├── How To Contribute.md └── README.md /How To Contribute.md: -------------------------------------------------------------------------------- 1 | # How To Contribute 2 | Thank you for your interest in contributing! Your contributions will help make this repository a valuable resource for students and self-learners across the globe. Below are the guidelines to help you get started: 3 | 4 | ## 1. Types of Contributions 5 | You can contribute in various ways, such as: 6 | * Adding new resources (textbooks, lecture notes, competitions, etc.). 7 | * Improving or updating existing materials. 8 | * Organizing or categorizing content more effectively. 9 | * Fixing issues (typos, broken links, etc.). 10 | 11 | ## 2. Submitting Contributions 12 | + **Fork the repository**: Start by forking this repository to your GitHub account. 13 | + **Create a new branch**: Make changes in a branch specific to the contribution you're making (e.g., add-new-resource, fix-typos). 14 | * **Make your changes**: Follow the contribution type guidelines and ensure your additions are relevant and accurate. 15 | * **Commit with a clear message**: Use clear and concise commit messages that explain your changes (e.g., "Added Algebra textbook for high school level"). 16 | * **Submit a pull request (PR)**: Once you're satisfied with your changes, submit a PR and provide a description of your contribution. 17 | 18 | ## 3. Content Guidelines 19 | * **Quality**: Ensure that all resources are high quality and trustworthy. Avoid uploading incomplete or unreliable materials. 20 | * **Relevance**: Resources should be directly related to mathematics and appropriate for the level of study indicated. 21 | ***Attribution:*** When contributing external resources (e.g., textbooks or articles), ensure proper attribution and include the source or author where applicable. 22 | 23 | ## 4. Code of Conduct 24 | Please be respectful and constructive when contributing to discussions or submitting pull requests. We're building a supportive community for learners of all levels. 25 | 26 | ## 5. Communication 27 | * **Open an issue**: If you’re unsure about what to contribute or how to make changes, feel free to open an issue to discuss your ideas before submitting. 28 | * **Join the conversation**: Engage with other contributors in the repository’s discussions or issues tab. Collaboration and feedback are key! 29 | 30 | ## 6. License 31 | By contributing to this repository, you agree that your contributions will be licensed under the same license as this repository, which is MIT License. 32 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Mathematics-Mastery-Resources---from-high-school-to-graduate-level 2 | 🤗🤗🤗This is a comprehensive collection of mathematics resources designed to support self-study from high school to graduate-level topics. Starring this repository will enable it to reach larger audience! 👍👍 3 | 4 | ‼️**Disclaimer**‼️ As you progress in your mathematics journey, you should not have the wrong mindset that a single book might solve all your problems. Most times, you might need to consult multiples books, coupled with YouTube videos and so on, in order to fully understand the particular topic you are studying. 5 | 6 | # Classification of Mathematics 7 | [American Mathematical Society](https://mathscinet.ams.org/mathscinet/msc/msc2020.html) (AMS) has the most comprehensive file on the classification of mathematics. It is about 230 pages. 8 | 9 | # High School 10 | [Khan Academy](https://www.khanacademy.org/) is the best resource to learn grade 1 to 12 mathematics topics. It is also the official platform to prepare for [SAT](https://satsuite.collegeboard.org/sat/registration), as well good (not fully sufficient) for [IGCSE](https://www.cambridgeinternational.org/programmes-and-qualifications/cambridge-upper-secondary/cambridge-igcse/), [AP exam](https://satsuite.collegeboard.org/sat/registration), [IB exam](https://www.ibo.org/programmes/diploma-programme/assessment-and-exams/) and [A-level exam](https://www.cambridgeinternational.org/programmes-and-qualifications/cambridge-advanced/cambridge-international-as-and-a-levels/). Depending on your mathematics goals, if you are someone (e.g undergraduate, working professional) that quickly want to revisit your old mathematics knowledge, Khan Academy is your surest bet. 11 | 12 | If you prefer books, you can download these books via the websites given below: 13 | * Cambridge IGCSE, AS & A level coursebooks 14 | * Haese Mathematics coursebooks for IB exam 15 | * AP books 16 | - Calculus AB and BC: Barron's AP Calculus, Princeton Review's Cracking the AP Calculus AB & BC Exams 17 | - Statistics: Princeton Review AP Statistics Prep, Barron’s AP Statistics and 5 Steps to a 5: AP Statistics 18 | * [Pauls Online Math Notes](https://tutorial.math.lamar.edu/) - an excellent online resource! 19 | 20 | # Undergraduate 21 | ## Foundations 22 | ### Calculus 23 | * [MIT 18.01 Single Variable Calculus*](https://ocw.mit.edu/courses/18-01-single-variable-calculus-fall-2006/) - This introductory calculus course covered differentiation and integration of functions of one variable, with applications. 24 | * [MIT 18.02 Multivariable Calculus](https://ocw.mit.edu/courses/18-02-multivariable-calculus-fall-2007/) - Covers vector and multi-variable calculus. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space. 25 | * Calculus, 4th edition [_by Michael Spivak_] - One of the most popular calculus book for undergraduates. 26 | * Calculus Early Transcendentals, 11 edition [_by Anton, Bivens, Davis_] - Covers both single variable, multivariable variable and vector calculus. It is easy to understand, with a lot of excercises. 27 | * Calculus of a Single Variable, 10th edition [_by Ron Larson_] - A top-notch book for single variable calculus. 28 | * Calculus Early Transcendentals, 9th edition [_by James Stewart, Saleem Watson, Daniel Clegg_] - Similar to Anthon-Bivens-Davis book. 29 | * Vector Calculus, 4th edition [_by Susan Jane Colley_] - Similar to Anton boo, but slightly mathematically more intense. 30 | * Vector Calculus, 6th edition [_by Anthony Tombra, Jerrold E. Marsden_] - Very similar to Susan Jane book. 31 | 32 | ### Proof Writing 33 | * Mathematical Proofs: A Transition to Advanced Mathematics, 4th edition [_by Ping Zhang, Albert D. Polimeni, Gary Chartrand_] - Covers set theory, mathematical induction, logical reasoning, equivalence revaltions, functinos, nuber theory, combinatorics, calculus, group theory, ring theory , linear algebra, etc. It is highly recommended. 34 | * How to Prove It, 3rd edition [_by Velleman Daniel_] - A very nice book. 35 | * [Introduction to Proof Writing](https://www.youtube.com/watch?v=nGEUOLCYbng) - A full 12-hour YouTube video by **MathMajor**. 36 | * Book of Proof [_by Richard Hammack_] - A great book and less advanced compared to Mathematical Proofs by Ping Zhang. [Here](https://youtube.com/playlist?list=PLISEtDmihMo395ECdd9fqsIZ9y2LWXnLZ&si=JplKxyt6BK5lmDUj) is the YouTube playlist for the book. 37 | * [Introduction to Mathematical Thinking](https://www.coursera.org/learn/mathematical-thinking) - A popular Coursera course by _Dr. Keith Kelvin_ from Stanford University. 38 | * Proofs [_by Jay Cummings_] - Very intuitive and fun! 39 | 40 | ## Algebra 41 | * Haese Mathematics HL (Option): Sets, relations and groups [_by Catherine Quinn, Robert Haese, Michael Haese_] - A beginner-friendly intrdouction to abstract algebra. 42 | * A First Course in Abstract Algebra, 8th edition [_by John B. Freleigh, Neal Brand_] - A very rigorous introduction to abstract algebra(groups, rings & fields, in that order) and briefly covers advanced concepts like Galois theory. 43 | * Contemporary Abstract Algebra [_by Joseph A. Gallan_] - One of the highly recommended books for beginners in abstract algebra. It is rich both in theory and calculation exercises. [Kimberly Brehm](https://youtube.com/playlist?list=PLl-gb0E4MII1YlnI7OBsUHQ5E42RA-ZVI&si=02JzNNpTNXzZLSG) covers the group parts on her YouTube channel. 44 | * Abstract Algebra [_Thomas W. Judson_] - Covers the theoretical aspects of grops, rings, and fields. Moreover, it treats their applications in coding theory and cryptography. 45 | * [Visual Group Theory](https://youtube.com/playlist?list=PLwV-9DG53NDxU337smpTwm6sef4x-SCLv&si=mLpng62whN93gltI) - Taught by Professor Macauley from Clemson University and should very conducive to self-study. [This](https://www.math.clemson.edu/~macaule/classes/f22_math4120/) is the course website. 46 | * [Abstract (Modern) Algebra Course](https://youtube.com/playlist?list=PLmU0FIlJY-Mn3Pt-r5zQ_-Ar8mAnBZTf2&si=_trrfbpVqGm0gFdo) - Taught in Spring of 2018 by Professor Bill Kinney at Bethel University. It contained 68 videos on group, ring, field and Galois theories. 47 | * [Abstract Algebra I](https://youtube.com/playlist?list=PLBY4G2o7DhF0JCgapYKrqibGaJuvV4Gkb&si=mp1LkbsGC4u3GmNG) - Taught by Professor James Cook in Fall 2016. [This](http://www.supermath.info/AbstractAlgebra.html) is the course website which contained solutions to numerous questions. 48 | * Introduction to Linear Algebra, 5th edition [_by Gilbert Strang_] - This is a golden book for introductory linear algebra course. Professor Gilbert is a legend and famously konown for this course globally. Check [MIT 18.06SC Linear Algebra](https://ocw.mit.edu/courses/18-06sc-linear-algebra-fall-2011/) and the [YouTube playlist](https://youtube.com/playlist?list=PL221E2BBF13BECF6C&si=tIeA7rD5pDkrdLWa) for his lesson videos. 49 | * Elementary Linear Algebra, 8th edition [_by Ron Larson_] - A very beginner-friendly introductory to Linear Algebra. 50 | * Linear Algebra Done Right, 4th edition [_by Sheldon Axler_] - A rigorous introductory course, most suitable after finishing Gilbert's or Ron's book. 51 | * Linear Algebra [_by Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence_] - An excellent and elaborate introductory book but demands sufficiently high mathematical maturity from its readers. 52 | 53 | ## Analysis 54 | * Theory of Infinite Sequences and Series [_by Ludmila Bourchtein, Andrei Bourchtein_] - Covers a lot of theprem extensively on series and sequences than a standard single variable calculus book 55 | * Real Analysis via Series and Sequences, 2015 edition [_by Charles H.C. Little, Kee L. Teo, Bruce van Brunt_] - Requires the mastery of single variable calculus and foundational proof writing. 56 | * Real Analysis: A Long-Form Mathematics Textbookb [_by Jay Cummings_] - The author has a knack for explaining advanced concepts in funny and intuitive ways. 57 | * Principles of Mathemamtical Analysis [_by Walter Rudin_] - Colloquially known as _"PMA"_ or _"Baby Rudin"_. It is a famous book but requires rich mathematical maturity! 58 | * [MIT 18.100A Real Analysis](https://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/) - Contains MIT lecture notes, videos, assignments and examinations. 59 | * A First Course in Complex Analysis with Applications by Dennis G. Zill - Its only prerequisite is multivariable and vector calculus. 60 | * [Lebesgue Measure and Integration by Presidomath](https://youtube.com/playlist?list=PLPluXkAqV1FFi2BxxsHVgKIXA-ThQQ5sN&si=nsWq4PoKWWpe-OoD) - Useful playlist to learn lebesgue measure and integration. 61 | 62 | ## Logic and Set Theory 63 | * Introduction to mathematical logic, 6th edition [_by Elliott Mendelson_] - Covers first-order logic, number theory, axiomatic set theory & computability. 64 | * Mathematical Logic [_by Ian Chiswell and Wilfrid Hodges_] - Covers natural deduction, propositional logic, quantifier-free logic, first-order logic. 65 | * A friendly introduction to mathematical logic [_by Christopher C. Leary and Lars Kristiansen_] - covers the central topics of first-order mathematical logic such as Incompleteness theorems, computability theory, completeness and compactness. 66 | * Elements of Set Theory [_by Herbert B. Enderton_] - Highly respected book but might not be the best for self studying. 67 | * A first course in mathematical logic and set theory [_by Michael L. O'Leary_] - covers the necessary basics in a very friendly approach. 68 | 69 | 70 | ## Topology & Geometry 71 | * Topology [_by James R. Munkres_] - The standard undergraduate book in most universities. 72 | * [General Topology by Presidomath](https://youtube.com/playlist?list=PLPluXkAqV1FG7WFEiud9JLWISY6Y5_j9G&si=mIZQEKLq_a420UQl) - An excellent playlist to learn the basics of general toplology. 73 | * Elementary Topology Problem Textbook [_by Viro, Ivanov, Netsvetaev, Kharlamov_] - Really good for improving problem solving skills in topology. 74 | * Undergraduate Topology: A Working Textbook [_by Aisling McCluskey, Brian McMaster_] - Short and wonderful book to sharpen your problem solving skills. 75 | * Differential Geometry of Curves and Surfaces, 2nd edition [_by Manfredo P. Do Carmo_] - Well-respected book that covers differential geometry from a classical approach. 76 | * Elementary Differential Geometry, 2nd edition [_by Barret O'Neill_] - It uses differential forms approach and requires only the knowledge of calculus and linear algebra courses. 77 | * John Lee's 3 book series: (In ascending order of study) Introduction to Topological Manifolds, Introduction to Smooth Manifolds, and Introduction to Riemannian Manifolds - Good for beginning-level graduate study. 78 | 79 | ## Probability & Statistics 80 | * Introduction to Probability Models, 10th edition [_by Sheldon Ross_] - A golden textbook which covers basic probability theory, markov chains, renewal theory, queuing theory, etc. 81 | * Introduction to Probability [_by Dimitri P. Bertsekas and John N. Tsitsiklis_] - Quite rigorous and should not be used as a first exposure to probability unless you've built an excellent mathematical maturity. Its online version can be found on [MITx](https://www.edx.org/learn/probability/massachusetts-institute-of-technology-probability-the-science-of-uncertainty-and-data). 82 | * Probability & Statistics for Engineers and Scientists, 9th edition [_by Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying Ye_] - Very easy to understand and really suitable for beginners in engineering/statistics field.  83 | 84 | ## Number Theory 85 | * Elementary Number Theory [_by David Burton_] - A good book to start your number theory journey. 86 | * Methods of Solving Number Theory Problems [_by Ellina Grigorieva_] - Doesn't require more than high-school mathematics. 87 | * Elementary Number Theory [_by Thomas Koshy_] - An excellent introductory book with less emphasis on rigorous proofs. 88 | * Problems in Algebraic Number Theory [_by M. Ram Murty Jody Esmonde_] - Contains a collection of 500 problems with solutions. 89 | 90 | ## Discrete Mathematics 91 | * Essential Discrete Mathematics for Computer Science [_by Harry Lewis_] - Beginner-level book with interesting topics like set theory, logic, graph theory, automata theory, probability, cryptography. 92 | * Discrete Mathematics with Applications [_by Kenneth H. Rosen_] - Doesn't require any prerequisites other than sufficient maturity to use it. 93 | 94 | 95 | ## Statistics & Data Science 96 | * The Elements of Statistical Learning (ESL) [_by Trevor Hastie, Robert Tibshirani, Jerome Friedman_] - A must-read book if you are serious about machine learning. 97 | * Introduction to Statistical Learning (ISL) - Written by same authors, you can start with ISL if ESL is too advanced for you. ISL has both Python and R editions.  98 | * Introduction to Probability for Data Science [_by Stanley H. Chan_] - Highly recommended and contains most needed knowledge for a typical machine learning/data science job, coupled with Python and MATLAB codes. 99 | 100 | 101 | ## Computational & Applied Mathematics 102 | * Elementary Differential Equations and Boundary Value Problems [_by Boyce, Diprima , Meade_] - Very explanatory and suitable for beginners. It also covers basics of PDEs. Its online version can be found via [MIT OCW](https://ocw.mit.edu/courses/18-03-differential-equations-spring-2010/) 103 | * Understanding Engineering Mathematics [_by John Bird_] - Started from middle-school mathematics up the way to PDEs, Fourier and Laplace transforms. 104 | * Advanced Engineering Mathematics [_by Dennis G. Zill_] - Covers differential equations, PDEs, Laplace & Integral transforms, numerical analysis, vector and matrix calculus, complex analysis. 105 | * Mathematical Methods for Engineers and Scientists (Book 1,2 and 3) [_by K.T Tang_] - Covers vector analysis, ODEs, Laplace transforms, matrix analysis, complex analysis, tensor analysis, Fourier analysis, Sturm-Liouville theory and special functions, PDEs. 106 | 107 | # Graduate 108 | 109 | # How to Find Prerequisites For Mathematics Topics 110 | It's simple using the internet. See an example: "Prerequisites of functional analysis AAA" on any search engine. AAA should be replaced with Reddit, Quora, Math stack exchange or Math oveflow. In addition, you should always read the _**preface**_ of any mathematics book you are studying. 111 | 112 | # Mathematics Competitions 113 | Here is a list of famous prestigious mathematics competitions you can participate in. 114 | 1. [International Mathematics Olympiad](https://www.imo-official.org/) (IMO) - The most prestigious international competition for high school students! 115 | 2. [International Mathematical Kangaroo](https://www.mathkangaroo.in/) - For grade 1 to grade 12 students. 116 | 3. [Harvard MIT Mathematics Tournament](https://www.hmmt.org/) - Occurs yearly in Februarys and Novembers for high school students. 117 | 4. [International Mathematical Modelling Challenge](https://immchallenge.org/) - For middle and high school students. 118 | 5. [Mathematical Contest in Modeling](https://www.comap.com/contests/mcm-icm) - For undergraduates. 119 | 6. [International Mathematics Competition for University Students](https://www.imc-math.org.uk/) (IMC) - Similar to Williams Putnam exam's style. 120 | 7. [Mental Math World Cup & Global Mental Math Olympiad](https://livemcl.com/) 121 | 8. [SIMIODE Challenge Using DifferentiaL Equation Modeling](https://qubeshub.org/community/groups/scudem/overview) - For both high school and undergraduate studeents. 122 | 9. [William Lowell Putnam Mathemmatical Competition](https://maa.org/putnam/) - The most prestigious competition for undegraduates in USA and Canada. 123 | 10. [Alibaba Global Mathematics Competition](https://damo.alibaba.com/alibaba-global-mathematics-competition?language=en) - A global mathematics competition for EVERYONE, with a prize pool of $300,000+. 124 | 11. [Simon Marais Mathematics Competition](https://www.simonmarais.org/) - Similar to Williams Putnam exam's style. 125 | 12. [Vojtech Jarnick International Mathematics Competition](https://vjimc.osu.cz/) - For undergraduates. 126 | 13. [Open Mathematical Olympiad for University Students]() - For both bachelor and master's students. 127 | 14. [North Countries Universities Mathematical Competition](https://mathdep.itmo.ru/ncumc/) - Students from the rest of the world can also participate. 128 | 15. [International Student Team Competition in Mathematics](http://istcim.math.us.edu.pl/) - For bachelor’s, master’s and postgraduate students. 129 | 16. [Imperial Cambridge Mathematics Competition](https://icmathscomp.org/) - For undergraduate and master's students in United Kingdom. 130 | 17. [South Eastern European Mathematical Olympiad for University Students](http://www.massee-org.eu/index.php/mathematical/seemous) (SEEMOUS) 131 | 132 | **NOTE:** Excellent resources to prepare for some of these competitions are [AoPs](https://artofproblemsolving.com/), [Mathematics Olympiads Discord Server](https://mathematics.isodn.org/), et cetera. 133 | 134 | # Software Packages for Mathematics 135 | [Open-Source Softwares for Mathematics](https://en.wikipedia.org/wiki/List_of_open-source_software_for_mathematics) contains a list of free mathematics software packages you can install on your computer devices to aid your learning. 136 | 137 | # Popular Mathematics Communities 138 | + [Math Overflow](https://mathoverflow.net/) - An advanced mathematics community mainly for professional mathematicians and graduate students. Of course, anyone is free to join. 139 | + [Mathematics Stack Exchange](https://math.stackexchange.com/) - Question & Answer community for people studying math at any level and professionals in related fields. 140 | 141 | # Where to download free online books? 142 | These are some of the websites to download millions of books freely! 143 | 1. [PDF Drive](https://www.pdfdrive.com/) 144 | 2. [Z Library](https://z-lib.io/): This requires you to sign up using either your email address or gmail acount. Next, follow these steps to download books of your choice: 145 | - Join the [discord server](https://discord.gg/mtkdHp9Xqq) or click on "click here". 146 | - Type the ***correct name*** of the book or the author in the search bar and click on the search button. 147 | - Scroll down a little bit and copy the code in front of _"Request Code"._ 148 | - Open the discord and paste the code in either _"book-request"_ or _"book-request-2"_ channel. 149 | - Click on the generated link it brings and finally download your book. 150 | - **NOTE:** Click on _"Mirror"_ or _"Proxy"_ in case the download option didn't work directly. 151 | 3. [PDFCOFFEE](https://pdfcoffee.com/) 152 | 4. **Internet:** At times, all you need to do is to append the word "pdf" to the title of the book and paste on internet search tools (e.g Google Search, Firefox, etc). 153 | --------------------------------------------------------------------------------