SP.srt │ ├── 2-11 captions EN.srt │ ├── 2-11 captions SP.srt │ ├── 2-2 captions EN.srt │ ├── 2-2 captions SP.srt │ ├── 2-3 captions EN.srt │ ├── 2-3 captions SP.srt │ ├── 2-4 captions EN.srt │ ├── 2-4 captions SP.srt │ ├── 2-5 captions EN.srt │ ├── 2-5 captions SP.srt │ ├── 2-6 captions EN.srt │ ├── 2-6 captions SP.srt │ ├── 2-7 captions EN.srt │ ├── 2-7 captions SP.srt │ ├── 2-8 captions EN.srt │ ├── 2-8 captions SP.srt │ ├── 2-9 captions EN.srt │ ├── 2-9 captions SP.srt │ ├── 3-1 captions EN.srt │ ├── 3-1 captions SP.srt │ ├── 3-2 captions EN.srt │ ├── 3-2 captions SP.srt │ ├── 3-3 captions EN.srt │ ├── 3-3 captions SP.srt │ ├── 3-4 captions EN.srt │ ├── 3-4 captions SP.srt │ ├── 3-5 captions EN.srt │ ├── 3-5 captions SP.srt │ ├── 3-6 captions EN.srt │ ├── 3-6 captions SP.srt │ ├── 3-7 captions EN.srt │ └── 3-7 captions SP.srt ├── binomial coefficient scripts.md ├── scripts-module-1.html ├── scripts-module-1.md ├── scripts-module-2.md ├── scripts-module-3.md ├── scripts-module-4.md └── scripts-module-5.md ├── archive ├── .DS_Store ├── discrete2-archive │ ├── 2017-04-13_14-38-22.png │ ├── Compositions.ipynb │ ├── Counting Permutations in-class exercise.ipynb │ ├── DirectProof.ipynb │ ├── ExampleBST.jpg │ ├── Frameworks for Proofs (P.1 and P.2).ipynb │ ├── Jupyter-tutorial.ipynb │ ├── JupyterEDU-BOF-sample-activity.ipynb │ ├── PartialOrderings.ipynb │ ├── ProofAnalysis-P3P4.ipynb │ ├── ProofAnalysis.png │ ├── ProofByContradiction.ipynb │ ├── ProofByContrapositive.ipynb │ ├── README.md │ ├── RRsolver-assignment.ipynb │ ├── RelationProperties.ipynb │ ├── Relations-digraphs.ipynb │ ├── Relations_Digraphs.ipynb │ ├── SymPy-LADemo.ipynb │ ├── The Jupyter Notebook environment.ipynb │ ├── Transitive+closure.html │ ├── TransitiveClosure.ipynb │ ├── TreesIntroduction.ipynb │ ├── azure-open.png │ ├── bfgraph.png │ ├── bookfacematrix.png │ ├── clustering_coefficients.ipynb │ ├── cp14-FibonacciTrees.ipynb │ ├── diameter-apl.ipynb │ ├── minspanningtrees.ipynb │ ├── networkX-guide.ipynb │ ├── roads.png │ ├── roads_mst.png │ ├── roads_mst2.png │ ├── roads_weighted.png │ ├── rooted-tree.png │ ├── smc-create.png │ ├── stargraph.png │ └── vertex_coloring.ipynb ├── lessons │ ├── .DS_Store │ ├── .ipynb_checkpoints │ │ ├── Lesson1-checkpoint.ipynb │ │ ├── Lesson2-checkpoint.ipynb │ │ ├── LessonTemplate-checkpoint.ipynb │ │ ├── Untitled-checkpoint.ipynb │ │ ├── dh-lesson6-solutions-checkpoint.ipynb │ │ ├── lesson10-checkpoint.ipynb │ │ ├── lesson11-checkpoint.ipynb │ │ ├── lesson12-checkpoint.ipynb │ │ ├── lesson13-checkpoint.ipynb │ │ ├── lesson14-checkpoint.ipynb │ │ ├── lesson15-checkpoint.ipynb │ │ ├── lesson16-checkpoint.ipynb │ │ ├── lesson1718-checkpoint.ipynb │ │ ├── lesson19-checkpoint.ipynb │ │ ├── lesson20-checkpoint.ipynb │ │ ├── lesson22-checkpoint.ipynb │ │ ├── lesson3-checkpoint.ipynb │ │ ├── lesson4-checkpoint.ipynb │ │ ├── lesson5-checkpoint.ipynb │ │ ├── lesson6-checkpoint.ipynb │ │ ├── lesson7-checkpoint.ipynb │ │ ├── lesson8-checkpoint.ipynb │ │ └── lesson9-checkpoint.ipynb │ ├── Konigsberg_bridges.png │ ├── Konigsberg_bridges2.png │ ├── Konigsberg_graph.png │ ├── L17-dh1.png │ ├── L18-dh2.png │ ├── L18-dh3.png │ ├── L18-dh4.png │ ├── Lesson1.html │ ├── Lesson1.ipynb │ ├── Lesson2.html │ ├── Lesson2.ipynb │ ├── LessonTemplate.ipynb │ ├── Untitled.ipynb │ ├── bfgraph.png │ ├── chicken.jpg │ ├── color2.png │ ├── comm_colors2.png │ ├── comm_colors2.svg │ ├── committee_color.png │ ├── committees.png │ ├── committees.svg │ ├── committeessub.png │ ├── dh-lesson6-solutions.ipynb │ ├── g1iso.png │ ├── g1iso2.png │ ├── g4iso2.png │ ├── g5-1.png │ ├── g5-1b.png │ ├── hanoi.jpeg │ ├── hanoi2.png │ ├── hanoiflip.jpeg │ ├── help.gif │ ├── improper_coloring.png │ ├── incomplete_grade_instruction.docx │ ├── k10.png │ ├── k4.png │ ├── l13pa1.png │ ├── l13pa2.png │ ├── lesson10.ipynb │ ├── lesson11.ipynb │ ├── lesson12.ipynb │ ├── lesson13.ipynb │ ├── lesson14.ipynb │ ├── lesson15.ipynb │ ├── lesson16.ipynb │ ├── lesson1718.ipynb │ ├── lesson19.ipynb │ ├── lesson20.ipynb │ ├── lesson22.ipynb │ ├── lesson3.ipynb │ ├── lesson4.ipynb │ ├── lesson5.ipynb │ ├── lesson6.ipynb │ ├── lesson7.ipynb │ ├── lesson8.ipynb │ ├── lesson9.ipynb │ ├── office_map.png │ ├── posethd.png │ ├── proofanalysis.png │ ├── roads.png │ ├── roads_mst.png │ ├── roads_mst2.png │ ├── roads_weighted.png │ ├── sagekernel-gif.gif │ ├── tabcomplete.gif │ ├── treeexamples.png │ └── tstreets.png ├── miniprojects │ ├── .DS_Store │ ├── .ipynb_checkpoints │ │ ├── miniproject1-checkpoint.ipynb │ │ ├── miniproject10-checkpoint.ipynb │ │ ├── miniproject13-checkpoint.ipynb │ │ ├── miniproject14-checkpoint.ipynb │ │ ├── miniproject2-checkpoint.ipynb │ │ ├── miniproject3-checkpoint.ipynb │ │ ├── miniproject4-checkpoint.ipynb │ │ ├── miniproject5-checkpoint.ipynb │ │ ├── miniproject6-checkpoint.ipynb │ │ ├── miniproject7-checkpoint.ipynb │ │ ├── miniproject8-checkpoint.ipynb │ │ └── miniproject9-checkpoint.ipynb │ ├── 20cities.png │ ├── hasse-mp7.png │ ├── jupyter-html.gif │ ├── miniproject1.ipynb │ ├── miniproject10.ipynb │ ├── miniproject13.ipynb │ ├── miniproject14.ipynb │ ├── miniproject2.ipynb │ ├── miniproject3.ipynb │ ├── miniproject4.ipynb │ ├── miniproject5.ipynb │ ├── miniproject6.ipynb │ ├── miniproject7.ipynb │ ├── miniproject8.ipynb │ ├── miniproject9.ipynb │ ├── rrsolverexamples.png │ └── stargraph.png └── mth225-fall2020 │ ├── activities │ ├── 225-4a-dp.md │ ├── 225-4b-dp.md │ ├── 225-python.md │ ├── 225-startup.md │ ├── dadshirt.jpeg │ ├── inclass-template.tex │ ├── module1 │ │ ├── M1A-dp.html │ │ ├── M1A-dp.pdf │ │ ├── M1A-preclass.md │ │ ├── M1B-preclass.html │ │ ├── M1B-preclass.md │ │ ├── M1B-preclass.pdf │ │ ├── MTH 225 Module 1B presentation.pdf │ │ ├── MTH 225-Module-1A-inclass.pdf │ │ ├── Module1-asynchronous.pdf │ │ ├── Module1-inclass.pdf │ │ ├── Module1-inclass.synctex.gz │ │ ├── Module1-inclass.tex │ │ ├── Module1B-asynchronous.pdf │ │ ├── Module1B-inclass.pdf │ │ ├── Module1B-inclass.synctex.gz │ │ ├── Module1B-inclass.tex │ │ ├── dp-template.md │ │ ├── inclass-template.tex │ │ ├── module1-planning.md │ │ └── shirt.jpg │ ├── module10 │ │ ├── 225-10a-dp.html │ │ ├── 225-10a-dp.md │ │ ├── 225-10a-dp.pdf │ │ ├── 225-10b-dp.html │ │ ├── 225-10b-dp.md │ │ ├── 225-10b-dp.pdf │ │ ├── 225-module10-planning.md │ │ ├── MTH 225 Module 10A presentation.pdf │ │ └── MTH 225 Module 10B presentation.pdf │ ├── module11 │ │ ├── 201-11a-dp.html │ │ ├── 201-11a-dp.md │ │ ├── 201-11a-dp.pdf │ │ ├── 201-11b-dp.html │ │ ├── 201-11b-dp.md │ │ ├── 201-11b-dp.pdf │ │ ├── 201-module11-planning.md │ │ └── MTH 225 Module 11A presentation.pdf │ ├── module12 │ │ ├── 225-12a-dp.html │ │ ├── 225-12a-dp.md │ │ ├── 225-12a-dp.pdf │ │ ├── 225-12b-dp.md │ │ ├── 225-module12-planning.md │ │ └── MTH 225 Module 12B presentation.pdf │ ├── module2 │ │ ├── 225-2a-dp.html │ │ ├── 225-2a-dp.md │ │ ├── 225-2a-dp.pdf │ │ ├── 225-2b-dp.html │ │ ├── 225-2b-dp.md │ │ ├── 225-2b-dp.pdf │ │ ├── 2a-async.tex │ │ ├── MTH 225 Module 2B presentation.pdf │ │ ├── Module1B-inclass.tex │ │ ├── Module2A-inclass.pdf │ │ ├── Module2A-inclass.synctex.gz │ │ ├── Module2A-inclass.tex │ │ ├── Module2A-inclass.vrb │ │ ├── Module_2A_demos.ipynb │ │ ├── dp-template.md │ │ └── module2-planning.md │ ├── module3 │ │ ├── 225-3a-dp.html │ │ ├── 225-3a-dp.md │ │ ├── 225-3a-dp.pdf │ │ ├── 225-3b-dp.html │ │ ├── 225-3b-dp.md │ │ ├── 225-3b-dp.pdf │ │ ├── MTH 225 Module 3A presentation.pdf │ │ ├── MTH 225 Module 3B presentation.pdf │ │ └── module3-planning.md │ ├── module4 │ │ ├── 225-4a-dp.html │ │ ├── 225-4a-dp.md │ │ ├── 225-4a-dp.pdf │ │ ├── 225-4b-async.pdf │ │ ├── 225-4b-dp.html │ │ ├── 225-4b-dp.md │ │ ├── 225-4b-dp.pdf │ │ ├── 225-module4-planning.md │ │ ├── 4a-async-activities.pdf │ │ ├── MTH 225 Module 4A presentation.pdf │ │ └── MTH 225 Module 4B presentation.pdf │ ├── module5 │ │ ├── 225-5a-async.pdf │ │ ├── 225-5a-dp.html │ │ ├── 225-5a-dp.md │ │ ├── 225-5a-dp.pdf │ │ ├── 225-5b-async.pdf │ │ ├── 225-5b-dp.html │ │ ├── 225-5b-dp.md │ │ ├── 225-5b-dp.pdf │ │ ├── 225-module5-planning.md │ │ ├── MTH 225 Module 5A presentation.pdf │ │ ├── MTH 225 Module 5B presentation.pdf │ │ └── MTH201-04_totals.csv │ ├── module6 │ │ ├── 225-6a-dp.html │ │ ├── 225-6a-dp.md │ │ ├── 225-6a-dp.pdf │ │ ├── 225-6b-dp.html │ │ ├── 225-6b-dp.md │ │ ├── 225-6b-dp.pdf │ │ ├── 225-module6-planning.md │ │ ├── MTH 225 Module 6A presentation.pdf │ │ └── MTH 225 Module 6B presentation.pdf │ ├── module7 │ │ ├── 225-7a-dp.html │ │ ├── 225-7a-dp.md │ │ ├── 225-7a-dp.pdf │ │ ├── 225-7b-dp.html │ │ ├── 225-7b-dp.md │ │ ├── 225-7b-dp.pdf │ │ ├── 225-module7-planning.md │ │ ├── MTH 225 Module 7A presentation.pdf │ │ ├── MTH 225 Module 7B presentation.pdf │ │ ├── bc-video-2-script.md │ │ ├── bc-video-3-script.md │ │ ├── bc-video-4-script.md │ │ ├── bc-video-5-script.md │ │ ├── binomial-coefficient-video-1-script.txt │ │ └── module7b-video-outlines.md │ ├── module8 │ │ ├── 225-8a-dp.html │ │ ├── 225-8a-dp.md │ │ ├── 225-8a-dp.pdf │ │ ├── 225-8b-dp.html │ │ ├── 225-8b-dp.md │ │ ├── 225-8b-dp.pdf │ │ ├── 225-module8-planning.md │ │ ├── MTH 225 Module 8A presentation.pdf │ │ └── MTH 225 Module 8B presentation.pdf │ ├── module9 │ │ ├── 225-9a-dp.html │ │ ├── 225-9a-dp.md │ │ ├── 225-9a-dp.pdf │ │ ├── 225-module9-planning.md │ │ ├── MTH 225 Module 9A presentation.pdf │ │ └── MTH 225 Module 9B presentation.pdf │ └── pythonjuypter │ │ ├── 225-python.html │ │ ├── 225-python.md │ │ ├── 225-python.pdf │ │ ├── SharinginColab.gif │ │ ├── colab1.jpeg │ │ └── colab2.jpeg │ ├── assessments │ ├── aep │ │ ├── 225-aep-1.html │ │ ├── 225-aep-1.md │ │ ├── 225-aep-1.pdf │ │ ├── 225-aep-2.html │ │ ├── 225-aep-2.md │ │ ├── 225-aep-2.pdf │ │ ├── 225-aep-3.html │ │ ├── 225-aep-3.md │ │ ├── 225-aep-3.pdf │ │ ├── 225-aep-4.html │ │ ├── 225-aep-4.md │ │ ├── 225-aep-4.pdf │ │ ├── 225-aep-5.html │ │ ├── 225-aep-5.md │ │ ├── 225-aep-5.pdf │ │ ├── 225-aep-6.html │ │ ├── 225-aep-6.md │ │ ├── 225-aep-6.pdf │ │ ├── 225-aep-7.md │ │ ├── 225-aep-8.html │ │ ├── 225-aep-8.md │ │ ├── 225-aep-8.pdf │ │ └── aep-template.md │ ├── checkpoints │ │ ├── 225-checkpoint-info.html │ │ ├── 225-checkpoint-info.md │ │ ├── 225-checkpoint-info.pdf │ │ ├── 225-checkpoint1-sample.pdf │ │ ├── 225-checkpoint1-sample.tex │ │ ├── 225-checkpoint2-sample.pdf │ │ ├── 225-checkpoint2-sample.tex │ │ ├── 225-cp10.pdf │ │ ├── 225-cp11.pdf │ │ ├── 225-cp2.pdf │ │ ├── 225-cp6.pdf │ │ ├── 225-cp7.pdf │ │ ├── 225-cp8.pdf │ │ └── 225-cp9.pdf │ └── weeklypractice │ │ ├── 225-wp10.pdf │ │ ├── 225-wp3.pdf │ │ ├── 225-wp4.pdf │ │ ├── 225-wp6.pdf │ │ ├── 225-wp7.pdf │ │ ├── 225-wp8.pdf │ │ ├── Weekly Practice 5 key.pdf │ │ ├── Weekly Practice 6 key.pdf │ │ ├── Weekly Practice 7 key.pdf │ │ └── Weekly Practice 8 key.pdf │ ├── course-documentation │ ├── 225-announcements-template.html │ ├── 225-draft-syllabus.tex │ ├── 225-workflow.png │ ├── EMRN.png │ ├── MTH 225 grading slide.png │ ├── MTH225-Fall2020-Syllabus.docx │ ├── MTH225-Fall2020-Syllabus.html │ ├── MTH225-Fall2020-Syllabus.md │ ├── MTH225-Fall2020-Syllabus.pdf │ ├── MTH225-Learning-Targets (1).pdf │ ├── MTH225-Learning-Targets.docx │ ├── MTH225-Learning-Targets.html │ ├── MTH225-Learning-Targets.pdf │ ├── OLD-MTH225-Fall2020-Syllabus.pdf │ ├── OLD-MTH225-Fall2020-syllabus.md │ ├── OLD-MTH225-Fall2020-syllabus.md~HEAD │ ├── The grading system in MTH 225.png │ ├── V2-MTH225-F2020-Syllabus.md │ ├── partial-syllabus.md │ ├── partial-syllabus.tex │ └── rt-template.tex │ ├── design-notes │ ├── 225-AEP-ideas.md │ ├── 225-TechAssessment.md │ ├── 225-assessment-grading.md │ ├── 225-grading-writeup.md │ ├── 225-learningobjectives.md │ ├── 225-meetings-activities.md │ ├── 225-modules.md │ └── ReplicateThisNotebook.ipynb │ └── templates │ ├── dp-template.md │ ├── followup-template.tex │ └── inclass-template.tex └── materials ├── Digraph_review.ipynb └── Tree traversal intro.md /.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/.DS_Store -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | 2 | MTH225-Fall2023/.DS_Store 3 | MTH225-Fall2023/assignments/.DS_Store 4 | MTH225-Fall2023/assignments/checkpoints/.DS_Store 5 | .DS_Store 6 | -------------------------------------------------------------------------------- /.vscode/settings.json: -------------------------------------------------------------------------------- 1 | { 2 | } -------------------------------------------------------------------------------- /LICENSE.md: -------------------------------------------------------------------------------- 1 | This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. 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| 5 | - Students engage with as much or as little as desired; this will stand in for weekly homework or whatever assessment I choose. 6 | - Or do I want to require some initial portion of this for all students -- then they can go deeper? 7 | - **Liking this approach** -- require the "trunk" of this minicourse for all, then open it up for further exploration as an option for showing mastery of math concepts. Give c 8 | - Includes programming assignments 9 | - Needs explicit ties back to the math concepts 10 | 11 | 12 | 13 | ## Very basic outline 14 | 15 | - Fundamentals 16 | - Plaintext, ciphertext, key 17 | - Specific cryptosystems 18 | - Substitution ciphers 19 | - Caesar; shift 20 | - Cryptograms (monoalphabetic) 21 | - Number of keys for a cryptogram (*factorial*) 22 | - Decimation; affine 23 | - Valid keys for decimation cipher (*concept of GCD and Euclidean algorithm*) 24 | - Vigenere (polyalphabetic) 25 | - Transposition ciphers 26 | - Rail fence, columnar transposition, etc. 27 | - One time pad 28 | - Computer ciphers 29 | - XOR 30 | - S-DES 31 | - Public-key 32 | - Kid Crypto 33 | - RSA 34 | - El Gamal 35 | - Other crypto concepts 36 | - Shared secret keys 37 | - Digital signatures 38 | -------------------------------------------------------------------------------- /MTH225-Fall2021/design-notes/mth225-activities-planning.md: -------------------------------------------------------------------------------- 1 | # MTH 225 general activity planning 2 | 3 | - The course meets MWF for 50 minutes. 4 | - 10 + 30 + 10: 5 | - 10 minutes of recap and Q&A 6 | - 30 minutes of activity on main topics/advanced objectives 7 | - 10 minutes of wrapup/metacognition 8 | 9 | 10 | ## Preclass activities 11 | 12 | - The usual, video and text with exercises to complete 13 | - But also: 14 | - What did you already know about this topic that could guide your learning? 15 | - What is the most confusing thing about this topic so far? 16 | 17 | "1 point" for completing the pre-class on time, no gaps, no BS. 18 | 19 | 20 | ## Ideas for activities in class 21 | 22 | - First 10 23 | - Polling 24 | - Quizzes 25 | - Finish a blank copy of preclass 26 | - "1 point" for satisfactory completion of the startup activity. So 2 "points" total. 27 | - Middle 30 28 | - Hands-on activities with sharing out 29 | - Could be polling 30 | - Could be doing computations, truth tables, etc. 31 | - Always involves presenting/explaining work and reasoning. 32 | - **THERE IS NO LECTURING** unless it's a spot lecture -- **trust the preclass activities** 33 | - Final 10 34 | - Polling to isolate main ideas 35 | - A single feedback form for questions, metacognition that we use every class 36 | - What is the least clear point of this topic? *The most confusing thing about today's lesson was...* 37 | - What worked for you today? *Something that really helped me learn today was...* 38 | - *Something I still need to learn is...* 39 | -------------------------------------------------------------------------------- /MTH225-Fall2021/design-notes/mth225-communication-plan.md: -------------------------------------------------------------------------------- 1 | # How will we communicate? 2 | 3 | - Early in the class, maybe at end of week 1: Questionnaire on how it's going, what do you need, etc. 4 | - Daily: Form at end of class for questions and comments 5 | - Biweekly: Check-in using the five-question summary + open ended questions; and post summaries 6 | - MIT for around week 7 or 8 7 | - Ongoing: 8 | - Office hours: Ask students early how they want this. In person or virtual? And when/how often? 9 | - Discussion board or Slack 10 | - Make up a guide on how to ask questions 11 | - Weekly guides posted Friday afternoons 12 | - Forms: Token requests, feedback/suggestions that's anonymous, grade discrepancies -------------------------------------------------------------------------------- /MTH225-Fall2021/design-notes/mth225-learning-targets.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Fall2021/design-notes/mth225-learning-targets.pdf -------------------------------------------------------------------------------- /MTH225-Fall2021/design-notes/mth225-schedule-draft.md: -------------------------------------------------------------------------------- 1 | # Timetable for MTH 225 module coverage 2 | 3 | 4 | 5 | ## Modules 6 | 7 | | Module | Focus | Days (using schedule below) | 8 | | :---: | :---: | :---: | 9 | | 1 | Arithmetic | 4 | 10 | | 2 | Logic | 6 | 11 | | 3 | Sets and functions | 9 | 12 | | 4 | Combinatorics | 8 | 13 | | 5 | Sequences, Recursion, and Induction | 10 | 14 | 15 | 16 | ## Schedule draft 17 | 18 | 19 | | Week | Dates | Focus | Notes | 20 | | --- | ------ | ----- | ----- | 21 | | 1 | Aug 30-Sept 3 | Onboarding + Module 1 | First day onboarding | 22 | | 2 | Sept 6-10 | Module 1 | Labor Day Sept 6 | 23 | | 3 | Sept 13-17 | Module 2 | | 24 | | 4 | Sept 20-24 | Module 2 | | 25 | | 5 | Sept 27-Oct 1 | Module 3 | | 26 | | 6 | Oct 4-8 | Module 3 | | 27 | | 7 | Oct 11-15 | Module 3 | | 28 | | 8 | Oct 18-22 | Module 4 | | 29 | | 9 | Oct 25-29 | Module 4 | Fall Break Oct 25 | 30 | | 10 | Nov 1-5 | Module 4 | | 31 | | 11 | Nov 8-12 | Module 5 | | 32 | | 12 | Nov 15-19 | Module 5 | | 33 | | 13 | Nov 22-26 | Module 5 | Thanksgiving Nov 24-26 | 34 | | 14 | Nov 29-Dec 3 | Module 5 | | 35 | | 15 | Dec 6-10 | Catch-up and review | | -------------------------------------------------------------------------------- /MTH225-Fall2021/design-notes/mth225-topic-map.md: -------------------------------------------------------------------------------- 1 | # MTH 225 2 | 3 | ## Computer arithmetic 4 | 5 | - Number bases 6 | - Representation in base 2, 8, 10, and 16 7 | - Arithmetic in binary 8 | - Modular arithmetic 9 | - The division algorithm 10 | - The `MOD` (`%`) operator 11 | 12 | ## Logic 13 | 14 | - Propositions and logic operations 15 | - Propositions 16 | - AND, OR, and NOT 17 | - Conditional statements, converse, contrapositive 18 | - Truth tables 19 | - Truth tables for basic logic operations 20 | - Truth tables for compound propositions 21 | - Logical equivalence 22 | - Predicates 23 | - Predicates vs. propositions 24 | - Truth set of a predicate 25 | - Quantification 26 | - Existential and universal quantifiers 27 | - Double quantified statements 28 | - Truth of quantified statements; underdetermined statements 29 | - Negating quantified statements 30 | 31 | ## Sets and Functions 32 | 33 | - Set definition and notation 34 | - Definition of a set; finite vs infinite sets; the empty set 35 | - Roster and set-builder notation 36 | - Elements of sets 37 | - Subsets and set equality 38 | - Power set of a set 39 | - Set operations 40 | - Intersection 41 | - Union 42 | - Difference and complement 43 | - Cartesian product 44 | - Functions 45 | - Definition of a function 46 | - Function properties 47 | - Injective 48 | - Surjective 49 | - Bijective 50 | - Special functions for CS 51 | - Floor 52 | - Ceiling 53 | - Factorial 54 | - `DIV` and `MOD` 55 | 56 | 57 | ## Combinatorics 58 | 59 | - Basic counting techniques 60 | - Additive principle 61 | - Multiplicative principle 62 | - The binomial coefficient 63 | - As the solution to a counting problem (introduction to recursion) 64 | - As the entries of Pascal's triangle 65 | - As a formula 66 | - Advanced techniques 67 | - Combinations and permutations 68 | - Stars and bars 69 | - Principle of inclusion and exclusion 70 | - Combinatorial proofs 71 | 72 | ## Sequences and recursion 73 | 74 | - Defining and computing sequences 75 | - With a closed formula 76 | - With a recursive definition 77 | - Solving recurrence relations 78 | - Checking a proposed solution 79 | - Solving recurrence relations with characteristic roots 80 | - Mathematical induction 81 | - The Principle of Mathematical Induction 82 | - Framework for an induction proof 83 | - Identifying the predicate 84 | - Establishing the base case 85 | - Stating the inductive hypothesis 86 | - Proving the inductive step 87 | - Critical analysis of an induction proof 88 | - Writing induction proofs 89 | -------------------------------------------------------------------------------- /MTH225-Fall2021/design-notes/mth225-video-list.md: -------------------------------------------------------------------------------- 1 | Onboarding (4) 2 | ---------- 3 | 4 | - 0.1 Introduction to MTH 225 5 | - 0.2 Overview of the syllabus and course policies 6 | - 0.3 Examples of how the grading system works 7 | - 0.4 How to succeed in MTH 225 8 | 9 | Module 1 (10) 10 | -------- 11 | 12 | - 1.1 Representing an integer in base 10 and base 2 13 | - 1.2 Representation in base 8 and 16 14 | - 1.3 Algorithm for changing representations 15 | - 1.4 Addition in different bases 16 | - 1.5 Subtraction in different bases 17 | - 1.6 Multiplication in different bases 18 | - 1.7 Division in different bases 19 | - 1.8 Using two's complement to represent negative integers 20 | - 1.9 The division algorithm 21 | - 1.10 The MOD `%` operator 22 | 23 | Module 2 (12) 24 | -------- 25 | 26 | What is a logical proposition 27 | AND, OR, and NOT 28 | Conditional statements, converse, contrapositive 29 | When is a conditional statement true? 30 | Truth tables for basic logic operations 31 | Truth tables for compound propositions 32 | Logical equivalence 33 | Predicates vs. propositions 34 | Domain and truth set of a predicate 35 | Existential and universal quantifiers; when these are true 36 | Double quantified statements 37 | Negation of quantified statements 38 | 39 | 40 | Module 3 (14) 41 | -------- 42 | 43 | Definition of a set; finite vs infinite sets; empty set 44 | Roster and set-builder notation 45 | Set membership; Determining if an object is an element of a set 46 | Subsets and set equality 47 | Power set of a set and cardinality 48 | Intersection 49 | Union 50 | Difference and complement 51 | Cartesian product 52 | What is a function vs. a non function; the domain, codomain, and range of a function 53 | Injective functions 54 | Surjective functions 55 | Bijective functions 56 | Special functions: Ceiling, floor, factorial, DIV, MOD 57 | 58 | Module 4 (9) 59 | -------- 60 | 61 | Additive principle 62 | Multiplicative principle 63 | BC As the solution to a counting problem (introduction to recursion) 64 | BC As the entries of Pascal's triangle 65 | BC As a formula 66 | Combinations and permutations 67 | Stars and bars 68 | Principle of inclusion and exclusion 69 | How to choose the right counting method 70 | 71 | Module 5 (12) 72 | -------- 73 | 74 | Sequences With a closed formula 75 | Sequences With a recursive definition 76 | Sigma notation 77 | Arithmetic and geometric series 78 | Finding a recurrence relation for a sequence 79 | Checking a proposed solution to a recurrence relation 80 | Solving recurrence relations with characteristic roots 81 | Intro to the principle of mathematical induction 82 | Framework for a proof by induction 83 | More examples of a framework for a proof by induction 84 | Performing a critical analysis of a proof 85 | How to write induction proofs 86 | 87 | -------------------------------------------------------------------------------- /MTH225-Fall2021/f21-startup.md: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Fall2021/f21-startup.md -------------------------------------------------------------------------------- /MTH225-Fall2023/.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Fall2023/.DS_Store -------------------------------------------------------------------------------- /MTH225-Fall2023/.vscode/settings.json: -------------------------------------------------------------------------------- 1 | {} -------------------------------------------------------------------------------- /MTH225-Fall2023/activities/.ipynb_checkpoints/Fibonacci-checkpoint.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 4, 6 | "id": "bf68fb40-ff79-4d69-8df9-4a24251a8150", 7 | "metadata": { 8 | "tags": [] 9 | }, 10 | "outputs": [], 11 | "source": [ 12 | "# Computes the nth Fibonacci number recursively\n", 13 | "\n", 14 | "def F(n): \n", 15 | " if n == 1 or n == 2: \n", 16 | " return 1\n", 17 | " else: \n", 18 | " return F(n-1) + F(n-2) " 19 | ] 20 | }, 21 | { 22 | "cell_type": "code", 23 | "execution_count": 9, 24 | "id": "7e81ecd9-4a3a-4c15-8f85-3ba7e99558f7", 25 | "metadata": { 26 | "tags": [] 27 | }, 28 | "outputs": [], 29 | "source": [ 30 | "# Computes the sum of the first k Fibonacci numbers\n", 31 | "\n", 32 | "def sum_fib(k): \n", 33 | " return sum([F(i) for i in range(1,k+1)])" 34 | ] 35 | } 36 | ], 37 | "metadata": { 38 | "kernelspec": { 39 | "display_name": "Python 3 (ipykernel)", 40 | "language": "python", 41 | "name": "python3" 42 | }, 43 | "language_info": { 44 | "codemirror_mode": { 45 | "name": "ipython", 46 | "version": 3 47 | }, 48 | "file_extension": ".py", 49 | "mimetype": "text/x-python", 50 | "name": "python", 51 | "nbconvert_exporter": "python", 52 | "pygments_lexer": "ipython3", 53 | "version": "3.10.12" 54 | } 55 | }, 56 | "nbformat": 4, 57 | "nbformat_minor": 5 58 | } 59 | -------------------------------------------------------------------------------- /MTH225-Fall2023/activities/.ipynb_checkpoints/Untitled-checkpoint.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [], 3 | "metadata": {}, 4 | "nbformat": 4, 5 | "nbformat_minor": 5 6 | } 7 | -------------------------------------------------------------------------------- /MTH225-Fall2023/activities/Basic connectives and negating conditional statements.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Fall2023/activities/Basic connectives and negating conditional statements.pdf -------------------------------------------------------------------------------- /MTH225-Fall2023/activities/Characteristic_root_check.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 1, 6 | "metadata": {}, 7 | "outputs": [], 8 | "source": [ 9 | "def a(n):\n", 10 | " return 13/5*(4)**n + 12/5*(-1)**n" 11 | ] 12 | }, 13 | { 14 | "cell_type": "code", 15 | "execution_count": 3, 16 | "metadata": {}, 17 | "outputs": [ 18 | { 19 | "data": { 20 | "text/plain": [ 21 | "[5.0, 8.0, 44.0, 164.0, 668.0, 2660.0, 10652.0, 42596.0, 170396.0, 681572.0]" 22 | ] 23 | }, 24 | "execution_count": 3, 25 | "metadata": {}, 26 | "output_type": "execute_result" 27 | } 28 | ], 29 | "source": [ 30 | "[a(n) for n in range(10)]" 31 | ] 32 | }, 33 | { 34 | "cell_type": "code", 35 | "execution_count": 4, 36 | "metadata": {}, 37 | "outputs": [], 38 | "source": [ 39 | "def b(n):\n", 40 | " if n == 0: return 5\n", 41 | " elif n == 1: return 8\n", 42 | " else:\n", 43 | " return 3*b(n-1) + 4*b(n-2)" 44 | ] 45 | }, 46 | { 47 | "cell_type": "code", 48 | "execution_count": 5, 49 | "metadata": {}, 50 | "outputs": [ 51 | { 52 | "data": { 53 | "text/plain": [ 54 | "[5, 8, 44, 164, 668, 2660, 10652, 42596, 170396, 681572]" 55 | ] 56 | }, 57 | "execution_count": 5, 58 | "metadata": {}, 59 | "output_type": "execute_result" 60 | } 61 | ], 62 | "source": [ 63 | "[b(n) for n in range(10)]" 64 | ] 65 | }, 66 | { 67 | "cell_type": "code", 68 | "execution_count": null, 69 | "metadata": {}, 70 | "outputs": [], 71 | "source": [ 72 | "Maruszczyk" 73 | ] 74 | } 75 | ], 76 | "metadata": { 77 | "kernelspec": { 78 | "display_name": "base", 79 | "language": "python", 80 | "name": "python3" 81 | }, 82 | "language_info": { 83 | "codemirror_mode": { 84 | "name": "ipython", 85 | "version": 3 86 | }, 87 | "file_extension": ".py", 88 | "mimetype": "text/x-python", 89 | "name": "python", 90 | "nbconvert_exporter": "python", 91 | "pygments_lexer": "ipython3", 92 | "version": "3.11.5" 93 | } 94 | }, 95 | "nbformat": 4, 96 | "nbformat_minor": 2 97 | } 98 | -------------------------------------------------------------------------------- /MTH225-Fall2023/activities/Fibonacci.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 4, 6 | "id": "bf68fb40-ff79-4d69-8df9-4a24251a8150", 7 | "metadata": { 8 | "tags": [] 9 | }, 10 | "outputs": [], 11 | "source": [ 12 | "# Computes the nth Fibonacci number recursively\n", 13 | "\n", 14 | "def F(n): \n", 15 | " if n == 1 or n == 2: \n", 16 | " return 1\n", 17 | " else: \n", 18 | " return F(n-1) + F(n-2) " 19 | ] 20 | }, 21 | { 22 | "cell_type": "code", 23 | "execution_count": 9, 24 | "id": "7e81ecd9-4a3a-4c15-8f85-3ba7e99558f7", 25 | "metadata": { 26 | "tags": [] 27 | }, 28 | "outputs": [], 29 | "source": [ 30 | "# Computes the sum of the first k Fibonacci numbers\n", 31 | "\n", 32 | "def sum_fib(k): \n", 33 | " return sum([F(i) for i in range(1,k+1)])" 34 | ] 35 | } 36 | ], 37 | "metadata": { 38 | "kernelspec": { 39 | "display_name": "Python 3 (ipykernel)", 40 | "language": "python", 41 | "name": "python3" 42 | }, 43 | "language_info": { 44 | "codemirror_mode": { 45 | "name": "ipython", 46 | "version": 3 47 | }, 48 | "file_extension": ".py", 49 | "mimetype": "text/x-python", 50 | "name": "python", 51 | "nbconvert_exporter": "python", 52 | "pygments_lexer": "ipython3", 53 | "version": "3.10.11" 54 | } 55 | }, 56 | "nbformat": 4, 57 | "nbformat_minor": 5 58 | } 59 | -------------------------------------------------------------------------------- /MTH225-Fall2023/activities/Induction practice.md: -------------------------------------------------------------------------------- 1 | # Practice with mathematical induction frameworks 2 | 3 | ## MTH 225, 2023-09-29 4 | 5 | 6 | 7 | ### Activity 1 8 | 9 | You just made a conjecture that for all natural numbers $n$, 10 | 11 | $$1 + 2 + 4 + 8 + \cdots + 2^n = 2^{n+1} - 1$$ 12 | 13 | 14 | 15 | 1. What is the predicate in this conjecture? Write it out: $P(n)$ is…. 16 | 17 | 18 | 19 | 2. What value of $n$ is the base case? 20 | 21 | 22 | 23 | 3. Show that the base case holds, by a direct computation or demonstration. 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 4. Write out the inductive hypothesis in precise terms, without using the notation "$P(n)$" . (Start with the phrase "Assume that…") 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 5. State what you would need to prove next, in the inductive step. 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | Then watch the board for an actual proof. Later in the course you will be learning how to write one of these yourself. 54 | 55 | 56 | 57 | 58 | 59 | ### Activity 2 60 | 61 | 62 | 63 | Here's another conjecture: **For all natural numbers $n \geq 4$, $2^n \geq n^2$.** 64 | 65 | 1. What is the predicate in this conjecture? Write it out: $P(n)$ is…. 66 | 67 | 68 | 69 | 2. What value of $n$ is the base case? 70 | 71 | 72 | 73 | 3. Show that the base case holds, by a direct computation or demonstration. 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 | 82 | 83 | 4. Write out the inductive hypothesis in precise terms, without using the notation "$P(n)$" . (Start with the phrase "Assume that…") 84 | 85 | 86 | 87 | 88 | 89 | 90 | 91 | 5. State what you would need to prove next, in the inductive step. 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 | 101 | 102 | 103 | Then watch the board for an actual proof. Later in the course you will be learning how to write one of these yourself. 104 | 105 | -------------------------------------------------------------------------------- /MTH225-Fall2023/activities/Induction practice.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Fall2023/activities/Induction practice.pdf -------------------------------------------------------------------------------- /MTH225-Fall2023/activities/Quantifying predicates activity.md: -------------------------------------------------------------------------------- 1 | # Quick Activity: Quantifying predicates 2 | 3 | ## MTH 225, 2023-09-20 4 | 5 | Below are several predicates, and next to each one is a box for the *existentially quantified* predicate and a box for the *universally quantified* predicate. 6 | 7 | If you believe the existentially or universally quantified predicate is a *proposition*, then determine whether it's **TRUE** or **FALSE** and put your result in the appropriate box. 8 | 9 | If you believe the existentially or universally quantified predicate is a *predicate* whose truth value depends on the value of an input, write **PREDICATE** in the box. 10 | 11 | The domain of each predicate below is the set of all non-negative integers: $\{ 0, 1, 2, 3, \dots \}$. (We will soon refer to this set as the set of all **natural numbers**.) 12 | 13 | 14 | 15 | | Predicate $P(n)$ | Existentially quantified $\exists n P(n)$ | Universally quantified $\forall n P(n)$ | 16 | | ------------------------------------------------------------ | ----------------------------------------- | --------------------------------------- | 17 | | The number $n$ is less than $5$. | | | 18 | | The number $n$ is between $0$ and $1$ (but not equal to $0$ or $1$). | | | 19 | | The number $n$ , when divided by 2, has a remainder of either 0 or 1. | | | 20 | 21 | **Bonus question**: Can you come up with a predicate $Q(n)$ whose domain is the natural numbers (like above), where $\exists n Q(n)$ is **FALSE** but $\forall n Q(n)$ is **TRUE**? If so, write that predicate out. If not, be ready to explain why not. -------------------------------------------------------------------------------- /MTH225-Fall2023/activities/Truth tables and logical equivalence.md: -------------------------------------------------------------------------------- 1 | # Truth tables and logical equivalence 2 | 3 | ## MTH 225, 2023-09-15 4 | 5 | 6 | 7 | ### Warm-up 8 | 9 | **Write a truth table for $\neg (P \rightarrow Q)$.** Questions to ask first: How many rows will it have? What should the columns be? What goes in each row/column and how do you tell? 10 | 11 | 12 | 13 | 14 | 15 | ### Basic practice and application to logical equivalence 16 | 17 | First: recall that the truth table for $P \rightarrow Q$ is 18 | 19 | | $P$ | $Q$ | $P \rightarrow Q$ | 20 | | :--: | :--: | :---------------: | 21 | | T | T | T | 22 | | T | F | F | 23 | | F | T | T | 24 | | F | F | F | 25 | 26 | 27 | 28 | 1. Write a truth table for $(\neg P) \vee Q$. (How many rows? What are the columns? How do you fill them in?) 29 | 30 | 2. Write a truth table for $P \wedge (\neg Q)$. (How many rows? What are the columns? How do you fill them in?) 31 | 32 | 3. Write a truth table for $(\neg P) \rightarrow (\neg Q)$. 33 | 34 | 4. To which of the three propositions above is $P \rightarrow Q$ logically equivalent? (*What does that term mean? How do you know when two propositions are logically equivalent?*) 35 | 36 | 5. Which of the statements in questions 1-3 is logically equivalent to $\neg (P \rightarrow Q)$? 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | ### More complex truth tables 45 | 46 | Exercises are on the slides for today. -------------------------------------------------------------------------------- /MTH225-Fall2023/activities/Untitled.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": null, 6 | "id": "c9994960-a4d7-4f92-baaf-2840ed6861e6", 7 | "metadata": {}, 8 | "outputs": [], 9 | "source": [] 10 | } 11 | ], 12 | "metadata": { 13 | "kernelspec": { 14 | "display_name": "Python 3 (ipykernel)", 15 | "language": "python", 16 | "name": "python3" 17 | }, 18 | "language_info": { 19 | "codemirror_mode": { 20 | "name": "ipython", 21 | "version": 3 22 | }, 23 | "file_extension": ".py", 24 | "mimetype": "text/x-python", 25 | "name": "python", 26 | "nbconvert_exporter": "python", 27 | 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/MTH225-Spring2022/.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Spring2022/.DS_Store -------------------------------------------------------------------------------- /MTH225-Spring2022/build/Assessment ideation.md: -------------------------------------------------------------------------------- 1 | # Ideating the assessment scheme for 225 2 | 3 | Skills based learning targets 4 | - Regular quizzing: At least weekly. Require two successful demonstrations. 5 | - Alternatives to quizzing: Presentation in class; live oral quiz via appointment or drop in hours. 6 | 7 | 8 | Problems 9 | - These are like AEPs, in fact I might call them that 10 | - Fewer in number and fewer required; maybe only 1 for a C 11 | - Graded EMRN 12 | - Assign in batches -- as many as possible in weeks 1-2 13 | - Can submit two things a week -- Two new submissions, two revisions, or one of each 14 | - Use to satisfy "problem solving" standards 15 | 16 | Final exam: 17 | - Could just be a final reattempt of Learning Targets 18 | - Or put up something more summative, perhaps using Blackboard and multiple-choice questions? Require 60% for A, 50% for B, etc. 19 | 20 | Daily Prep 21 | - Completeness and effort 22 | - Maybe use Perusall? 23 | - Answering basic reading/viewing questions + doing simple exercises 24 | - Completeness and effort only 25 | 26 | Something like a "Practice Portfolio" 27 | - Students work on applying the concepts from the class to simple problems and explaining their work 28 | - Assign weekly -- 5-10 problems each 29 | - Turn in on Blackboard 30 | - Graded Pass/Revise based on full correctness 31 | 32 | **Never mind on the above**, that is way too much grading. Instead, electronic homework practice. 33 | - Weekly sets of 10-12 problems automatically graded 34 | - Require a reasonable number of these completed each week 35 | - Time allowed in class for practice and questions 36 | - *Use WeBWorK* and use excerpts from WW in weekly quizzes. 37 | 38 | **The idea here is that the class will be "truly flipped" with the vast majority of assessed work taking place *during* the synchronous meetings, and most out of class stuff is just reading, viewing, asking questions.** 39 | 40 | ## First pass at the grade construction 41 | 42 | Course grade is based on: 43 | - Daily Prep completion 44 | - Weekly practice completion 45 | - Number of Learning Targets mastered -- split into core and non-core 46 | - Number of AEPs completed at passing level or above 47 | - Final exam 48 | 49 | -------------------------------------------------------------------------------- /MTH225-Spring2022/build/Class activities ideation.md: -------------------------------------------------------------------------------- 1 | # Ideating class activities 2 | 3 | ## General thoughts 4 | 5 | - Each class is 1:00-3:15 which is 135 minutes long. 6 | - Structure into pomodoros: 7 | - 1:00-1:25, then a break -- For review and q/a on preclass work 8 | - 1:30-1:55, then a break -- For focused group work where we're all working on the same thing 9 | - 2:00-2:25, then a break -- Continuation of P3 10 | - 2:30-3:00, then a break -- For continued work, or stations, or online homework 11 | - 3:00-3:15 for wrapping up and metacognition 12 | - Unless we take a pomorodo for assessments: 13 | - 1:00-1:25, then a break -- For review and q/a on preclass work 14 | - 1:30-1:55, then a break -- For focused group work where we're all working on the same thing 15 | - 2:00-2:25, then a break -- For continued work, or stations, or online homework 16 | - 2:30-2:45 for wrap-up/metacognition 17 | - 2:45-3:15 assessment 18 | - Focus each day on one, maybe two learning targets and practice 19 | - What needs to happen each day: 20 | - Warmup and review, q/a on new material (pomodoro 1) 21 | - Practice on new material -- all focus on new content (pomodoro 2+3) 22 | - Free time for practice on whatever -- split into stations (pomodoro 4) 23 | - Replace station practice with assessment on assessment days 24 | 25 | ## Class activities 26 | 27 | - For warmup and review, polling activities (PollEverywhere) 28 | - Pomodoro 2 activities: Students doing focused work in working groups -- problems on Jamboard (or whatever) then debrief and present 29 | - All activities have these in common: 30 | - They look like/instantiate the Learning Target quizzes *or* build up some significant piece of an AEP *or* they result in some cool discovery *or* illustration of an important point 31 | - They are done either collaboratively, or first individually and then collaboratively 32 | - The work is made visible by doing it on a board or in a Google Doc (and curated in an ongoing Class Page) 33 | - They end result is made available for questions and is saved for later reference 34 | - Students reflect on what they are doing 35 | 36 | 37 | Remember: 38 | ![Construction of understanding ecosystem](http://rtalbert.org/content/images/2022/01/2022-01-26_9-04-30.png) -------------------------------------------------------------------------------- /MTH225-Spring2022/build/First pass at grading system.md: -------------------------------------------------------------------------------- 1 | # First pass at grading system 2 | 3 | ## Components 4 | 5 | - Learning Target "demonstrations of skill" (includes but not limited to quizzes): 21 LTs, 8 core. 6 | - AEPs (maybe around 6-8 of these) 7 | - Practice 8 | - Daily Prep 9 | - Final exam 10 | 11 | ## The system 12 | 13 | | | Learning Targets completed (21) | All 8 Core Learning Targets complete? | AEP marks | Practice points (60+) | Daily Prep (20) | Final Exam score (70) | 14 | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | 15 | | A | 18 | Yes | 1 E and 1 M+ | 50 | 17 | 42 | 16 | | B | 15 | Yes | 1 M+ | 42 | 14 | 35 | 17 | | C | 12 | No | none | 34 | 11 | 28 | 18 | | D | 9 | No | none | 26 | 8 | 21 | 19 | 20 | F = Not all the requirements for a D are met. 21 | 22 | **Plus/minus:** 23 | 24 | * Plus: Meet all the requirements for a grade plus next level higher in two of Standards Completed, AEPs, or Final Exam. 25 | * Minus: Meet all the requirements for a grade except one, and that one cannot be more than one level lower. 26 | 27 | ## Tokens 28 | 29 | - Third AEP submission in a week 30 | - 24-hour deadline extension 31 | - Assessment on a "Retired" Learning Target -------------------------------------------------------------------------------- /MTH225-Spring2022/build/SPEED ROUND.md: -------------------------------------------------------------------------------- 1 | # SPEED ROUND 2 | 3 | ## Modules 4 | 5 | - ~~Binary~~ Computer arithmetic 6 | - Logic 7 | - Sets and Functions 8 | - Sequences and recursion 9 | - Combinatorics 10 | - Introduction to proof and mathematical induction 11 | 12 | Early insertion: What constitutes a good argument or solution; recursion early 13 | 14 | **Learning targets attached to each of the "skills" outcomes in the modules** 15 | 16 | 17 | 18 | ## Assessment types 19 | 20 | See/copy from: https://gradingforgrowth.com/p/case-study-hubert-muchalskis-hybrid?s=r 21 | 22 | - Quizzes covering the learning targets (most learning targets in the lower half of Bloom) 23 | - Give twice weekly? Tues/Thurs with lt's appearing on three consecutive ones 24 | - Final exam = recertification on LTs 25 | - Homework for computation practice (just the LTs with maybe some higher level stuff) -- ideally this is electronic and self-graded 26 | - Problems -- upper levels of Bloom, give these whenever with expiration dates, grade EMRN; group these off by topic 27 | 28 | ## Definition of A and C 29 | 30 | - An "A" in this class looks like: All the core learning targets are passed (with two separate demonstrations of skill); nearly all the non-core ones are passed; reasonable engagement with practice problems has taken place; strong recertification on the final exam has happened; and at least a couple of problems from each group have been successfully (M+) completed with several Es. In other words: Evidence of mastery on the skills with strong showings on the applications and more difficult problems. 31 | - A "C" in this class looks like: Demonstrated skill on all core LTs but not necessarily mastery; also skill on half? of the non-core ones; a handful (small!) of problems solved successfully. 32 | 33 | *I'm noticing I'm not even thinking about Daily Prep. Is this a time when flipping a class isn't a good idea?* 34 | 35 | ## Feedback loop 36 | 37 | - AEP's/problems are easy: They submit them on Bb or whatever, I grade them, they redo them, up to twice a week. Continue until passed. 38 | - If I can manage online homework, the feedback is in the system -- but students can also get help through a discussion board? (Maybe? These never seem to work out) 39 | - Quizzes -- students take the quiz, they get marks and written feedback, but I can also create solution videos at least for the first attempts; then they can retake. Offer live office hours reattempts up to two targets per week by appointment and ending in week 5. -------------------------------------------------------------------------------- /MTH225-Spring2022/build/Spr2022-initial-notes.md: -------------------------------------------------------------------------------- 1 | # Initial notes for Spring 2022 MTH 225 2 | 3 | ## Draft timetable 4 | 5 | | Day | Topics | 6 | | :--: | :-----: | 7 | | 1 - May 9 | Onboarding | 8 | | 2 - May 10 | Integer representation; binary addition/subtraction | 9 | | 3 - May 11 | Multiplication and division in binary; special functions | 10 | | 4 - May 12 | Propositions and conditional statements; Assessment 1 | 11 | | 5 - May 16 | Truth tables; predicates; quantified statements | 12 | | 6 - May 17 | Sets, set notation, subsets, set operations | 13 | | 7 - May 18 | Functions, domain, range, injective, etc. | 14 | | 8 - May 19 | Additive and multiplicative principles; Assessment 2 | 15 | | 9 - May 23 | Binomial coefficient | 16 | | 10 - May 24 | Permutations, $k$-permutations; stars and bars | 17 | | 11 - May 25 | Open practice with counting problems | 18 | | 12 - May 26 | Sequences and recursion; Assessment 3 | 19 | | 13 - May 30 | Sigma notation; summing sequences; arithmetic and geometric sequences | 20 | | 14 - May 31 | Coming up with and checking recurrence relations | 21 | | 15 - June 1 | Characteristic root method | 22 | | 16 - June 2 | | 23 | | 17 - June 6 | | 24 | | 18 - June 7 | | 25 | | 19 - June 8 | | 26 | | 20 - June 9 | | 27 | | 21 - June 13 | | 28 | | 22 - June 14 | | 29 | | 23 - June 15 | | 30 | | 24 - June 16 | | -------------------------------------------------------------------------------- /MTH225-Spring2022/build/Student onboarding.md: -------------------------------------------------------------------------------- 1 | # Student to-do list prior to start of semester 2 | 3 | - Sign in to WeBWorK and complete onboarding course 4 | - Obtain some way of writing on a screen 5 | - Learn how to scan and upload PDF 6 | - Submit a survey with background and group work style for assignment into working groups 7 | - Perusall: 8 | - Set up account and sign in 9 | - Annotate copy of the syllabus with a question or comment 10 | - Annotate an image 11 | - Annotate on a video 12 | - Leave a note on Jamboard or whatever whiteboarding tool I use 13 | - Complete syllabus quiz 14 | 15 | 16 | ## Tools 17 | 18 | - Whiteboarding tool 19 | - Perusall 20 | - Other: hackmd, Google Forms, Poll Everywhere -- no training required 21 | 22 | 23 | ## Perusall specifically 24 | 25 | - How to create an account and sign on 26 | - How to find assignments 27 | - What you can do 28 | - Read 29 | - Highlight 30 | - Take notes 31 | - Comment 32 | - Ask questions 33 | - Reply to comments and answer questions 34 | - Perusall's auto grading 35 | - Download and print 36 | 37 | 38 | https://www.youtube.com/watch?v=_PfAc0D2erk -------------------------------------------------------------------------------- /MTH225-Spring2022/course-docs/class-page-sp22.md: -------------------------------------------------------------------------------- 1 | --- 2 | tags: 225-spr22, class-page 3 | --- 4 | 5 | # MTH 225 Spring 2022 Class Page 6 | 7 | ## BIG LINKS 8 | 9 | | | | | 10 | | :--: | :--: | :--: | 11 | | :book: [Textbook](http://discrete.openmathbooks.org/dmoi3.html) | :tv: [Video playlist](https://vimeo.com/showcase/8667148) | :calendar: Class calendar | 12 | | :link: [Class meeting Zoom link](https://gvsu-edu.zoom.us/j/6163318968?pwd=bnFudTBGbE4xbG1DMitDbGhtYkFGdz09) | :male-student: [Drop-in hours Zoom link](https://gvsu-edu.zoom.us/j/6163318968?pwd=bnFudTBGbE4xbG1DMitDbGhtYkFGdz09) | :question: [Padlet for Questions](https://padlet.com/talbertr1/6itl6dvga4zytpc1) | 13 | | Learning Target list | Standards | *Final exam info (coming later)* | 14 | | Daily Preps | AEPs | Learning Target quizzes | 15 | 16 | ## Week 1 (May 9-12) 17 | 18 | ### Day 1: May 9 19 | -------------------------------------------------------------------------------- /MTH225-Spring2022/course-docs/startup-mth225-sp22-pdf.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Spring2022/course-docs/startup-mth225-sp22-pdf.pdf -------------------------------------------------------------------------------- /MTH225-Spring2022/course-docs/syllabus-mth225-sp22-DOCX.docx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Spring2022/course-docs/syllabus-mth225-sp22-DOCX.docx -------------------------------------------------------------------------------- /MTH225-Spring2022/course-docs/syllabus-mth225-sp22-PDF.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Spring2022/course-docs/syllabus-mth225-sp22-PDF.pdf -------------------------------------------------------------------------------- /MTH225-Spring2022/lt-quizzes/Learning Target Quiz 1 Key.md: -------------------------------------------------------------------------------- 1 | --- 2 | tags: 225-spr22, mth225, lt-quiz 3 | --- 4 | 5 | # Learning Target Quiz 1 Key 6 | 7 | -------------------------------------------------------------------------------- /MTH225-Spring2022/lt-quizzes/Learning Target Quiz 1.md: -------------------------------------------------------------------------------- 1 | --- 2 | tags: 225-spr22, mth225, lt-quiz 3 | --- 4 | 5 | # Learning Target Quiz 1 6 | 7 | :::info 8 | 9 | This is your first Learning Target quiz! This quiz contains questions for **Learning Targets 1 and 2**. 10 | 11 | * It's to your advantage to attempt as many problems as possible. But you *do not* need to attempt all the problems. Only attempt the ones you believe you are ready to take. 12 | * Do your work on separate pages with **each Learning Target on its own separate page**. *Please do not put multiple Learning Targets on the same page.* 13 | * Make sure to consult the [Standards for Assessments in MTH 225](/KoT83ezHRYO3DqPyXMMMag) document before starting on your work, so you're clear on what is expected and what constitutes a "successful" attempt. 14 | * When you are done: **Scan** each Learning Target to a clear, legible, black-and-white PDF and **upload the PDF** to the designated folder on Blackboard. Remember *do not just take a picture with your camera* --- use a scanning app to create a PDF, and upload the PDF. 15 | 16 | ::: 17 | 18 | ## Learning Target 1 19 | 20 | :::warning 21 | I can represent an integer in base 2, 8, 10, and 16 including negative integers in base 2. 22 | ::: 23 | 24 | Do **all** of the following: 25 | 26 | 1. Convert the base 10 integer $334$ to binary. *Show your work and circle your answer*. 27 | 2. Convert the base 8 integer $725$ to decimal. *Show your work and circle your answer*. 28 | 3. Convert the base 2 integer `10110011` to hexadecimal. *Show your work and circle your answer*. 29 | 4. The 8-bit binary representation of the decimal number $77$ is `01001101`. Write the 8-bit binary representation of $-77$ using two's complement notation. *Show your work and circle your answer*. 30 | 31 | **Success criteria:** All four answers are correct, and the work leading to each answer is clear and legible. Up to two simple errors are allowed. 32 | 33 | 34 | ## Learning Target 2 35 | 36 | :::warning 37 | (**CORE**) I can add, subtract, multiply, and divide numbers in base 2. 38 | ::: 39 | 40 | Do **all** of the following: 41 | 42 | 1. Add the base-2 integers `10011100` and `0110111`. *Show your work and circle your answer*. 43 | 2. Subtract the base-2 integers `10011100` and `0110111`. *Show your work and circle your answer*. 44 | 3. Multiply the base-2 integers `11011` and `110`. *Show your work and circle your answer*. 45 | 4. Divide the base-2 integer `11001101` by `110`. *Show your work and circle your answer*. 46 | 47 | **Success criteria:** All four answers are correct, and the work leading to each answer is clear and legible. Up to two simple errors are allowed. -------------------------------------------------------------------------------- /MTH225-Spring2022/lt-quizzes/lt-q1.md: -------------------------------------------------------------------------------- 1 | --- 2 | tags: 225-spr22, mth225, lt-quiz 3 | --- 4 | 5 | # Learning Target Quiz 1 6 | 7 | :::info 8 | 9 | This is your first Learning Target quiz! This quiz contains questions for **Learning Targets 1 and 2**. 10 | 11 | * It's to your advantage to attempt as many problems as possible. But you *do not* need to attempt all the problems. Only attempt the ones you believe you are ready to take. 12 | * Do your work on separate pages with **each Learning Target on its own separate page**. *Please do not put multiple Learning Targets on the same page.* 13 | * Make sure to consult the [Standards for Assessments in MTH 225](/KoT83ezHRYO3DqPyXMMMag) document before starting on your work, so you're clear on what is expected and what constitutes a "successful" attempt. 14 | * When you are done: **Scan** each Learning Target to a clear, legible, black-and-white PDF and **upload the PDF** to the designated folder on Blackboard. Remember *do not just take a picture with your camera* --- use a scanning app to create a PDF, and upload the PDF. 15 | 16 | ::: 17 | 18 | ## Learning Target 1 19 | 20 | :::warning 21 | I can represent an integer in base 2, 8, 10, and 16 including negative integers in base 2. 22 | ::: 23 | 24 | Do **all** of the following: 25 | 26 | 1. Convert the base 10 integer $334$ to binary. *Show your work and circle your answer*. 27 | 2. Convert the base 8 integer $725$ to decimal. *Show your work and circle your answer*. 28 | 3. Convert the base 2 integer `10110011` to hexadecimal. *Show your work and circle your answer*. 29 | 4. The 8-bit binary representation of the decimal number $77$ is `01001101`. Write the 8-bit binary representation of $-77$ using two's complement notation. *Show your work and circle your answer*. 30 | 31 | **Success criteria:** All four answers are correct, and the work leading to each answer is clear and legible. Up to two simple errors are allowed. 32 | 33 | 34 | ## Learning Target 2 35 | 36 | :::warning 37 | (**CORE**) I can add, subtract, multiply, and divide numbers in base 2. 38 | ::: 39 | 40 | Do **all** of the following: 41 | 42 | 1. Add the base-2 integers `10011100` and `0110111`. *Show your work and circle your answer*. 43 | 2. Subtract the base-2 integers `10011100` and `0110111`. *Show your work and circle your answer*. 44 | 3. Multiply the base-2 integers `11011` and `110`. *Show your work and circle your answer*. 45 | 4. Divide the base-2 integer `11001101` by `110`. *Show your work and circle your answer*. 46 | 47 | **Success criteria:** All four answers are correct, and the work leading to each answer is clear and legible. Up to two simple errors are allowed. -------------------------------------------------------------------------------- /MTH225-Spring2022/prep/Plan for mathematical induction week.md: -------------------------------------------------------------------------------- 1 | # Plan for mathematical induction week 2 | 3 | ## Day 1 4 | 5 | - Daily Prep: Read "handout" on mathematical induction and maybe a video or two, answer questions about base case, induction hypothesis, inductive step 6 | - In class: 7 | - Example: Sums of binomial coefficients 8 | - Example: Sums of powers of 2 9 | - Example: Something visual? 10 | - Polling activity -- pick out the parts of the framework 11 | 12 | ## Ready to go following day 1: 13 | 14 | - AEP 6: Like AEP from Fall 15 | - Blackboard quiz over frameworks (complete with 9/10 to pass, 3 attempts) 16 | - Perusall discussion area 17 | 18 | 19 | ## Day 2 20 | 21 | - Activity with 2-3 statements. Write out the frameworks. Write completed proofs 22 | - Miniquiz including LT 21 23 | - Set to autopost later - video debrief of the examples and miniquiz problem 24 | 25 | ## Day 3 26 | 27 | - Activity with 2-3 statements. Write out the frameworks. Write completed proofs 28 | - Another miniquiz with just LT 21 on it 29 | - Set to autopost later - video debrief of the example and quiz problem 30 | 31 | ## Day 4 32 | 33 | - Just a quiz with 21 targets on it -------------------------------------------------------------------------------- /MTH225-Winter2024/.vscode/settings.json: -------------------------------------------------------------------------------- 1 | {} -------------------------------------------------------------------------------- /MTH225-Winter2024/assignments/Fall 2023 Checkpoint 2 solutions.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Winter2024/assignments/Fall 2023 Checkpoint 2 solutions.pdf -------------------------------------------------------------------------------- /MTH225-Winter2024/assignments/Fall 2023 MTH 225 Checkpoint 11.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Winter2024/assignments/Fall 2023 MTH 225 Checkpoint 11.pdf -------------------------------------------------------------------------------- /MTH225-Winter2024/assignments/challengeproblem4.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Winter2024/assignments/challengeproblem4.png -------------------------------------------------------------------------------- /MTH225-Winter2024/assignments/checkpoints/.ipynb_checkpoints/Checkpoint1_answers-checkpoint.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [], 3 | "metadata": {}, 4 | "nbformat": 4, 5 | "nbformat_minor": 5 6 | } 7 | -------------------------------------------------------------------------------- /MTH225-Winter2024/assignments/checkpoints/Checkpoint 3 guide_files/libs/bootstrap/bootstrap-icons.woff: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Winter2024/assignments/checkpoints/Checkpoint 3 guide_files/libs/bootstrap/bootstrap-icons.woff -------------------------------------------------------------------------------- /MTH225-Winter2024/assignments/checkpoints/Checkpoint 3 guide_files/libs/quarto-html/tippy.css: -------------------------------------------------------------------------------- 1 | .tippy-box[data-animation=fade][data-state=hidden]{opacity:0}[data-tippy-root]{max-width:calc(100vw - 10px)}.tippy-box{position:relative;background-color:#333;color:#fff;border-radius:4px;font-size:14px;line-height:1.4;white-space:normal;outline:0;transition-property:transform,visibility,opacity}.tippy-box[data-placement^=top]>.tippy-arrow{bottom:0}.tippy-box[data-placement^=top]>.tippy-arrow:before{bottom:-7px;left:0;border-width:8px 8px 0;border-top-color:initial;transform-origin:center top}.tippy-box[data-placement^=bottom]>.tippy-arrow{top:0}.tippy-box[data-placement^=bottom]>.tippy-arrow:before{top:-7px;left:0;border-width:0 8px 8px;border-bottom-color:initial;transform-origin:center bottom}.tippy-box[data-placement^=left]>.tippy-arrow{right:0}.tippy-box[data-placement^=left]>.tippy-arrow:before{border-width:8px 0 8px 8px;border-left-color:initial;right:-7px;transform-origin:center left}.tippy-box[data-placement^=right]>.tippy-arrow{left:0}.tippy-box[data-placement^=right]>.tippy-arrow:before{left:-7px;border-width:8px 8px 8px 0;border-right-color:initial;transform-origin:center right}.tippy-box[data-inertia][data-state=visible]{transition-timing-function:cubic-bezier(.54,1.5,.38,1.11)}.tippy-arrow{width:16px;height:16px;color:#333}.tippy-arrow:before{content:"";position:absolute;border-color:transparent;border-style:solid}.tippy-content{position:relative;padding:5px 9px;z-index:1} -------------------------------------------------------------------------------- /MTH225-Winter2024/assignments/checkpoints/Checkpoint 5.5 guide.md: -------------------------------------------------------------------------------- 1 | # Checkpoint 5.5 guide 2 | 3 | ## C1 4 | 5 | Original statement: *If the rug is dirty, then it should be vacuumed.* 6 | 7 | 1. The rug is dirty 8 | 2. The rug should be vacuumed 9 | 3. If the rug needs to be vacuumed, then it's dirty. 10 | 4. If the rug doesn't need to be vacuumed, then it isn't dirty. 11 | 5. If the rug is not dirty, then it shouldn't be vacuumed. 12 | 6. The rug is dirty but it does not need to be vacuumed. 13 | 14 | ### Common mistakes 15 | 16 | - **Forming the converse by reversing the order of the sentence but without changing the hypothesis and conclusion:** This would look like "*The rug should be vacuumed if it's dirty.*" Note the word "if" here: What follows the word "if" is the hypothesis of the statement, no matter where it is located. And it's the same hypothesis as the initial statement; the logic of the conditional statement hasn't changed, so this isn't the converse. 17 | - **Forming the negation incorrectly:** The negation of $P \rightarrow Q$ is $P \wedge (\neg Q)$ (that is, " $P$ and not $Q$"). In particular the negation of this statement **is not** another if-then statement. 18 | 19 | ## C2 20 | 21 | Proposition: For every integer $n \geq 1$, the number $3^n - 1$ is a multiple of $2$. 22 | 23 | 1. The predicate $P(n)$ is " $3^n - 1$ is a multiple of $2$.". 24 | 2. $n=1$ 25 | 3. Suppose $n=1$. Then $3^n - 1 = 3^1 - 1 = 3 - 1 = 2$. This is a multiple of $2$ (since $2= 2 \times 1$) so the base case holds. 26 | 4. Assume that for some integer $k>1$, $3^k - 1$ is a multiple of $2$. 27 | 5. Prove that $3^{k+1} - 1$ is a multiple of $2$. 28 | 29 | ### Common mistakes 30 | 31 | - **Including the universal quantifier when stating the predicate:** That is, stating that the predicate is the entire statement "For every integer $n \geq 1$, the number $3^n - 1$ is a multiple of $2$." Including the "for every..." quantifier is incorrect because if you quantify the predicate, the result is not a predicate any more. And note that the success criteria specifically state that the quantifier is not to be included, for that reason. 32 | - **Not putting the word "assume" in the inductive hypothesis:** The inductive hypothesis is important because it is an *assumption* that we make to begin an argument. You want to be clear to your reader that you are making an assumption; leaving the word "assume" off, makes this very unclear. 33 | - **Using "for all" instead of "for some" in the inductive hypothesis:** That is, stating "Assume that for *every* integer $k>1$, $3^k - 1$ is a multiple of $2$." We discussed in class why this is incorrect -- it amounts to assuming the very statement that you are proving. -------------------------------------------------------------------------------- /MTH225-Winter2024/assignments/checkpoints/MTH 225 Checkpoint 7.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Winter2024/assignments/checkpoints/MTH 225 Checkpoint 7.pdf -------------------------------------------------------------------------------- /MTH225-Winter2024/assignments/checkpoints/Mini Checkpoint S9 and S10 guide.md: -------------------------------------------------------------------------------- 1 | # Mini Checkpoint S9 and S10 guide 2 | 3 | ## S9 4 | 5 | | Part | Type of sequence | Closed formula | Recursive definition | 6 | | --- | ---- | ---- | --- | 7 | | 1 | Arithmetic | $a(n) = 4n+3$ | $a_0 = 3, a_n = a_{n-1} + 4$ | 8 | | 2 | Geometric | $a(n) = 3 \cdot 4^n$ | $a_0 = 3, a_n = 4a_{n-1}$ | 9 | | 3 | Neither | n/a | n/a | 10 | | 4 | Geometric | $a(n) = 10 \cdot \left( \frac{1}{2} \right)^n$ | $a_0 = 10, a_n = \frac{1}{2}a_{n-1}$ | 11 | 12 | 13 | ## S10 14 | 15 | The characteristic equation for the recurrence relation is 16 | $$r^2 = -4r + 12$$ 17 | Getting all the terms on the left gives $r^2 +4r - 12 = 0$. This factors into $(r+6)(r-2) = 0$ on the left, so the characteristic roots are $r = -6$ and $r=2$. 18 | 19 | The framework for the solution using those roots is: 20 | $$a(n) = c_1 (-6)^n + c_2 (2)^n$$ 21 | 22 | Plugging in $n=0$ gives the equation $1 = c_1 (-6)^0 + c_2(2)^0$ which simplifies to $c_1 + c_2 = 1$. 23 | 24 | Plugging in $n=1$ gives the equation $3 = c_1 (-6)^1 + c_2(2)^1$ which simplifies to $-6c_1 + 2c_2 = 3$. 25 | 26 | Using the "substitution" method for solving the system of equations, solve the first one for $c_2$ to get $c_2 = 1 - c_1$. Put this in for $c_2$ in the second one to get $-6c_1 + 2(1-c_1) = 3$. Simplifying this gives $2 - 8c_1 = 3$, so $c_1 = -1/8$. 27 | 28 | If $c_1 = -1/8$, then $c_2 = 1 - (-1/8) = 9/8$. 29 | 30 | So the final solution is 31 | $$a(n) = -\frac{1}{8} (-6)^n + \frac{9}{8} (2)^n$$ 32 | 33 | (Decimals instead of fractions is OK as well, as long as they are correct and you showed work on how you got them.) -------------------------------------------------------------------------------- /MTH225-Winter2024/assignments/checkpoints/Practice Checkpoint 3.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Winter2024/assignments/checkpoints/Practice Checkpoint 3.pdf -------------------------------------------------------------------------------- /MTH225-Winter2024/course-docs/MTH 225 Final Exam Fall 2023 -- Part A.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Winter2024/course-docs/MTH 225 Final Exam Fall 2023 -- Part A.pdf -------------------------------------------------------------------------------- /MTH225-Winter2024/course-docs/feedback_loop.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Winter2024/course-docs/feedback_loop.png -------------------------------------------------------------------------------- /MTH225-Winter2024/course-docs/sample_cp_0.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Winter2024/course-docs/sample_cp_0.png -------------------------------------------------------------------------------- /MTH225-Winter2025/.vscode/settings.json: -------------------------------------------------------------------------------- 1 | {} -------------------------------------------------------------------------------- /MTH225-Winter2025/assignments/.vscode/settings.json: -------------------------------------------------------------------------------- 1 | {} -------------------------------------------------------------------------------- /MTH225-Winter2025/assignments/Application Analysis Exam 1 MAKEUP VERSION.docx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Winter2025/assignments/Application Analysis Exam 1 MAKEUP VERSION.docx -------------------------------------------------------------------------------- /MTH225-Winter2025/assignments/Application Analysis Exam 1 Version 2.docx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Winter2025/assignments/Application Analysis Exam 1 Version 2.docx -------------------------------------------------------------------------------- /MTH225-Winter2025/assignments/Application Analysis Exam 1.docx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Winter2025/assignments/Application Analysis Exam 1.docx -------------------------------------------------------------------------------- /MTH225-Winter2025/assignments/Application Analysis Exam 2 MAKEUP.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Winter2025/assignments/Application Analysis Exam 2 MAKEUP.pdf -------------------------------------------------------------------------------- /MTH225-Winter2025/assignments/Application Analysis Exam 2.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH225-Winter2025/assignments/Application Analysis Exam 2.pdf -------------------------------------------------------------------------------- /MTH225-Winter2025/assignments/Key for Practice LT exam.md: -------------------------------------------------------------------------------- 1 | # MTH 225: Answers for Practice Learning Target Exam, 2025-01-17 2 | 3 | 4 | 5 | ## Learning Target 1 6 | 7 | 1. Quotient = $875$, remainder = $59$ 8 | 2. $\gcd(96,729) = 3$ 9 | 3. (a) 2, (b) 0, (c) 1 10 | 11 | [Video walkthrough of this problem](https://gvsu.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=a3864918-5353-4bf4-b558-b26e0153ebfe) 12 | 13 | 14 | ## Learning Target 2 15 | 16 | 1. $45$ 17 | 2. $505$ 18 | 3. $363$ 19 | 20 | [Video walkthrough of this problem](https://gvsu.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=f721762a-d81e-4cbe-a579-b26e0153ec8a) 21 | 22 | ## Learning Target 3 23 | 24 | 1. `1110000` 25 | 2. `1110` 26 | 3. `1111101` 27 | 4. Quotient = `10100`, remainder = `11` 28 | 29 | [Video walkthrough of this problem](https://gvsu.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=eef3a981-7107-41b5-b1ef-b26e0153ec32) 30 | 31 | ## Learning Target 4 32 | 33 | 1. Hypothesis: *The ground is wet*. Conclusion: *It's raining.* 34 | 2. If it's raining, then the ground is wet. 35 | 3. If it's not raining, then the ground isn't wet. 36 | 4. The ground is wet, but it's not raining. 37 | 38 | [Video walkthrough of this problem](https://gvsu.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=9097d678-8c82-400b-94e1-b26e0153ec5c) -------------------------------------------------------------------------------- /MTH225-Winter2025/assignments/Learning Target 10 Do-Over.md: -------------------------------------------------------------------------------- 1 | # Learning Target 10 Do-Over -- 2025-03-26 2 | 3 | 4 | 5 | 1. Below are several statements about sets and elements. Label each one as **TRUE** or **FALSE**. 6 | 7 | a) $\lbrace 1,2,3\rbrace \subseteq \lbrace 0,1,2,3,4\rbrace$ 8 | 9 | b) $25 \in \lbrace n^2 \, : \, n \in \{0,1,2,3,4,5\} \rbrace$ 10 | 11 | c) $3 \in \mathbb{N}$ 12 | 13 | d) $\emptyset \subseteq \mathbb{N}$ 14 | 15 | e) $\mathbb{Z} \subseteq \mathbb{N}$ 16 | 17 | 2. Here are three sets written in set-builder notation. For each, if the set is written using correct set syntax, rewrite it using roster notation. If the set is written using incorrect syntax, write **INCORRECT SYNTAX**. 18 | 19 | a) $\lbrace n \in \mathbb{N} : n+2 \rbrace$ 20 | 21 | b) $\lbrace 2^n :n \in \{1,2,3\} \rbrace$ 22 | 23 | c) $\lbrace x\in \lbrace 1,2,3,\dots 10 \rbrace :x \, \text{is odd} \rbrace$ -------------------------------------------------------------------------------- /MTH225-Winter2025/assignments/Learning Target Exam 1.md: -------------------------------------------------------------------------------- 1 | # MTH 225: Learning Target Exam 1 2 | 3 | This exam contains problems on Learning Targets 1--4. Do all your work in the spaces provided. For details on how these are graded, please see the [Standards for Student Work Document](https://github.com/RobertTalbert/discretecs/blob/master/MTH225-Winter2025/course-docs/Standards%20for%20Student%20Work%20MTH%20225%20W25.md). Note that in the Standards, unless a problem or part of a problem asks you to "state" something, you must provide work with your answer that completely justifies your answer. You may use a standard calculator but no other technology. 4 | 5 | ## Learning Target 1 6 | 7 | > (**CORE**) Given two integers $a$ and $b$, I can find the quotient and remainder when dividing $a$ by $b$, the greatest common divisor of $a$ and $b$ using the Euclidean Algorithm, and the value of `a % b`. 8 | 9 | 1. Use long division to find the quotient and remainder obtained when dividing $78294$ by $22$. 10 | 11 | 2. Use the Euclidean Algorithm to find $\gcd(250, 8)$. 12 | 13 | 3. State the values of each of the following: 14 | 15 | - (a) $1234 \, \% \, 56$ 16 | 17 | - (b) $123098091235 \, \% \, 2$ 18 | 19 | - (c) $7890 \, \% \, 3$ 20 | 21 | 22 | 23 |
24 | 25 | ## Learning Target 2 26 | 27 | >I can convert a positive integer between bases 2, 8, 10, and 16; and I can represent a negative integer in binary using twos complement. 28 | 29 | 1. Convert the integer $42B$ from hexadecimal (base 16) to decimal (base 10). 30 | 2. Convert the integer `11101111` from binary (base 2) to decimal (base 10). 31 | 3. Convert the integer 445 from decimal (base 10) to binary (base 2). 32 | 33 | 34 | 35 | 36 | 37 |
38 | 39 | ## Learning Target 3 40 | 41 | > I can perform arithmetic operations on binary numbers. 42 | 43 | 1. Compute `101111 + 101011`. 44 | 2. Compute `10101 - 10011`. 45 | 3. Compute `11001` $\times$ `110`. 46 | 4. Compute `1100111` $\div$ `11`. 47 | 48 | 49 | 50 | 51 | 52 |
53 | 54 | ## Learning Target 4 55 | 56 | >(**CORE**) I can identify the hypothesis and conclusion of a conditional statement and state its converse, contrapositive, and negation. 57 | 58 | Consider the implication: **Classes will be cancelled if the roads are bad.** 59 | 60 | 1. State the hypothesis and conclusion of this implication. Make sure to state which is which. 61 | 2. State the converse. 62 | 3. State the contrapositive. 63 | 4. 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You should read this document thoroughly at the start of the semester (it will be included in the Startup Activity) and then **refer back to it before submitting work**, so you can self-assess your work before turning it in. 6 | 7 | ## Standards for Practice Sets on WeBWorK 8 | 9 | ## Standards for Class Prep 10 | 11 | ## Standards for Application/Analysis 12 | 13 | ## Standards for Skill Quizzes 14 | 15 | ## Standards for Miniprojects -------------------------------------------------------------------------------- /MTH325-Fall2022/course-documentation/325-f22-course-banner.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2022/course-documentation/325-f22-course-banner.png -------------------------------------------------------------------------------- /MTH325-Fall2022/course-documentation/MTH 325 F22 Grade checklist.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2022/course-documentation/MTH 325 F22 Grade checklist.pdf -------------------------------------------------------------------------------- /MTH325-Fall2022/course-documentation/MTH 325 Fall 2022 Syllabus PDF.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2022/course-documentation/MTH 325 Fall 2022 Syllabus PDF.pdf -------------------------------------------------------------------------------- /MTH325-Fall2022/course-documentation/MTH 325 Fall 2022 Syllabus Word.docx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2022/course-documentation/MTH 325 Fall 2022 Syllabus Word.docx -------------------------------------------------------------------------------- /MTH325-Fall2022/course-documentation/Rplot.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2022/course-documentation/Rplot.png -------------------------------------------------------------------------------- /MTH325-Fall2022/course-documentation/Thumbs.db: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2022/course-documentation/Thumbs.db -------------------------------------------------------------------------------- /MTH325-Fall2022/course-documentation/css-dec07-chart: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2022/course-documentation/css-dec07-chart -------------------------------------------------------------------------------- /MTH325-Fall2022/course-documentation/css-dec07-chart.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2022/course-documentation/css-dec07-chart.png -------------------------------------------------------------------------------- /MTH325-Fall2022/design-notes/325W17-Banner.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2022/design-notes/325W17-Banner.png -------------------------------------------------------------------------------- /MTH325-Fall2022/design-notes/Class plans.md: -------------------------------------------------------------------------------- 1 | # Class plans for MTH 325 F22 2 | 3 | ## Week 1 4 | 5 | ### August 29 6 | 7 | - Welcome, get people into groups and explain how the room works 8 | - Activity: What the course is about 9 | - Jamboard with nodes for each student 10 | - Draw a line between you and another person if you have ever been enrolled in a class besides this one with that person 11 | - Draw an arrow from you to another person if you are shorter than that other person 12 | - Debrief of the graph activity 13 | - Notice? Wonder? 14 | - MTH 325 is about relationships -- what they look like, what information they contain, what we can learn from them. 15 | - What are you good at doing and how did you get that way 16 | - Ending: 17 | - Startup activity -- do it tonight, due at end of week 18 | - Daily Prep for next time, where to find it and what to do 19 | - Time for reflection 20 | 21 | ### August 31 22 | 23 | - Review of Daily Prep questions 24 | - Activity: Collatz conjecture true or false? 25 | - Recursion in the daily prep activities 26 | - Activity in finding recursive formula for a new visual pattern 27 | - Conjecture a formula -- what will prove that it works? Not examples 28 | 29 | ### Sept 2 30 | 31 | ## Week 2 32 | 33 | ### Sept 5 -- Labor day 34 | 35 | ### Sept 7 36 | 37 | ### Sept 9 -------------------------------------------------------------------------------- /MTH325-Fall2022/design-notes/Course calendar draft.md: -------------------------------------------------------------------------------- 1 | # Course schedule 2 | 3 | - M 8/29: Introduction/startup 4 | - W 8/31: Review of induction 5 | - F 9/2: Review of conditional statements + direct proof 6 | 7 | --- 8 | 9 | - M 9/5: No class (Labor Day) 10 | - W 9/7: Review contrapositive + proof by contrapositive 11 | - F 9/9: Review negations + proof by contradiction 12 | 13 | --- 14 | 15 | - M 9/12: Critical analysis of proofs 16 | - W 9/14: Time for CSS quiz 17 | - F 9/16: G.1 + G.2 18 | 19 | --- 20 | 21 | - M 9/19: G.3 22 | - W 9/21: G.4 23 | - F 9/23: Finish G.4 + CSS quiz 2 24 | 25 | --- 26 | 27 | - M 9/26: G.5 28 | - W 9/28: G.6 29 | - F 9/30: catchup + CSS quiz 3 30 | 31 | --- 32 | 33 | - M 10/3: G.7 34 | - W 10/4: G.7 + CSS quiz 3 35 | - F 10/6: No class (Leadership in Higher Ed conference) 36 | 37 | --- 38 | 39 | - M 10/10: G.8 40 | - W 10/12: G.8 + review 41 | - F 10/14: DR.1 + CSS quiz 4 42 | 43 | --- 44 | 45 | - M 10/17: DR.2 46 | - W 10/19: DR.3 47 | - F 10/21: Review + CSS quiz 5 48 | 49 | --- 50 | 51 | M 10/24: No class (Fall Break) 52 | W 10/26: DR.4 53 | F 10/28: DR.5 54 | 55 | --- 56 | 57 | M 10/31: DR.5 58 | W 11/2: No class (Ed Spaces); CSS quiz 6 59 | F: 11/4: TBA 60 | 61 | --- 62 | 63 | M 11/7: DR.6 64 | W 11/9: CSS quiz 7 65 | F 11/11: T.1 66 | 67 | --- 68 | 69 | M 11/14: T.2 70 | W 11/16: No class (ASU) 71 | F 11/18: No class (ASU) - Quiz 8 set up 72 | 73 | --- 74 | 75 | M 11/21: T.3 76 | W 11/23: No class (Thanksgiving) 77 | F 11/25: No class (Thanksgiving) 78 | 79 | --- 80 | 81 | M 11/28: Quiz 9 82 | W 11/30: TBA 83 | F 12/2: Mini-quiz just on the T standards 84 | 85 | --- 86 | 87 | M 12/5: Quiz 10 88 | W 12/7: TBA (course retrospective) 89 | F 12/9: Mini quiz on T standards 90 | 91 | -------------------------------------------------------------------------------- /MTH325-Fall2022/design-notes/MTH 325 Course Banner f22.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2022/design-notes/MTH 325 Course Banner f22.png -------------------------------------------------------------------------------- /MTH325-Fall2022/design-notes/MTH 325 Fall 2022 assessment plan.md: -------------------------------------------------------------------------------- 1 | # MTH 325 Fall 2022 Assessment, Marking, and Feedback 2 | 3 | ## Assessments 4 | 5 | - There are 20 content skill standards (or just content skills or just content standards). A standard is "met" once a student provides two successful demonstrations of skill. 6 | - Through content standard quizzes, given periodically in class; consisting of problems, one standard per problem; cumulative through the semester. 7 | - Or through doing an oral content standard quiz, available in person or on Zoom by request. 8 | - Or through making a video of a custom quiz problem, available upon request and posted privately to Flipgrid. 9 | - Each (nearly each) class has Daily Prep: 10 | - Reading, viewing, and/or experiments to run. Reading and viewing coordinated through Perusall. 11 | - Assignment is always to leave a substantive comment on Perusall and then answer questions on a Google Form. 12 | - Graded on the basis of completeness and effort. They will remain open until they are graded, the morning of the class. Never graded before 11:59pm ET. 1 point for complete good-faith effort. 13 | - Proof badge 14 | - See document on content standards for what this involves 15 | - Proof problems posted in a running document, populated at the beginning of the semester; submit proofs typed up as PDFs. Get feedback; no grades on these, just feedback, in a loop until I tell you that it's good to go. 16 | - Applications badge 17 | - See document on content standards for what this involves 18 | - Application problems posted off and on through the semester as we cover content. Write up solutions in a PDF. Get feedback; no grades on these, just feedback, in a loop until I tell you that it's good to go. 19 | 20 | 21 | ## Marking 22 | 23 | - Content standards: 24 | - One column per standard in the gradebook 25 | - Each *individual demonstration* is marked with a check if it's successful or X if not, feedback given 26 | - Each *standard* marked in the gradebook with 0, 1, or 2 representing the *number of successful attempts so far*. See individual submissions for the latest one. 27 | - Daily Prep: Marked Check or X 28 | - Nothing else is marked. 29 | - Essay for the badges will include an inventory of which proofs/application problems you want considered. 30 | 31 | ## Feedback 32 | 33 | - Feedback on proofs and application problems comes on the PDF. 34 | - No feedback on Daily Prep but answers discussed in class. 35 | - Keys posted for Skill quizzes; feedback given if needed on the PDF. -------------------------------------------------------------------------------- /MTH325-Fall2022/design-notes/MTH 325 W17 Learning Targets.mdown: -------------------------------------------------------------------------------- 1 | # MTH 325 Learning Targets from Winter 2017 2 | 3 | ## Proof 4 | 5 | + P.1: I can set up a framework of assumptions and conclusions for proofs using direct proof, proof by contraposition, and proof by contradiction. 6 | + P.2: I can identify the predicate being used in a proof by mathematical induction and use it to set up a framework of assumptions and conclusions for an induction proof. 7 | + P.3: I can identify the parts of a proof, including the technique used and the assumptions being made. 8 | + P.4: I can perform a critical analysis of a written proof and provide a detailed explanation of the steps used in the proof. 9 | 10 | ## Graphs 11 | 12 | + G.1: I can create a graph given information or rules about nodes and edges. 13 | + G.2: I can give examples of graphs having combinations of various properties and examples of graphs of special ("named") types. 14 | + G.3: I can represent a graph in different ways and change representations from one to another. 15 | + G.4: I can take any representation of a graph and determine information about the entire graph or parts of the graph. 16 | + G.5: I can determine whether two graphs are isomorphic. 17 | + G.6: I can give a valid vertex coloring for a graph and determine a graph's chromatic number. 18 | + G.7: I can determine whether a graph has an Euler path or cycle, and whether it has a Hamilton path or cycle. 19 | + G.8: I can construct a spanning tree for a (connected) graph, and I can construct a minimal spanning tree for a weighted graph using Prim's Algorithm and Kruskal's Algorithm. 20 | 21 | ## Relations 22 | 23 | + R.1: I can represent a relation in different ways and change representations from one to another. 24 | + R.2: I can give examples of relations on a set that have combinations of the properties of reflexivity, symmetry, antisymmetry, and transitivity. 25 | + R.3: I can compute the composition of two relations (and determine when a composition cannot be computed) and raise a relation on a set to a positive integer power. 26 | + R.4: I can determine whether two points in a set with a relation belong to the transitive closure of that relation, and I can use Warshall’s Algorithm to find the matrix for the transitive closure of a relation. 27 | + R.5: I can determine when a relation is an equivalence relation, and I can determine the equivalence class for an element and determine whether two elements belong to the same equivalence class. 28 | + R.6: I can determine when a set with a relation is a partially ordered set, a totally ordered set, and a well-ordered set. 29 | 30 | ## Trees 31 | 32 | + T.1: I can give examples of trees with combinations of important properties and determine information about a tree as a whole or about parts of the tree. 33 | + T.2: I can list the nodes of a tree in the correct order when visited using preorder, postorder, and inorder traversals. 34 | -------------------------------------------------------------------------------- /MTH325-Fall2022/design-notes/MTh 325 F22 course grade plan.md: -------------------------------------------------------------------------------- 1 | # MTH 325 Fall 2022 course grading 2 | 3 | | Grade | Daily Preps | Content Standards | Badges earned | 4 | | :----: | :-------: | :---------------: | :------------: | 5 | | A | (85% of max) | 18 | Both Proof and Applications | 6 | | B | (75% of max) | 15 (16?) | Either Proof or Applications | 7 | | C | (65% of max) | 12 (14?) | Either Proof or Applications | 8 | | D | (35% of max) | 6 | None required | 9 | 10 | - A grade of F is given if not all the requirements of a D are met. 11 | - Content standards for A, B, and C grades must include: P.1, P.2, G.1, G.2, and DR.1. Failure to meet all five results in a one letter grade deduction after all other tabulations are done. 12 | - Plus/minus grades: 13 | - Plus: Given if you complete both, not just one of the badges OR if you meet the number of content standards for the next letter grade up. 14 | - Minus: Given if you meet all the requirements for a grade except for Daily Prep. Grade adjustment in this case given at RTs discretion. 15 | 16 | -------------------------------------------------------------------------------- /MTH325-Fall2022/design-notes/Skill Quiz Prototype.md: -------------------------------------------------------------------------------- 1 | # Prototype Skills Quiz 2 | 3 | >Skill: I can find a spanning tree for a graph, and a minimal spanning tree for a weighted graph. 4 | 5 | 1. Find a spanning tree for the following (unweighted) graph and fully explain your process. Give the resulting tree as an edge list. 6 | 7 | ![Random graph](random_graph.png) 8 | 9 | 2. Using Kruskal's Algorithm, find a minimum spanning tree for the following weighted graph. Clearly show each step of the algorithm and clearly indicate your final answer. 10 | 11 | (Figure out how to generate nice-looking random weighted graphs) 12 | 13 | 14 | >Success criteria: Both results are spanning trees for their respective graphs; the tree in the second item is a correct output of Kruskal's algorithm and the process correctly implements Kruskal's algorithm; and all steps in each part are correct and clearly stated. Up to two simple errors allowed. 15 | 16 | --- 17 | 18 | **The feedback loop:** 19 | - Correct answers would be provided on a separate key. 20 | - Run-of-the-mill errors would be given response "See the key for a correct answer; practice with this problem until you are getting a correct result." 21 | - Other errors will be given more detailed feedback. 22 | - They can try again on a later quiz, through a video, or through a live drop-in hours quiz. -------------------------------------------------------------------------------- /MTH325-Fall2022/design-notes/Startup activity outline.md: -------------------------------------------------------------------------------- 1 | # MTH 325 F22 startup activity 2 | 3 | - Perusall activity: Read and mark up syllabus 4 | - Syllabus quiz -- no grading stuff on it because that's going in a separate quiz 5 | - Quiz on grading system 6 | - Facts of the system 7 | - Practice with assigning grades 8 | - Personal info survey 9 | - Programming experience: Which languages, how long, comfort level 10 | - Do you know how to scan a printed doc to a PDF 11 | - Do you know how to upload a PDF to Blackboard --> Take these two Q's and form special assignment if needed 12 | - Experience with math courses 13 | - See MTH 350 survey: https://docs.google.com/forms/d/e/1FAIpQLSdghzrmF136DX8fE-M1PaUW3powl9v0WKtNbDnYtpKOg5GZqA/viewform 14 | 15 | Complete all parts of this by Wednesday Sept 7 at class time -------------------------------------------------------------------------------- /MTH325-Fall2022/design-notes/Taylor Short MTH 325 syllabus.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2022/design-notes/Taylor Short MTH 325 syllabus.pdf -------------------------------------------------------------------------------- /MTH325-Fall2022/design-notes/random_graph.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2022/design-notes/random_graph.png -------------------------------------------------------------------------------- /MTH325-Fall2022/materials/Conditional Statements and Direct Proof.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2022/materials/Conditional Statements and Direct Proof.pdf -------------------------------------------------------------------------------- /MTH325-Fall2022/materials/Critical analyses of proofs.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2022/materials/Critical analyses of proofs.pdf -------------------------------------------------------------------------------- /MTH325-Fall2022/materials/Directed graph review activity.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2022/materials/Directed graph review activity.pdf -------------------------------------------------------------------------------- /MTH325-Fall2022/materials/Isomorphism Hamiltonian circuits.md: -------------------------------------------------------------------------------- 1 | **Proposition:** If $G$ and $H$ are isomorphic graphs and $G$ has a Hamiltonian cycle, then $H$ has a Hamiltonian cycle. (That is, the property of having a Hamiltonian cycle is an isomorphism invariant.) 2 | 3 | **Proof:** Suppose $G$ and $H$ are isomorphic and $G$ has a Hamiltonian cycle. Let's say that $G$ has $n$ vertices and that the Hamilton cycle, given as a sequence of vertices, is $v_1, v_2, v_3, \dots, v_n, v_1$. 4 | 5 | Since $G$ and $H$ are isomorphic, there is a bijection $f$ mapping the vertices of $G$ onto the vertices of $H$ in such a way that $(a,b)$ is an edge in $G$ if and only if $(f(a), f(b))$ is an edge in $H$. Because $f$ maps the vertices of $G$ to vertices in $H$, the outputs $f(v_1), f(v_2), \dots, f(v_n)$ are vertices in $H$. We claim that the sequence $f(v_1), f(v_2), \dots, f(v_n), f(v_1)$ is a Hamilton cycle in $H$. There are three things to show: (1) each vertex in this sequence is adjacent to the one before it in the sequence, (2) all vertices in $H$ are visited in this sequence, and (3) no vertex of $H$ is visited more than once in this sequence (except the starting and ending vertex). 6 | 7 | **Adjacency:** Take any two consecutive vertices in the sequence $v_1, v_2, v_3, \dots, v_n, v_1$, and call then $v_i$ and $v_{i+1}$. Then $(v_i, v_{i+1})$ is an edge in $G$. Therefore since $f$ is an isomorphism, $(f(v_i), f(v_{i+1}))$ is an edge in $H$. Therefore any consecutive vertices in the sequence $f(v_1), f(v_2), \dots, f(v_n), f(v_1)$ are adjacent. 8 | 9 | **Every vertex in $H$ is visited:** All the vertices in $G$ appear in the original sequence $v_1, v_2, v_3, \dots, v_n, v_1$. Since $f$ is a bijection, it is injective, and so if two different vertices are plugged into $f$, the outputs will also be different. Therefore all of the vertices $f(v_1), f(v_2), \dots, f(v_n)$ are different. Note that since $G$ and $H$ are isomorphic, we have previously shown they must have the same number of vertices. The graph $G$ has $n$ vertices; there are $n$ vertices in this sequence and they are all different. Therefore the sequence must contain all the vertices of $H$. 10 | 11 | **No vertex in $H$ is visited more than once:** Because there are *exactly* $n$ vertices in the sequence $f(v_1), f(v_2), \dots, f(v_n)$, none of the $n$ vertices of $H$ is duplicated. 12 | 13 | We have shown that $f(v_1), f(v_2), \dots, f(v_n), f(v_1)$ is a sequence of adjacent vertices in $H$ that visits every vertex and no vertex other than the start and end is visited more than once. This makes it a Hamilton cycle, which is what we wanted to prove. 14 | -------------------------------------------------------------------------------- /MTH325-Fall2022/materials/Mathematical Induction.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2022/materials/Mathematical Induction.pdf -------------------------------------------------------------------------------- /MTH325-Fall2022/materials/Proof by proving the contrapositive.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2022/materials/Proof by proving the contrapositive.pdf -------------------------------------------------------------------------------- /MTH325-Fall2022/materials/Proof setup practice part 2.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2022/materials/Proof setup practice part 2.pdf -------------------------------------------------------------------------------- /MTH325-Fall2022/materials/Proof setup practice.md: -------------------------------------------------------------------------------- 1 | For all positive integers $n$, if a set has $n$ elements, then the number of $2$-element subsets that is has is $n(n-1)/2$. 2 | 3 | 4 | 5 | For all integers $n \geq 1$, the number $5^n - 1$ is a multiple of $4$. 6 | 7 | 8 | 9 | For all integers $n \geq 1$, $1^2 + 2^2 + \cdots + n^2 = \dfrac{n(n+1)(2n+1)}{6}$. 10 | 11 | 12 | 13 | For all positive integers $n$, $1 + 2 + 4 + 8 + \cdots + 2^n = 2^{n+1} - 1$. 14 | 15 | 16 | 17 | For all integers $n \geq 4$, $2^n < n!$. (Note: $n!$ is "$n$ factorial" which you learned in MTH 225) 18 | 19 | 20 | 21 | For all integers $n \geq 1$, $6$ divides $n^3 - n$. 22 | 23 | 24 | 25 | For all positive integers $n$, $11^n - 6$ is divisible by $5$. 26 | 27 | 28 | 29 | --- 30 | 31 | 32 | 33 | If $x$ is an even integer and $y$ is an odd integer, then $x+y$ is an odd integer. 34 | 35 | 36 | 37 | If $x$ is an even integer and $y$ is any other integer, then $xy$ is an even integer. 38 | 39 | 40 | 41 | If $x$ and $y$ are odd integers, then $x+y$ is an even integer. 42 | 43 | 44 | 45 | For every integer $n$ (positive, negative, or zero), if $n$ is an odd integer then $n^3$ is an odd integer. 46 | 47 | 48 | 49 | For every integer $n$ (positive, negative, or zero), if $n$ is a multiple of $4$ then $n^2 - 1$ is a multiple of $4$. 50 | 51 | 52 | 53 | If $S$ is a set with $n$ elements, then $S$ has $2^n$ subsets. 54 | 55 | 56 | 57 | If $S$ is a set with $n$ elements (and $n \geq 3$), then it has $\dfrac{n^3 - 3n^2 + 2n}{6}$ 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(3,4,.34), 8 | (4,23,.34), (4,18,.07), (4,21,.22), (5,21,.09), (5,6,.16), (5,15,.23), (6,7,.34), (6,16,.07), (7,12,.12), (7,8,.15), (8,9,.21), (8,13,.25), (9,10,.06), (10,11,.21), (10,12,.51), (11,300,.12), (12,17,.18), (13,14,.39), (13,16,.25), (14,15,.28), (15,16,.18), (17,18,.34), (21,22,.18), (22,23,.18), (22,24,.04), (23,24,.34)] -------------------------------------------------------------------------------- /MTH325-Fall2024/assignments/btree.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2024/assignments/btree.png -------------------------------------------------------------------------------- /MTH325-Fall2024/course-docs/325-logo.png: -------------------------------------------------------------------------------- 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/MTH325-Fall2024/course-docs/Standards for student work.md: -------------------------------------------------------------------------------- 1 | # Standards for Student Work -- MTH 325, Fall 2024 2 | 3 | -------------------------------------------------------------------------------- /MTH325-Fall2024/course-docs/sample-final-10.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2024/course-docs/sample-final-10.png -------------------------------------------------------------------------------- /MTH325-Fall2024/course-docs/sample-final-11.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/MTH325-Fall2024/course-docs/sample-final-11.png 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You can find the materials in the subdirectory `MTH225-Fall2023`.** 4 | 5 | --- 6 | 7 | This repository contains materials for MTH 225 (Discrete Structures for Computer Science 1) and MTH 325 (Discrete Structures for Computer Science 2) at [Grand Valley State University](http://gvsu.edu). These materials were created and are maintained by me, [Robert Talbert](http://rtalbert.org). 8 | 9 | Everything here is free and licensed under a [Creative Commons Attribution-ShareAlike 3.0 license](http://creativecommons.org/licenses/by-sa/3.0/us/). Please click the link or the `LICENSE.md` file to learn the terms of the license. Basically, you can use and reuse whatever you want as long as you give me attribution as the author. 10 | 11 | For more information, contact me at talbertr@gvsu.edu or visit my website at http://rtalbert.org. 12 | 13 | ## How things are organized 14 | 15 | There are two different courses housed in this repo, MTH 225 and MTH 325. While there are a lot of similarities between different instances of the same course, they're different enough to warrant keeping them in separate directories. These are labeled with the **course name** followed by a hyphen followed by the **semester**. For example, my MTH 325 class coming up in Fall 2022 is in `MTH 325-Fall2022`. 16 | 17 | Then, within each course you will find subdirectories for different materials. If you are specifically looking for syllabi, them those are usually in a directory called `course-documentation`. 18 | 19 | There are some archival directories at the top level: 20 | 21 | - `video` is contains the scripts and captions, for the instructional videos I made for this course. [Those videos are located here.](https://vimeo.com/showcase/8667148). 22 | - `archive` contains instances of the course prior to Fall 2021. 23 | 24 | -------------------------------------------------------------------------------- /archive/.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/.DS_Store -------------------------------------------------------------------------------- /archive/discrete2-archive/2017-04-13_14-38-22.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/discrete2-archive/2017-04-13_14-38-22.png -------------------------------------------------------------------------------- /archive/discrete2-archive/ExampleBST.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/discrete2-archive/ExampleBST.jpg -------------------------------------------------------------------------------- /archive/discrete2-archive/ProofAnalysis.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/discrete2-archive/ProofAnalysis.png -------------------------------------------------------------------------------- /archive/discrete2-archive/README.md: -------------------------------------------------------------------------------- 1 | # Discrete Structures for Computer Science 2 | 3 | This repository contains course materials for MTH 225: Discrete Structures for Computer Science 1 and MTH 325: Discrete Structures for Computer Science 2, at Grand Valley State University. This is a two-semester course sequence required for all computer science majors. The rough breakdown of course content is: 4 | 5 | + MTH 225: Sets, functions, counting, sequences, mathematical induction, logic, and proof techniques. 6 | + MTH 325: Graphs, graph applications, relations, and trees. 7 | 8 | Both courses are organized on the principle of [computational thinking](https://csta.acm.org/Curriculum/sub/CurrFiles/CompThinkingFlyer.pdf) and employ Python programming, on the [Jupyter notebook platform](http://jupyter.org/), to explore concepts. Work with graph theory in MTH 325 uses the [networkX](https://networkx.github.io/) library. 9 | 10 | The textbook for the course is _Discrete Mathematics: An Open Introduction_ by Oscar Levin. The text is a free interactive e-book found [here](http://discretetext.oscarlevin.com/dmoi/). Downloadable versions are found [here](http://discretetext.oscarlevin.com/download.php). 11 | 12 | There is a folder for each class. Contained in each folder are subfolders for: 13 | 14 | + __Course documentation__: Includes the course syllabus and other core documentation for students. 15 | + __Assignments__: Homework sets, programming assignments, quizzes, and other graded work. 16 | + __Lesson plans__: In situations where homemade notes are used in addition to or instead of the Levin book, those are housed here as Jupyter notebooks. 17 | 18 | There is also an Archive folder for materials from the older versions of MTH 225 and MTH 325. These materials are only loosely organized. 19 | 20 | The professor of record for MTH 325 is Robert Talbert, whose website is at [http://rtalbert.org](http://rtalbert.org). Follow on Twitter at [@RobertTalbert](http://twitter.com/RobertTalbert). 21 | -------------------------------------------------------------------------------- /archive/discrete2-archive/azure-open.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/discrete2-archive/azure-open.png -------------------------------------------------------------------------------- /archive/discrete2-archive/bfgraph.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/discrete2-archive/bfgraph.png -------------------------------------------------------------------------------- /archive/discrete2-archive/bookfacematrix.png: -------------------------------------------------------------------------------- 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| "\n", 27 | "List video content, text, links. \n", 28 | "\n", 29 | "---\n", 30 | "\n", 31 | "## Preview Activities\n", 32 | "\n", 33 | "### Activities\n", 34 | "\n", 35 | "### Submission instructions\n", 36 | "\n", 37 | "---\n", 38 | "\n", 39 | "## Daily Homework\n", 40 | "\n" 41 | ] 42 | }, 43 | { 44 | "cell_type": "code", 45 | "execution_count": null, 46 | "metadata": { 47 | "collapsed": true 48 | }, 49 | "outputs": [], 50 | "source": [] 51 | } 52 | ], 53 | "metadata": { 54 | "kernelspec": { 55 | "display_name": "Python 3", 56 | "language": "python", 57 | "name": "python3" 58 | }, 59 | "language_info": { 60 | "codemirror_mode": { 61 | "name": "ipython", 62 | "version": 3 63 | }, 64 | "file_extension": ".py", 65 | "mimetype": "text/x-python", 66 | "name": "python", 67 | "nbconvert_exporter": "python", 68 | "pygments_lexer": "ipython3", 69 | "version": "3.4.3" 70 | } 71 | }, 72 | "nbformat": 4, 73 | "nbformat_minor": 0 74 | } 75 | 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"cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Lesson 1: Recursively Defined Structures \n", 8 | "\n", 9 | "## Overview \n", 10 | "\n", 11 | "__Summary:__ Blah blah\n", 12 | "\n", 13 | "This lesson addresses the following learning target(s): \n", 14 | "\n", 15 | "+ __RI.1:__ I can construct several instances of a recursively defined structure, such as integer sequences, graphs, and trees.\n", 16 | "\n", 17 | "---\n", 18 | "\n", 19 | "## Background\n", 20 | "\n", 21 | "Text to read and things to do. \n", 22 | "\n", 23 | "---\n", 24 | "\n", 25 | "## Other resources for learning \n", 26 | "\n", 27 | "List video content, text, links. \n", 28 | "\n", 29 | "---\n", 30 | "\n", 31 | "## Preview Activities\n", 32 | "\n", 33 | "### Activities\n", 34 | "\n", 35 | "### Submission instructions\n", 36 | "\n", 37 | "---\n", 38 | "\n", 39 | "## Daily Homework\n", 40 | "\n" 41 | ] 42 | }, 43 | { 44 | "cell_type": "code", 45 | "execution_count": null, 46 | "metadata": { 47 | "collapsed": true 48 | }, 49 | "outputs": [], 50 | "source": [] 51 | } 52 | ], 53 | "metadata": { 54 | "kernelspec": { 55 | "display_name": "Python 3", 56 | "language": "python", 57 | "name": "python3" 58 | }, 59 | "language_info": { 60 | "codemirror_mode": { 61 | "name": "ipython", 62 | "version": 3 63 | }, 64 | "file_extension": ".py", 65 | "mimetype": "text/x-python", 66 | "name": "python", 67 | "nbconvert_exporter": "python", 68 | "pygments_lexer": "ipython3", 69 | "version": "3.4.3" 70 | } 71 | }, 72 | "nbformat": 4, 73 | "nbformat_minor": 0 74 | } 75 | -------------------------------------------------------------------------------- /archive/lessons/bfgraph.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/lessons/bfgraph.png -------------------------------------------------------------------------------- /archive/lessons/chicken.jpg: 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-------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/inclass-template.tex: -------------------------------------------------------------------------------- 1 | \documentclass{beamer} 2 | 3 | \usepackage[utf8]{inputenc} 4 | \usetheme{Warsaw} 5 | 6 | %Information to be included in the title page: 7 | \title{MTH 201: Calculus} 8 | \subtitle{Module 1, Day 1: Representing integers in different bases} 9 | \author{Prof. Talbert} 10 | \institute{GVSU} 11 | \date{\today} 12 | 13 | 14 | \begin{document} 15 | 16 | \frame{\titlepage} 17 | 18 | 19 | \begin{frame}{Agenda for today} 20 | \begin{itemize} 21 | \item<1-> Review of Daily Prep assignment and Q+A 22 | \item<2-> 23 | \end{itemize} 24 | \end{frame} 25 | 26 | \begin{frame} 27 | \frametitle{First activity} 28 | 29 | Hello 30 | 31 | \end{frame} 32 | 33 | \begin{frame} 34 | \frametitle{NEXT TIME...} 35 | 36 | \begin{itemize} 37 | \item To do list 1 38 | \item To do list 2 39 | 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module:** 18 | 19 | > (LT here) 20 | 21 | **BEFORE** your class meeting, use the Resources for Learning (below) to learn how to do the following: 22 | 23 | **DURING AND AFTER** your class meeting, you will learn how to do the following: 24 | 25 | 26 | ## Resources for Learning 27 | 28 | **Text:** Read through 29 | 30 | **Video:** At the MTH 201 playlist on YouTube (http://bit.ly/GVSUCalculus), watch the following videos. The total running time is xx:xx. 31 | 32 | - 33 | 34 | You are free to search for and use other resources in addition to, or instead of the above, as long as you can work the exercises below. 35 | 36 | 37 | ## Exercises 38 | 39 | The exercises for this assignment are found at the links below. 40 | 41 | 42 | ## Submission, grading, and getting help 43 | 44 | **Submitting your work:** 45 | 46 | **How this is graded:** Daily Prep assignments are graded on the basis of *completeness and effort*: If your submission has **all parts completed** (no blank entries, even if left blank accidentally) and **a good-faith effort to provide a correct solution or explanation is given** (no responses of "I don't know" or "I didn't understand") and **the work is submitted on time**, it gets a "check". Otherwise it gets an "x". If you are stuck on an item, you're expected to ask questions and give your best effort. 47 | 48 | **Getting help on this assignment:** *You may work with others on this assignment, but you may not copy each others' answers.* Evidence of copying will be treated as academic dishonesty. You may also ask questions on the #dailyprep channel on CampusWire, but you may not ask simply to be given the answers; giving and receiving answers on CampusWire will be treated as academic dishonesty. -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module1/inclass-template.tex: -------------------------------------------------------------------------------- 1 | \documentclass{beamer} 2 | 3 | \usepackage[utf8]{inputenc} 4 | \usetheme{Warsaw} 5 | 6 | %Information to be included in the title page: 7 | \title{MTH 201: Calculus} 8 | \subtitle{Module 1, Day 1: Representing integers in different bases} 9 | \author{Prof. Talbert} 10 | \institute{GVSU} 11 | \date{\today} 12 | 13 | 14 | \begin{document} 15 | 16 | \frame{\titlepage} 17 | 18 | 19 | \begin{frame}{Agenda for today} 20 | \begin{itemize} 21 | \item<1-> Review of Daily Prep assignment and Q+A 22 | \item<2-> 23 | \end{itemize} 24 | \end{frame} 25 | 26 | \begin{frame} 27 | \frametitle{First activity} 28 | 29 | Hello 30 | 31 | \end{frame} 32 | 33 | \begin{frame} 34 | \frametitle{NEXT TIME...} 35 | 36 | \begin{itemize} 37 | \item To do list 1 38 | \item To do list 2 39 | \end{itemize} 40 | 41 | \end{frame} 42 | 43 | \end{document} -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module1/module1-planning.md: -------------------------------------------------------------------------------- 1 | # Planning for MTH 225 Module 1 2 | 3 | Focus: Integer representation and binary arithmetic 4 | 5 | + Day 1: Representation in different bases including two's complement 6 | + Day 2: Binary arithmetic 7 | 8 | ## 1. Learning objectives 9 | 10 | LT's: 11 | 12 | + A.1: I can represent an integer in base 2, 8, 10, and 16. 13 | + A.2 (Core): I can add and multiply two integers written in binary. 14 | 15 | Micro-objectives: (Bold ones are day 1) 16 | 17 | - **Convert an integer from base 10 into bae 2, 8, and 16 and vice versa.** 18 | - **Implement the division/remainder algorithm for converting from decimal to base $r$**. 19 | - Represent a signed integer using 2's complement and convert a signed integer from base 8, 10, or 16 into binary using 2's complement. 20 | - Add, subtract, and multiply two binary integers (without changing representation). 21 | - Find the quotient and remainder when dividing one binary integer by another. 22 | 23 | 24 | ## 2. Sort 25 | 26 | Day 1 in order: 27 | 28 | - **Convert an integer from base 10 into bae 2, 8, and 16 and vice versa.** 29 | - **Implement the division/remainder algorithm for converting from decimal to base $r$**. 30 | 31 | Day 2 in order: Same as above. 32 | 33 | 34 | ## 3. Sketch of in-class activity 35 | 36 | Day 1 37 | 38 | - Review and QA over pre-class 39 | - Conceptual polling questions: 40 | - How to tell if binary integer is even 41 | - When we multiply a number in base 8 by 8, what happens? 42 | - Basic practice with changing representations using the algorithm 43 | - Minilecture: bin/dec/oct/hex in Python (Or make a video) (Or set up a Jupyter notebook) 44 | 45 | Day 2 46 | 47 | Include 2's complement here 48 | 49 | - Review and QA over pre-class 50 | - Conceptual polling questions 51 | - Review from Day 1 (What are the decimal values of 0111 and 0011) 52 | - What is the sum of 0111 and 0011? 53 | - What is -3 written using 2's complement? 54 | - The difference? 55 | - The product? 56 | - The quotient and remainder? 57 | - Review of process 58 | - 59 | - Students work out examples in pairs on Jamboard -- then go over answers 60 | 61 | 62 | Followup activities: 63 | 64 | Day 1 65 | 66 | - Randomly generated decimals, convert all to binary using the algorithm and show work. (Can check on WA) 67 | - Randomly generated signed decimals, convert to base 2, 8, 16 using 2's complement 68 | 69 | 70 | Day 2 71 | 72 | - Just more examples with each operation 73 | -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module1/shirt.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module1/shirt.jpg -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module10/225-10a-dp.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module10/225-10a-dp.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module10/225-10b-dp.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module10/225-10b-dp.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module10/225-module10-planning.md: -------------------------------------------------------------------------------- 1 | # Module 10 2 | 3 | - Explain the difference between a closed formula for a sequence and a recursive definition for a sequence. 4 | - Given a closed formula for a sequence, generate the first 5-10 terms of the sequence. 5 | - Given a recursive definition for a sequence, generate the first 5-10 terms of the sequence. 6 | - State the first 5-10 terms of the *triangular numbers* and the *Fibonacci numbers*. 7 | - Given a sequence, generate the first 5-10 terms of its sequence of partial sums. 8 | - Find a closed formula for a sequence using known closed formulas for related sequences. 9 | - Given a sequence of numbers or visual patterns, write a recursive definition that generates the sequence. 10 | - Write a sum or product using $\sum$ and $\prod$ notation; and calculate sums and products given using these notations. 11 | 12 | --- 13 | 14 | - State the definition of an *arithmetic* sequence, and find the common difference of an arithmetic sequence. 15 | - Determine whether a given sequence is arithmetic; if it is, find closed formulas and recursive definitions for it. 16 | - State the definition of an *geometric* sequence, and find the common ratio of an arithmetic sequence. 17 | - Determine whether a given sequence is geometric; if it is, find closed formulas and recursive definitions for it. 18 | - Find the sum of terms in an arithmetic sequence. 19 | - Find the sum of terms in a geometric sequence. 20 | -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module10/MTH 225 Module 10A presentation.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module10/MTH 225 Module 10A presentation.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module10/MTH 225 Module 10B presentation.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module10/MTH 225 Module 10B presentation.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module11/201-11a-dp.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module11/201-11a-dp.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module11/201-11b-dp.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module11/201-11b-dp.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module11/201-module11-planning.md: -------------------------------------------------------------------------------- 1 | # Module 11 2 | 3 | Subject: Solving recurrence relations (2.4) 4 | 5 | A: 6 | 7 | - What does it mean to "solve" a recurrence relation 8 | - Coming up with what you think is a closed formula 9 | - Proving that your guess is correct 10 | - Iteration 11 | 12 | B: 13 | 14 | - Solving via characteristic roots 15 | 16 | 17 | ## Part A planning 18 | 19 | Objectives: 20 | 21 | - Explain what it means to "solve" a recurrence relation and what a "solution" to a recurrence relation is. 22 | - Given a proposed solution for a recurrence relation, prove or disprove that it actually solves the recurrence relation. 23 | 24 | --- 25 | - Given a sequence of integers, determine a recurrence relation for it; guess a solution; then prove or disprove that your guess is correct. 26 | - Solve a recurrence relation using the techniques of telescoping or iteration. 27 | 28 | 29 | ## Part B planning 30 | -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module11/MTH 225 Module 11A presentation.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module11/MTH 225 Module 11A presentation.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module12/225-12a-dp.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module12/225-12a-dp.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module12/225-module12-planning.md: -------------------------------------------------------------------------------- 1 | # Module 12 2 | 3 | Part A: 4 | 5 | - What is a proof 6 | - Reminder of proofs we've seen -- combinatorial, proving that a function solves a RR 7 | - On that last one: Uses the recursive nature of the RR --- requires first step, and assuming that the function "works" at one step, show that it works at the next step 8 | - Structure of an induction argument 9 | - Formal principle of induction 10 | 11 | Part B: 12 | - Stating the parts of an induction proof 13 | - Analysis of an induction proof 14 | -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module12/MTH 225 Module 12B presentation.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module12/MTH 225 Module 12B presentation.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module2/225-2a-dp.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module2/225-2a-dp.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module2/225-2b-dp.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module2/225-2b-dp.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module2/MTH 225 Module 2B presentation.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module2/MTH 225 Module 2B presentation.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module2/Module2A-inclass.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module2/Module2A-inclass.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module2/Module2A-inclass.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module2/Module2A-inclass.synctex.gz -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module2/Module2A-inclass.vrb: -------------------------------------------------------------------------------- 1 | \frametitle{The multiplicative (decimation) cipher} 2 | 3 | Just like the shift cipher except multiply by the key instead of add. 4 | 5 | \begin{enumerate} 6 | \item User: Input a word to encrypt and a key $K$ (positive integer) 7 | \item For each letter in the word: 8 | \begin{enumerate} 9 | \item Convert to number $n$ between 0 and 25 10 | \item Compute $(n \times K) \, \% \, 26$ 11 | \item Convert back to letter 12 | \end{enumerate} 13 | \end{enumerate} 14 | 15 | Now look at a \textbf{Jupyter notebook with some Python code} that does this. 16 | 17 | -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module2/dp-template.md: -------------------------------------------------------------------------------- 1 | # MTH 225: Discrete Structures for Computer Science 1 2 | 3 | ## Daily Preparation, Module x: 4 | 5 | **Due by:** 6 | 7 | **Estimated time requirement:** About 45 minutes for the whole assignment. *If you have worked on this assignment for 30 minutes and you're not at least halfway done, DON'T work any further* --- instead, *stop and ask for help* on the `#dailyprep` channel on CampusWire. 8 | ======= 9 | 10 | 11 | ## Overview 12 | 13 | 14 | 15 | ## What you will learn 16 | 17 | **Learning Targets addressed in this module:** 18 | 19 | > (LT here) 20 | 21 | **BEFORE** your class meeting, use the Resources for Learning (below) to learn how to do the following: 22 | 23 | **DURING AND AFTER** your class meeting, you will learn how to do the following: 24 | 25 | 26 | ## Resources for Learning 27 | 28 | **Text:** Read through 29 | 30 | **Video:** At the MTH 201 playlist on YouTube (http://bit.ly/GVSUCalculus), watch the following videos. The total running time is xx:xx. 31 | 32 | - 33 | 34 | You are free to search for and use other resources in addition to, or instead of the above, as long as you can work the exercises below. 35 | 36 | 37 | ## Exercises 38 | 39 | The exercises for this assignment are found at the links below. 40 | 41 | 42 | ## Submission, grading, and getting help 43 | 44 | **Submitting your work:** 45 | 46 | **How this is graded:** Daily Prep assignments are graded on the basis of *completeness and effort*: If your submission has **all parts completed** (no blank entries, even if left blank accidentally) and **a good-faith effort to provide a correct solution or explanation is given** (no responses of "I don't know" or "I didn't understand") and **the work is submitted on time**, it gets a "check". Otherwise it gets an "x". If you are stuck on an item, you're expected to ask questions and give your best effort. 47 | 48 | **Getting help on this assignment:** *You may work with others on this assignment, but you may not copy each others' answers.* Evidence of copying will be treated as academic dishonesty. You may also ask questions on the #dailyprep channel on CampusWire, but you may not ask simply to be given the answers; giving and receiving answers on CampusWire will be treated as academic dishonesty. -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module2/module2-planning.md: -------------------------------------------------------------------------------- 1 | # MTH 225 Module 2 2 | 3 | Main concepts: 4 | 5 | - Division algorithm 6 | - The `%` operator 7 | - Arithmetic with the `%` operator 8 | - Cryptography 9 | 10 | Possible AEP material: 11 | - Extended Euclidean Algorithm and finding multiplicative inverses -- application to crypto 12 | 13 | 14 | Learning objectives 15 | 16 | - State the Division Algorithm and explain the main points 17 | - State the Euclidean Algorithm 18 | - Use the Euclidean Algorithm to find the gcd of two integers 19 | - Given two integers a, n with n > 0, find `a % n` 20 | - Use the repeated squaring technique to find large powers of a mod n 21 | - Employ basic cryptosystems involving modular arithmetic 22 | 23 | 24 | Remixed 25 | 26 | On second thought, no Euclidean Algorithm 27 | 28 | Module 2A: 29 | - Basic 30 | - State the Division Algorithm and explain the main points 31 | - Given two integers a, n with n > 0, find `a % n` 32 | - Encrypt and decrypt using the shift cipher given the key 33 | - Advanced 34 | - Decipher a shift cipher with no key (given ciphertext, or just brute force) 35 | - Encrypt and decrypt using the multiplicative cipher 36 | 37 | For later: 38 | - Use the repeated squaring technique to find large powers of a mod n 39 | 40 | 41 | ## In class 42 | 43 | ### Module 2A 44 | 45 | - Part 1: Review/QA 46 | - Part 2: Main ideas 47 | - Writing a program to do the shift cipher 48 | - Writing a program to decrypt the shift cipher -- do it without subtraction 49 | - Multiplicative cipher -- try it out 50 | - How to decrypt? Only certain numbers work 51 | - Part 3: Wrap up 52 | - What were the main points 53 | - Brief polling quiz 54 | - Feedback form 55 | 56 | 57 | - Recap of DP 58 | - Arithmetic with `%` 59 | - Application: Shift cipher 60 | - Application: Multiplicative cipher (which keys do you not want to use?) 61 | - Powers: Don't raise power first then `%` 62 | - Explanation of the technique 63 | - Then they practice 64 | 65 | ### Module 2B 66 | 67 | - Crypto challenge -- they learn the cryptosystems before class then come to class ready to work 68 | - Encrypt 69 | - Decrypt with a sample ciphertext 70 | - Decrypt with no ciphertext 71 | 72 | Systems: 73 | - Basic shift 74 | - Multiplicative 75 | - Basic public key () -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module3/225-3a-dp.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module3/225-3a-dp.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module3/225-3b-dp.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module3/225-3b-dp.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module3/MTH 225 Module 3A presentation.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module3/MTH 225 Module 3A presentation.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module3/MTH 225 Module 3B presentation.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module3/MTH 225 Module 3B presentation.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module4/225-4a-dp.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module4/225-4a-dp.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module4/225-4b-async.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module4/225-4b-async.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module4/225-4b-dp.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module4/225-4b-dp.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module4/225-module4-planning.md: -------------------------------------------------------------------------------- 1 | # Module 4 planning 2 | 3 | Focus on logical equivalence, quantification, predicates. 4 | 5 | Learning Targets: 6 | 7 | + L.2 **(Core)**: I can write the negation, converse, and contrapositive of a conditional statement and use DeMorgan's Laws to simplify symbolic logical expressions. 8 | + L.3: I can determine whether a quantified statement is true, false, or underdetermined, and state its negation. 9 | 10 | Micro targets: 11 | 12 | A: 13 | - Determine whether two statements are logically equivalent. 14 | - State DeMorgan's laws and use them to simplify a proposition involving negations, conjunctions, and disjunctions. 15 | - State an implication as a disjunction. 16 | - State the negation of an implication. 17 | 18 | B: 19 | 20 | - Define the term "predicate" and explain how a predicate is different from a proposition. 21 | - Identify the quantifiers $\exists$ and $\forall$. 22 | - Decide if a quantified statement is true, false, or underdetermined. 23 | - State the negation of a quantified statement with one quantifier. 24 | - State the negation of a quantified statement with two quantifiers. 25 | 26 | ## Part A 27 | 28 | 29 | - Determine whether two statements are logically equivalent. 30 | - State DeMorgan's laws. 31 | - Use DeMorgan's laws to simplify a proposition involving negations, conjunctions, and disjunctions. 32 | - State an implication as a disjunction. 33 | - State the negation of an implication. 34 | 35 | In class: 36 | - Construct truth tables to decide if statements are LE and build logic circuits to check 37 | - Prove laws of symbolic logic with truth tables 38 | - PE: Implication as disjunction, negation of implication, truth of predicates 39 | - 40 | 41 | 42 | ## Part B 43 | 44 | - Define the term "predicate" and explain how a predicate is different from a proposition. 45 | - Identify the quantifiers $\exists$ and $\forall$. 46 | - Decide if a quantified statement is true, false, or underdetermined. 47 | - State the negation of a quantified statement with one quantifier. 48 | - State the negation of a quantified statement with two quantifiers. 49 | 50 | In class: 51 | 52 | - The following predicate is always true, sometimes true, never true? State the negation 53 | 54 | ---- 55 | 56 | ## Throwaway code/LaTeX 57 | 58 | ```python 59 | def foo(a,b): 60 | if ((not a) or (not b) or (a) or (not a)): 61 | print("There was an error") 62 | else: 63 | print("The program executed successfully") 64 | ``` 65 | 66 | if a or (a and b): 67 | 68 | ```python 69 | def foo(a,b): 70 | if a or (a and b): 71 | print("You win!") 72 | else: 73 | print("You lose!") 74 | ``` 75 | -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module4/4a-async-activities.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module4/4a-async-activities.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module4/MTH 225 Module 4A presentation.pdf: 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relationship is a function, when stated as a diagram, formula, table of outputs, or visual image. 17 | + Find the composition of two functions. 18 | + Determine whether a function is an injection, surjection, or bijection. 19 | + Find the image and inverse image of a set under a function. 20 | + Define and use the *floor* and *ceiling* functions. 21 | 22 | Part A: Focus on definitions, working with functions including floor and ceiling; implementation in Python; maybe composition 23 | Part B: Focus on injection, surjection, bijection, image and inverse image of sets 24 | 25 | 26 | ## Part A 27 | 28 | + State the definition of a function. 29 | + Determine whether a relationship is a function, when stated as a diagram, formula, table of outputs, or visual image. 30 | + State the domain, codomain, and range of a function. 31 | + Define and use the *floor* and *ceiling* functions. *Maybe need video content for this* 32 | 33 | --- 34 | 35 | + Find the image of an input using a function using correct function notation. 36 | + Find the composition of two functions. 37 | 38 | 39 | Activities: 40 | 41 | - In class: Determine the domain, range, and codomain given as sets. Include Python functions. For fun: Collatz conjecture. 42 | - Pre class: Determine which are funtions; images of points; explain difference between range and codomain 43 | 44 | 45 | ## Part B 46 | 47 | + Determine whether a function is an injection, surjection, or bijection. 48 | + Find the image and inverse image of a set under a function. 49 | 50 | Activities: 51 | 52 | - Look at modular exponentiation -- when is it a surjection? 53 | - -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module6/MTH 225 Module 6A presentation.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module6/MTH 225 Module 6A presentation.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module6/MTH 225 Module 6B presentation.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module6/MTH 225 Module 6B presentation.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module7/225-7a-dp.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module7/225-7a-dp.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module7/225-7b-dp.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module7/225-7b-dp.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module7/225-module7-planning.md: -------------------------------------------------------------------------------- 1 | # Module 7 2 | 3 | ## Overall: 4 | 5 | First unit on counting. Learning Targets: 6 | 7 | - C.1 **(Core)**: I can use the additive and multiplicative principles and the Principle of Inclusion and Exclusion to formulate and solve counting problems. 8 | - C.2: I can calculate a binomial coefficient and correctly apply the binomial coefficient to formulate and solve counting problems. 9 | 10 | 11 | Micro-objectives: 12 | 13 | Module 7A: 14 | 15 | + Use the Additive Principle to count the number of ways a pair of disjoint events can occur. 16 | + Use the Multiplicative Principle to count the number of ways a linked pair of events can occur. 17 | + State the Additive and Multiplicative Principles. 18 | + Given an arrangement to count, determine whether the Additive Principle, the Multiplicative Principle, or neither applies. 19 | + State the Additive and Multiplicative Principles in terms of set operations. 20 | + Find the cardinality of a union of two sets. 21 | + Find the cardinality of a union of three sets. 22 | + Explain the Principle of Inclusion/Exclusion (PIE). 23 | 24 | Module 7B: 25 | 26 | - Define the binomial coefficient ${n} \choose {k}$ in terms of: 27 | - Counting $n$-bit strings of weight $k$ 28 | - Counting $k$-element subsets of a set with cardinality $n$ 29 | - Counting the number of lattice paths of length $n$ having $k$ steps to the right 30 | - Finding the coefficient of $x^ky^{n-k}$ in $(x+y)^n$ 31 | - The number of ways to select $k$ objects from a collection of $n$ objects 32 | - Explain why all of the above counting situations are counted the same way. 33 | - State the recurrence relation for ${n} \choose {k}$. 34 | - Write out Pascal's Triangle to $n$ levels. 35 | 36 | 37 | ## 7A 38 | 39 | + State the Additive and Multiplicative Principles. 40 | + Given an arrangement to count, determine whether the Additive Principle, the Multiplicative Principle, or neither applies. 41 | + State the Additive and Multiplicative Principles in terms of set operations. 42 | + Find the cardinality of a union of two sets. 43 | 44 | 45 | + Use the Additive Principle to count the number of ways a pair of disjoint events can occur. 46 | + Use the Multiplicative Principle to count the number of ways a linked pair of events can occur. 47 | + Find the cardinality of a union of three sets. 48 | + Explain the Principle of Inclusion/Exclusion (PIE). 49 | -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module7/MTH 225 Module 7A presentation.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module7/MTH 225 Module 7A presentation.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module7/MTH 225 Module 7B presentation.pdf: -------------------------------------------------------------------------------- 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of a collection of $n$ objects 22 | - Determine the number of $k$-permutations of $n$ objects 23 | - State a closed formula for ${n}\choose{k}$ 24 | 25 | --- 26 | 27 | - Solve counting problems that involve combinations and permutations 28 | 29 | 30 | 31 | -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module8/MTH 225 Module 8A presentation.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module8/MTH 225 Module 8A presentation.pdf -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module8/MTH 225 Module 8B presentation.pdf: -------------------------------------------------------------------------------- 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A: Stars and bars 10 | 11 | - Explain the kinds of problems that are solved by the stars-and-bars technique. 12 | - Given a problem that is solved using the stars-and-bars technique, draw the stars-and-bars chart for it. 13 | - Given a stars-and-bars for a counting problem, state the distribution of items that goes along with it. 14 | - Given a counting problem, identify whether stars-and-bars applies, and if so, solve the problem. 15 | 16 | 17 | B: PIE --- *or* this unit is just a catch-all for all counting problems we've seen and make PIE an AEP. <-- 18 | 19 | -------- 20 | 21 | 22 | 23 | 24 | 25 | -------------------------------------------------------------------------------- /archive/mth225-fall2020/activities/module9/MTH 225 Module 9A presentation.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/RobertTalbert/discretecs/a88522d33817477f2296d4888361156b54f37add/archive/mth225-fall2020/activities/module9/MTH 225 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\usepackage{ifxetex,ifluatex} 8 | \usepackage{graphicx} 9 | \usepackage{fixltx2e} % provides \textsubscript 10 | \ifnum 0\ifxetex 1\fi\ifluatex 1\fi=0 % if pdftex 11 | \usepackage[T1]{fontenc} 12 | \usepackage[utf8]{inputenc} 13 | \else % if luatex or xelatex 14 | \ifxetex 15 | \usepackage{mathspec} 16 | \usepackage{xltxtra,xunicode} 17 | \else 18 | \usepackage{fontspec} 19 | \fi 20 | \defaultfontfeatures{Mapping=tex-text,Scale=MatchLowercase} 21 | \newcommand{\euro}{€} 22 | \fi 23 | % use upquote if available, for straight quotes in verbatim environments 24 | \IfFileExists{upquote.sty}{\usepackage{upquote}}{} 25 | % use microtype if available 26 | \IfFileExists{microtype.sty}{% 27 | \usepackage{microtype} 28 | \UseMicrotypeSet[protrusion]{basicmath} % disable protrusion for tt fonts 29 | }{} 30 | \ifxetex 31 | \usepackage[setpagesize=false, % page size defined by xetex 32 | unicode=false, % unicode breaks when used with xetex 33 | xetex]{hyperref} 34 | \else 35 | \usepackage[unicode=true]{hyperref} 36 | \fi 37 | \usepackage[usenames,dvipsnames]{color} 38 | \hypersetup{breaklinks=true, 39 | bookmarks=true, 40 | pdfauthor={}, 41 | pdftitle={}, 42 | colorlinks=true, 43 | citecolor=blue, 44 | urlcolor=blue, 45 | linkcolor=magenta, 46 | pdfborder={0 0 0}} 47 | \urlstyle{same} % don't use monospace font for urls 48 | \setlength{\parindent}{0pt} 49 | \setlength{\parskip}{6pt plus 2pt minus 1pt} 50 | \setlength{\emergencystretch}{3em} % prevent overfull lines 51 | \providecommand{\tightlist}{% 52 | \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}} 53 | \setcounter{secnumdepth}{0} 54 | 55 | \date{} 56 | 57 | % Redefines (sub)paragraphs to behave more like sections 58 | \ifx\paragraph\undefined\else 59 | \let\oldparagraph\paragraph 60 | \renewcommand{\paragraph}[1]{\oldparagraph{#1}\mbox{}} 61 | \fi 62 | \ifx\subparagraph\undefined\else 63 | \let\oldsubparagraph\subparagraph 64 | \renewcommand{\subparagraph}[1]{\oldsubparagraph{#1}\mbox{}} 65 | \fi 66 | 67 | 68 | \begin{document} 69 | $body$ 70 | \end{document} -------------------------------------------------------------------------------- /archive/mth225-fall2020/design-notes/225-AEP-ideas.md: -------------------------------------------------------------------------------- 1 | AEP ideas 2 | ========= 3 | 4 | Fractions in binary (Module 1; programming option?) 5 | RSA encryption (Module 2, programming option) 6 | Finding multiplicative inverses (Module 2, programming option) 7 | Implementing the XOR cipher (Module 3, programming option) 8 | Program that prints off truth tables (Module 4, P) 9 | Logical equivalences with NAND and XOR (Module 4) 10 | Manipulating sets in Python (Module 5, P) 11 | Testing functions for injective, surjective, bijective (Module 6, P) 12 | Cryptograms (Module 8?) 13 | Donut problems (Module 9) 14 | Recursive visual patterns (Module 10-11) -------------------------------------------------------------------------------- /archive/mth225-fall2020/design-notes/ReplicateThisNotebook.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "nbformat": 4, 3 | "nbformat_minor": 0, 4 | "metadata": { 5 | "colab": { 6 | "name": "ReplicateThisNotebook.ipynb", 7 | "provenance": [], 8 | "authorship_tag": "ABX9TyOYAPTn1qhxWns3lyV09vEH" 9 | }, 10 | "kernelspec": { 11 | "name": "python3", 12 | "display_name": "Python 3" 13 | } 14 | }, 15 | "cells": [ 16 | { 17 | "cell_type": "markdown", 18 | "metadata": { 19 | "id": "ObjCykY54E3c", 20 | "colab_type": "text" 21 | }, 22 | "source": [ 23 | "# MTH 325 Technology Assessment\n", 24 | "\n", 25 | "## Text replication task\n", 26 | "\n", 27 | "**Computational thinking** is a framework for problem solving that is very important in MTH 225. It consists of four stages:\n", 28 | "\n", 29 | "1. Decomposition\n", 30 | "2. Pattern finding\n", 31 | "3. Abstraction\n", 32 | "4. Algorithm design\n", 33 | "\n", 34 | "For example, the *triangular number sequence* is the sequence $1, 3, 6, 10, 15, \\dots$ where each number tells you the number of dots that can be arranged in a triangular pattern. [This website illustrates the idea.](https://www.mathsisfun.com/algebra/triangular-numbers.html). \n", 35 | "\n", 36 | "What's the pattern in the numbers? Can you see it? Does the pattern always hold? Why? \n", 37 | "\n", 38 | "Later in the course we'll look at this sequence and find that a *recurrence relation* describes it: \n", 39 | "\n", 40 | "$$T_n = T_{n-1} + n$$ \n", 41 | "\n", 42 | "Here is some Python that will compute triangular numbers using this relation: " 43 | ] 44 | }, 45 | { 46 | "cell_type": "code", 47 | "metadata": { 48 | "id": "w2U5DGaQ3sxU", 49 | "colab_type": "code", 50 | "colab": {} 51 | }, 52 | "source": [ 53 | "def triangular(n): \n", 54 | " if n == 1: \n", 55 | " return 1\n", 56 | " else: return triangular(n-1) + n" 57 | ], 58 | "execution_count": 5, 59 | "outputs": [] 60 | } 61 | ] 62 | } -------------------------------------------------------------------------------- /archive/mth225-fall2020/templates/dp-template.md: -------------------------------------------------------------------------------- 1 | # MTH 225: Discrete Structures for Computer Science 1 2 | 3 | ## Daily Preparation, Module x: 4 | 5 | **Due by:** 6 | 7 | **Estimated time requirement:** About 45 minutes for the whole assignment. *If you have worked on this assignment for 30 minutes and you're not at least halfway done, DON'T work any further* --- instead, *stop and ask for help* on the `#dailyprep` channel on CampusWire. 8 | ======= 9 | 10 | 11 | ## Overview 12 | 13 | 14 | 15 | ## What you will learn 16 | 17 | **Learning Targets addressed in this module:** 18 | 19 | > (LT here) 20 | 21 | **BEFORE** your class meeting, use the Resources for Learning (below) to learn how to do the following: 22 | 23 | **DURING AND AFTER** your class meeting, you will learn how to do the following: 24 | 25 | 26 | ## Resources for Learning 27 | 28 | **Text:** Read through 29 | 30 | **Video:** At the MTH 201 playlist on YouTube (http://bit.ly/GVSUCalculus), watch the following videos. The total running time is xx:xx. 31 | 32 | - 33 | 34 | You are free to search for and use other resources in addition to, or instead of the above, as long as you can work the exercises below. 35 | 36 | 37 | ## Exercises 38 | 39 | The exercises for this assignment are found at the links below. 40 | 41 | 42 | ## Submission, grading, and getting help 43 | 44 | **Submitting your work:** 45 | 46 | **How this is graded:** Daily Prep assignments are graded on the basis of *completeness and effort*: If your submission has **all parts completed** (no blank entries, even if left blank accidentally) and **a good-faith effort to provide a correct solution or explanation is given** (no responses of "I don't know" or "I didn't understand") and **the work is submitted on time**, it gets a "check". Otherwise it gets an "x". If you are stuck on an item, you're expected to ask questions and give your best effort. 47 | 48 | **Getting help on this assignment:** *You may work with others on this assignment, but you may not copy each others' answers.* Evidence of copying will be treated as academic dishonesty. You may also ask questions on the #dailyprep channel on CampusWire, but you may not ask simply to be given the answers; giving and receiving answers on CampusWire will be treated as academic dishonesty. -------------------------------------------------------------------------------- /archive/mth225-fall2020/templates/followup-template.tex: -------------------------------------------------------------------------------- 1 | \documentclass{beamer} 2 | 3 | \usepackage[utf8]{inputenc} 4 | \usetheme{Warsaw} 5 | 6 | %Information to be included in the title page: 7 | \title{MTH 201: Calculus} 8 | \subtitle{Followup Activities --- Module xy} 9 | \author{Prof. Talbert} 10 | \institute{GVSU} 11 | \date{\today} 12 | 13 | 14 | \begin{document} 15 | 16 | \frame{\titlepage} 17 | 18 | \begin{frame}{Reminders:} 19 | 20 | \begin{itemize} 21 | \item Post-class activities are to be worked out in ClassKick. 22 | \item There is nothing to turn in --- your work is saved automatically on ClassKick. 23 | \item They are graded check/x on the basis of completeness and effort. 24 | \item You can work freely with others on these, but please for your own benefit, don't just copy work. 25 | \item If you need help or want Prof. Talbert to check your work, use the "raise hand" feature on ClassKick. 26 | \end{itemize} 27 | 28 | \end{frame} 29 | 30 | 31 | \begin{frame}[t] 32 | \frametitle{First activity} 33 | 34 | Hello 35 | 36 | \end{frame} 37 | 38 | 39 | 40 | \end{document} -------------------------------------------------------------------------------- /archive/mth225-fall2020/templates/inclass-template.tex: -------------------------------------------------------------------------------- 1 | \documentclass{beamer} 2 | 3 | \usepackage[utf8]{inputenc} 4 | \usetheme{Warsaw} 5 | 6 | %Information to be included in the title page: 7 | \title{MTH 201: Calculus} 8 | \subtitle{Module xy} 9 | \author{Prof. Talbert} 10 | \institute{GVSU} 11 | \date{\today} 12 | 13 | 14 | \begin{document} 15 | 16 | \frame{\titlepage} 17 | 18 | 19 | \begin{frame}{Agenda for today} 20 | \begin{itemize} 21 | \item<1-> First topic 22 | \item<2-> Second topic 23 | \end{itemize} 24 | \end{frame} 25 | 26 | \begin{frame} 27 | \frametitle{First activity} 28 | 29 | Hello 30 | 31 | \end{frame} 32 | 33 | \begin{frame} 34 | \frametitle{NEXT TIME...} 35 | 36 | \begin{itemize} 37 | \item To do list 1 38 | \item To do list 2 39 | \end{itemize} 40 | 41 | \end{frame} 42 | 43 | \end{document} --------------------------------------------------------------------------------