A text for a standard first undergraduate integral calculus 172 | course. Included are a substantial collection of problems with complete 173 | hints, answers and solutions. Many of those problems are taken from 174 | exams, midterms and quizzes given at UBC.
175 |A text for a standard first undergraduate vector calculus 172 | course. Included are a substantial collection of problems with complete 173 | hints, answers and solutions. Many of those problems are taken from 174 | exams, midterms and quizzes given at UBC.
175 |Topics include forces and moments; equilibrium of particles, rigid bodies, and structures; centroids and moments of inertia.
168 | 169 |This short expository note was authored in PreTeXt early in the development of PreTeXt itself (Summer 2013). The LaTeX output required very few adjustments to be acceptable to the journal's editorial processes.
41 | 42 |The XML source has been updated to reflect early changes in PreTeXt, and the HTML output was last built in March 2015. As of early 2020 the online version seems to still be rendering just fine, a testimony to certain fundamental technical decisions.
43 |The book that started it all, now converted to PreTeXt (its third source format).
43 |This book is aimed at mathematics majors, seeing their first course after calculus that stresses theorems and their proofs. It contains a very thorough introduction to the use of the open source system, Sage, for linear algebra. Besides an extensive collection of traditional exercises, there are also reading questions for each of the thirty-seven (daily) sections.
44 |The text begins with fundamentals such as invariant subspaces, refelctors, projectors, and positive semi-definite matrics. A chapter on matrix decompositions includes LU, QR, SVD, and Cholesky, with Schur planned. Canonical forms is mostly about Jordan canonical form, with plans for rational form. The final two chapters are applications and further topics.
48 | 49 |Notation agrees with, and cross-references point to, the author's A First Course in Linear Algebra.
50 |48 | The text will be structured in stand-alone modules, each related to a single social justice topic. 49 | Each module will begin with an overview of the topic, historical context, 50 | and a discussion of current questions and concerns related to the topic. 51 | This section may include particular case studies related to the topic, 52 | articles discussing the topic, and other resources. 53 | This section will followed by discussion prompts for faculty to use in helping students explore the issue. 54 |
55 |
56 | The mathematical content will follow.
57 | Each topic will be paired with 2
64 | Each module will end with homework exercises related to the social justice and mathematics topics, 65 | longer prompts intended to support more extensive explorations of the topics, 66 | and reflection questions to encourage students to consider what they’ve learned. 67 |
68 |A theorem sequence for an inquiry-based introductory topology course.
177 |Financial support from the Faculty of Science, University 221 | of Manitoba gratefully acknowledged.
222 |83 | Precalculus is taught at Mt. Hood Community College over two 10-week courses. 84 | This text aims to address all learning outcomes from the first course, suitable for use in a single 10-week term. 85 |
86 |Music Theory for the 21st-Century Classroom is an openly-licensed online four-semester college music theory textbook. This text differs from other music theory textbooks by focusing less on four-part (SATB) voiceleading and more on relating harmony to the phrase.
168 |49 | To promote mathematics among Indigenous learners, we have created a series of stories with mathematical themes. 50 | These stories are based on the storytelling tradition of Indigenous peoples. 51 | The fact that most of our stories have been translated into several Indigenous languages 52 | as well as French is probably the biggest recognition that an author could hope for. 53 |
54 |
55 | The first story,
55 | The five chapters are logic and sets, financial math, statistics, probability and the math of democracy (United States). Additional sections can be used from David Lippman's Math In Society. There are video lectures in each section of the book and corresponding fill-in notes. Group activity pages are also available under resources. A MyOpenMath course shell is available. We emphasize spreadsheets in the financial math chapter and also include the formulas. We use spreadsheets and GeoGebra in the statistics chapter except in the normal section we use the onlinestatbook.com normal calculator and spreadsheets. 56 |
57 |58 | The United States democracy chapter includes apportionment, voting methods, popular vote, electoral college and electoral power, gerrymandering and how to measure it and federal debt and deficit. The gerrymandering section focuses on how to calculate the efficiency gap. 59 |
60 |61 | The culturally responsive features are diverse names, gender pronouns and sexual orientations throughout the book. Each chapter begins with the biography of an underrepresented mathematician or economist who contributed to that subject. In the apportionment section we include the racial context of the formation of the United States, including race-based chattel slavery and the genocide of Native Americans. A timeline of major events runs parallel to the apportionment method timeline. Hamilton, Jefferson and Webster's relationship to slavery is discussed. The names in the examples for this section are the names of civil rights leaders and Black victims of police brutality. 62 |
63 |This free, online text is designed for a one-semester undergraduate mathematics course that combines an introduction to group theory with an introduction to modern geometries using the Kleinian paradigm.
162 | 163 |The chapter on groups develops the basic theory of groups and homomorphisms, culminating with group actions. The chapter on geometry makes use of group symmetries in the basic theory of Möbius, hyperbolic, elliptic, and projective geometries.
164 | 165 |The text is designed for active engagement, with carefully structured exercises throughout.
166 | 167 |The text assumes prerequisite courses in calculus, linear algebra, and experience with proof writing.
168 |An inquiry-based introduction to game theory.
168 |Appropriate for a non-majors quantitative reasoning course or an extra topics course at the secondary level.
169 |Includes discussion questions on game theory in popular culture.
170 |Complete instructor's guide available by request.
171 |45 | Open Resources for Community College Algebra (ORCCA) is an open-source, 46 | openly-licensed textbook package (eBook, print, and online homework) for basic and intermediate algebra. 47 | At Portland Community College, Part 1 is used in MTH 60, Part 2 is used in MTH 65, and Part 3 is used in MTH 95. 48 |
49 | 50 |51 | ORCCA is available as an interactive eBook, as a downloadable PDF (in B/W or color), and as a printed/bound copy. 52 |
53 |80 | ORCAA was awarded a 2018 Digital Learning Innovation Award, with a $10,000 prize, from the Online Learning Consortium. 81 |
82 |83 | Details 84 |
85 |77 | The materials begin with linear equations in two variables and extends through trigonometry. 78 | The materials can be used in various ways, particularly in online courses. 79 |
80 | 81 |82 | The material was written with review in mind, 83 | but there is enough detail that it would be useful for new students as well. 84 | All exercises in the content areas are fully keyed, with no steps excluded. 85 | The supplemental problem sets only include answers; they are not fully keyed. 86 | While video instruction is useful for many, there are also learners who prefer written exposition, 87 | hence the redundancy in presentation of material. 88 |
89 |A discovery-based approach to linear algebra.
48 |Extended material to cover a second course in linear algebra is being finalized and will be released Summer 2019.
49 |Introductory material in each of logic, set theory, graph theory, and combinatorics.
48 |Includes worksheets for in-class activities suitable for a partially-flipped classroom.
49 |
152 | These are the notes for the edX course Programming for High
153 | Performance
to be launched in late May 2019. This course
154 | uses matrix-matrix multiplication to illustrate how algorithms
155 | and architectures need to interact if high performance is to
156 | be attained.
157 |