Free Resources for Mathematics

A collection of free and publicly available mathematics resources (textbooks and lecture materials, etc). Of course, they are all legally available!

Links

• Mathematics Stack Exchange A site where you can ask and answer questions on mathematics.
• Wolfram Alpha Ultra-high-tech calculator that understands natural language .
• MIT OCW MIT Open Courseware．
• Free Computer Books A site with a collection of free books on programming and mathematics. Among similar sites, this site has fewer illegal ones.
• American Institute of Mathematics/Approved Textbooks Collection of books made open access by the American Institute of Mathematics.

linear algebra

Elevri

• Category: Website 🌐
• URL: https://www.elevri.com/
• License: unknown
• Subject: linear algebra, calculus

黒田紘敏先生の講義資料

• Category: Lecture Notes 📝
• URL: https://www7b.biglobe.ne.jp/~h-kuroda/lecture.html
• Lang: 日本語
• License: Publicly available by the author.
• Subject: calculus，linear algebra

嶺幸太郎先生の講義資料

• Category: Lecture Notes 📝
• URL: http://www.math.kanagawa-u.ac.jp/mine/linear_alg/index.html
• Lang: 日本語
• License: unknown
• Subject: linear algebra

Axler『Linear Algebra Done Right』

• Category: Book 📖
• URL: https://link.springer.com/book/10.1007/978-3-031-41026-0
• License: Springer Open Access
• Subject: linear algebra

Boyd, Vandenberghe『Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares』

• Category: Book 📖
• URL: https://web.stanford.edu/~boyd/vmls/
• License: unknown
• Subject: linear algebra

Margalit, Rabinoff『Interactive Linear Algebra』

• Category: Website 🌐
• URL: https://textbooks.math.gatech.edu/ila/
• License: GNU Free Documentation License
• Subject: linear algebra

Calculus

Elevri

• Category: Website 🌐
• URL: https://www.elevri.com/
• License: unknown
• Subject: linear algebra, calculus

黒田紘敏先生の講義資料

• Category: Lecture Notes 📝
• URL: https://www7b.biglobe.ne.jp/~h-kuroda/lecture.html
• Lang: 日本語
• License: Publicly available by the author.
• Subject: calculus，linear algebra

Trench 『Introduction to Real Analysis』

• Category: Book 📖
• URL: https://digitalcommons.trinity.edu/mono/7/
• License: Creative Commons Attribution-NonCommercial-ShareAlike 3.0
• Subject: calculus

Number Theory and Cryptography

Stein『Elementary Number Theory』

• Category: Book 📖
• URL: https://wstein.org/ent/
• License: Publicly available by the author.
• Solutions of Exercises: available
• Subject: Elementary Number Theory

Shoup『A Computational Introduction to Number Theory and Algebra』

• Category: Book 📖
• URL: https://shoup.net/ntb/
• License: Attribution-NonCommercial-NoDerivs 3.0
• Subject: Elementary Number Theory, Algebra

Yet Another Introductory Number Theory Textbook (Cryptology Emphasis Version)

• Category: Book 📖
• URL: https://open.umn.edu/opentextbooks/textbooks/673
• License: CC BY-SA
• Subject: Number Theory，Cryptography

Keune『Number Fields』

• Category: Book 📖
• URL: https://radbouduniversitypress.nl/site/books/m/10.54195/IPVU4488/
• License: CC BY-NC-ND 4.0 DEED
• Subject: Algebraic Number Theory

Rosulek『The Joy of Cryptography』

• Category: Book 📖
• URL: https://joyofcryptography.com/
• License: Creative Commons BY-NC-SA 4.0
• Subject: Cryptography

CryptoHack

• Category: Website 🌐
• URL: https://cryptohack.org
• License: publicly available by the authors
• Subject: Cryptography, Python, SageMath

Aravind『Computational Number Theory』

• Category: Book 📖
• URL: https://people.iith.ac.in/aravind/Files-CS5610/CNT-NotesInProgress.pdf
• Course URL: https://people.iith.ac.in/aravind/cs5610.html
• License: Publicly available by the author.
• Subject: Computational Number Theory

Algebra

Altman, Kleiman『A term of Commutative Algebra』

• Category: Book 📖
• URL: https://dspace.mit.edu/handle/1721.1/116075.2
• License: CC BY-NC-SA 3.0 US DEED
• Solutions of Exercises: available
• Subject: Commutative Algebra

Scherk『Algebra: A Computational Introduction』

• Category: Book 📖
• URL: https://www.math.toronto.edu/scherk/
• License: CC BY-NC-SA 2.5 CA DEED
• Subject: Group Theory, Galois Theory, Field Theory

Leinster『Galois Theory』

• Category: Lecture Notes 📝
• URL: https://www.maths.ed.ac.uk/~tl/gt/gt.pdf
• License: Publicly available by the author.
• Subject: Galois Theory

Essential Coding Theory

• Category: Book 📖
• URL: https://cse.buffalo.edu/faculty/atri/courses/coding-theory/book/
• License: CC BY-NC-ND 3.0 DEED
• Subject: Coding Theory

Category Theory

Leinster『Basic Category Theory』

• Category: Book 📖
• URL: https://www.maths.ed.ac.uk/~tl/bct/
• License: CC NC-BY-SA 4.0
• Solutions of Exercises: https://positron0802.wordpress.com/basic-category-theory-leinster/
• Subject: Category Theory

Riehl『Category theory in Context』

• Category: Book 📖
• URL: https://math.jhu.edu/~eriehl/context
• License: "free to view and download for personal use only. Not for re-distribution, re-sale or use in derivative works"
• Subject: Category Theory

Machine Learning

Mohri, Rostamizadeh, Talwalkar『Foundations of Machine Learning』

• Category: Book 📖
• URL: https://cs.nyu.edu/~mohri/mlbook/
• License: Creative Commons CC-BY-NC-ND
• Subject: machine learning

Shalev-Shwartz, Ben-David『Understanding Machine Learning: From Theory to Algorithms』

• Category: Book 📖
• URL: https://www.cs.huji.ac.il/~shais/UnderstandingMachineLearning/
• License: "Users may download a copy for personal use only. Not for distribution."
• Solutions of Exercises: https://www.cs.huji.ac.il/~shais/UnderstandingMachineLearning/MLbookSol.pdf
• Subject: machine learning

Bertsekas『A Course in Reinforcement Learning』

• Category: Book 📖
• URL: https://web.mit.edu/dimitrib/www/RLbook.html
• License: Publicly available by the author.
• Subject: machine learning, reinforcement learning

筑波大学OCW『機械学習』

• Category: Course 🧑‍🏫
• URL: https://ocw.tsukuba.ac.jp/course/systeminformation/machine_learning/
• Lang: 日本語
• License: OCW
• SUbject: Machine Learning

CS50’s Introduction to Artificial Intelligence with Python

• Category: Course 🧑‍🏫
• URL: https://cs50.harvard.edu/ai/2024/
• License: CC BY-NC-SA 4.0
• Subject: Machine Learning, Python

EE104/CME107: Introduction to Machine Learning

• Category: Course 🧑‍🏫
• URL: https://ee104.stanford.edu/
• License: Publicly available by the author.
• Subject: Julia, Machine Learning

Griffin『Mathematics of Machine Learning』

• Category: Book 📖
• URL: https://bpb-us-e1.wpmucdn.com/sites.psu.edu/dist/d/166843/files/2023/06/SA486X.pdf
• License: CC BY-NC-SA 3.0 US DEED
• Subject: Machine Learning

MIT 6.S191 Introduction to Deep Learning

• Category: Course 🧑‍🏫
• URL: http://introtodeeplearning.com/2020/index.html
• License: Open Courseware
• Subject: Machine Learning, Deep Learning

Element of AI

• Category: Course 🧑‍🏫
• URL: https://www.elementsofai.com/
• License: Open Courseware
• Subject: Artificial Intelligence

The Elements of Differentiable Programming

• Category: Book 📖
• URL: https://arxiv.org/abs/2403.14606
• License: Publicly available by the author.
• Subject: Machine Learning, Differentiable Programming

Mathematical Optimization

Boyd, Vandenverghe『Convex Optimization』

• Category: Book 📖
• Book URL: https://web.stanford.edu/~boyd/cvxbook/
• License: Publicly available by the author.
• Solutions of Exercises: https://egrcc.github.io/docs/math/cvxbook-solutions.pdf
• Subject: convex optimization

Bertsekas『Convex Optimization Theory』

• Category: Book 📖
• Book URL: https://web.mit.edu/dimitrib/www/Convex_Theory_Entire_Book.pdf
• License: Unknown, but available on the publisher's domain.
• Solutions of Exercises: http://www.athenasc.com/convexduality.html
• Subject: convex optimization

Convex Analysis And Optimization

• Category: Course 🧑‍🏫
• URL: https://ocw.mit.edu/courses/6-253-convex-analysis-and-optimization-spring-2012/
• License: MIT OpenCourseWare
• Subject: convex optimization

Optimization Methods in Business Analytics

• Category: Course 🧑‍🏫
• URL: https://openlearninglibrary.mit.edu/courses/course-v1:MITx+15.053x+3T2016/about
• License: MIT Open Learning Library
• Subject: linear programming, Julia

Julia Programming for Operations Research

• Category: Book 📖
• URL: https://www.chkwon.net/julia/
• License: Publicly available by the author.
• Subject: Julia, Operations Research

Algorithms for Optimization

• Category: Book 📖
• URL: https://algorithmsbook.com/optimization/
• License: Creative Commons CC-BY-NC-ND
• Subject: Julia, Mathematical Optimization

Algorithms

早水桃子研究室『離散数学入門』

• Category: Lecture Video 🎥
• URL: https://www.youtube.com/playlist?list=PLCo60G1m_ibpJgfB4WcGwWybC6sfyawoL
• Lang: 日本語
• License: Youtube Standard License
• Subject: Algorithms

岡本吉央先生の講義資料

• Category: Course 🧑‍🏫
• URL: http://dopal.cs.uec.ac.jp/okamotoy/lect/
• Lang: 日本語
• License: Publicly available by the author.
• Subject: Algorithms, Computer Science, Combinatorial Optimization

Erickson『Algorithms』

• Category: Book 📖
• URL: https://jeffe.cs.illinois.edu/teaching/algorithms/
• 日本語版: https://inzkyk.xyz/algorithms/
• License: CC BY 4.0 DEED
• Subject: Algorithms

Williamson, Shmoys『The Design of Approximation Algorithms』

• Category: Book 📖
• URL: https://www.designofapproxalgs.com/
• License: unknown
• Subject: Approximation Algorithm

Schrijver『A Course in Combinatorial Optimization』

• Category: Book 📖
• URL: https://homepages.cwi.nl/~lex/files/dict.pdf
• License: Publicly available by the author.
• Subject: Algorithms

『Parameterized Algorithms』

• Category: Book 📖
• URL: https://www.mimuw.edu.pl/~malcin/book/
• License: Available with the publisher's permission.
• Subject: Algorithms

Morin『Open Data Structures』

• Category: Book 📖
• URL: https://opendatastructures.org/
• License: CC BY 2.5 CA DEED
• 日本語版: https://sites.google.com/view/open-data-structures-ja/home
• Subject: Data Structures and Algorithms, Python, C++, Java

アルゴ式

• Category: Website 🌐
• URL: https://algo-method.com/
• Lang: 日本語
• Subject: Algorithms, Computer Programming

Introduction To Algorithms

• Category: Course 🧑‍🏫
• URL: https://ocw.mit.edu/courses/6-006-introduction-to-algorithms-spring-2020/
• License: MIT OCW
• Subject: Algorithms

Control Theory

awesome-control-theory

• Category: Awesome List 😎
• URL: https://github.com/A-make/awesome-control-theory?tab=readme-ov-file#books
• Subject: control theory

Liberzon『Calculus of Variations and Optimal Control Theory: a Concise Introduction』

• Category: Book 📖
• URL: http://liberzon.csl.illinois.edu/publications.html
• License: Publicly available by the author.
• Subject: optimal control

Anderson, Moore『Optimal Control: Linear Quadratic Methods』

• Category: Book 📖
• URL: https://users.cecs.anu.edu.au/~john/papers/BOOK/B03.PDF
• License: Publicly available by the author.
• Subject: optimal control

Evans『An Introduction to Mathematical Optimal Control Theory』

• Category: Book 📖
• URL: https://math.berkeley.edu/~evans/control.course.pdf
• License: Publicly available by the author.
• Subject: optimal control

Principles Of Optimal Control

• Category: Course 🧑‍🏫
• URL: https://ocw.mit.edu/courses/16-323-principles-of-optimal-control-spring-2008/
• License: MIT OpenCourseWare
• Subject: optimal control, MATLAB¹

Unclassified

Hatcher『Algebraic Topology』

• Category: Book 📖
• URL: https://pi.math.cornell.edu/~hatcher/AT/ATpage.html
• License: Publicly available by the author.
• Subject: Algebraic Topology

Trench『Elementary Differential Equations』

• Category: Book 📖
• URL: https://digitalcommons.trinity.edu/mono/8/
• License: Creative Commons Attribution-NonCommercial-ShareAlike 3.0
• Subject: Differential Equations

『A First Course in Complex Analysis』

• Category: Book 📖
• URL: https://matthbeck.github.io/complex.html
• License: unknown
• Subject: Complex Analysis

Leinster『General Topology』

• Category: Lecture Notes 📝
• URL: https://www.maths.ed.ac.uk/~tl/topology/topology_notes.pdf
• License: Publicly available by the author.
• Subject: General Topology

Guichard『An Introduction to Combinatorics and Graph Theory』

• Category: Book 📖
• URL: https://www.whitman.edu/mathematics/cgt_online/cgt.pdf
• License: CC BY-NC-SA 3.0 DEED
• Subject: Combiantorics, Graph Theory

Diez, Rundel, Barr『OpenIntro Statistics』

• Category: Book 📖
• URL: https://www.openintro.org/book/os/
• 日本語版: http://www.kunitomo-lab.sakura.ne.jp/2021-3-3Open(S).pdf
• License: CCl
• Subject: Statistics

3Blue1Brown

• Category: Lecture Video 🎥
• URL: https://www.youtube.com/c/3blue1brown
• 日本語版: https://www.youtube.com/@3Blue1BrownJapan
• License: Youtube Standard License
• Subject: Mathematics

予備校のノリで学ぶ「大学の数学・物理」

• Category: Lecture Video 🎥
• URL: https://www.youtube.com/@yobinori
• Lang: 日本語
• License: Youtube Standard License
• Subject: Mathematics

Kaya『Math 320 Set Theory』

• Category: Lecture Notes 📝
• URL: https://users.metu.edu.tr/burakk/lecturenotes/320lecturenotes.pdf
• License: Publicly available by the author.
• Subject: Set Theory

東京工業大学OCW

• Category: Course 🧑‍🏫
• URL: https://www.ocw.titech.ac.jp/
• Lang: 日本語, English
• Subject: General

EE 376A: Information Theory

• Category: Lecture Notes 📝
• Note URL: https://web.stanford.edu/class/ee376a/files/scribes/lecture_notes.pdf
• Course URL: https://web.stanford.edu/class/ee376a/
• License: Publicly available by the author.
• Subject: Information Theory

Combinatorial Theory: Hyperplane Arrangements

• Category: Course 🧑‍🏫
• URL: https://ocw.mit.edu/courses/18-315-combinatorial-theory-hyperplane-arrangements-fall-2004/
• License: MIT OCW
• Subject: Discrete Mathematics

Algorithms for Decision Making

• Category: Book 📖
• URL: https://algorithmsbook.com/#
• License: Creative Commons CC-BY-NC-ND
• Subject: Mathematical Engineering, Julia

数値計算法基礎

• Category: Course 🧑‍🏫
• URL: http://www.cas.cmc.osaka-u.ac.jp/~paoon/Lectures/2023-8Semester-NA-basic/
• License: Publicly available by the author.
• Lang: 日本語
• Subject: Numerical Analysis, Julia

Open Logic Project

• Category: Book 📖
• URL: https://builds.openlogicproject.org/
• Source: https://github.com/OpenLogicProject/OpenLogic
• License: CC BY 4.0 DEED

実験数学

• Category: Course 🧑‍🏫
• URL: https://yutomiyatake.github.io/2024expmath1/
• License: Publicly available by the author.
• Lang: 日本語
• Subject: Numerical Analysis, Julia, C

Computer Programming

CS50’s Web Programming with Python and JavaScript

• Category: Course 🧑‍🏫
• URL: https://cs50.harvard.edu/web/2020/
• License: CC BY-NC-SA 4.0
• Subject: Web Development, Python, JavaScript

CS50’s Introduction to Cybersecurity

• Category: Course 🧑‍🏫
• URL: https://cs50.harvard.edu/cybersecurity/2023/
• License: CC BY-NC-SA 4.0
• Subject: Cybersecurity

CS50’s Introduction to Databases with SQL

• Category: Course 🧑‍🏫
• URL: https://cs50.harvard.edu/sql/2024/
• License: CC BY-NC-SA 4.0
• Subject: Database

Full Stack open

• Category: Course 🧑‍🏫
• URL: https://fullstackopen.com/en/
• License: Creative Commons BY-NC-SA 3.0
• Subject: Web Development, JavaScript

Haskell Mooc

• Category: Course 🧑‍🏫
• URL: https://haskell.mooc.fi/
• Source: https://github.com/moocfi/haskell-mooc
• License: CC BY-SA 4.0 DEED
• Subject: Haskell, Functional Programming

Introduction to Computational Thinking

• Category: Course 🧑‍🏫
• URL: https://computationalthinking.mit.edu/Fall23/
• Source: https://github.com/mitmath/computational-thinking
• License: code is under MIT, text is under CC BY-SA 4.0
• Subject: Julia, Computer Science, Mathematics

Introduction To Computational Thinking With Julia, With Applications To Modeling The COVID-19 Pandemic

• Category: Course 🧑‍🏫
• URL: https://ocw.mit.edu/courses/18-s190-introduction-to-computational-thinking-with-julia-with-applications-to-modeling-the-covid-19-pandemic-spring-2020/
• Source: https://github.com/mitmath/6S083
• License: code is under MIT, text is under CC BY-NC-SA
• Subject: Julia, data science, artificial intelligence, Mathematics

Haskell 99

• Category: Website 🌐
• URL: https://wiki.haskell.org/H-99:_Ninety-Nine_Haskell_Problems
• License: the simple permissive license
• Subject: Haskell, Functional Programming

mostly adequate guide

• Category: Website 🌐
• URL: https://mostly-adequate.gitbook.io/mostly-adequate-guide
• License: CC BY-SA 4.0 DEED
• Subject: Functional Programming, JavaScript

Coding Train

• Category: Video 🎥
• URL: https://www.youtube.com/@TheCodingTrain
• License: Youtube Standard License
• Subject: Programming, Visualization, JavaScript