rossant/awesome-math

# Awesome Math [](https://github.com/sindresorhus/awesome) 精选的优质数学资源列表。 所有资源均可免费获取，标有 💲 图标的除外。 # 目录 * [目录](#contents) * [通用资源](#general-resources) * [学习平台](#learning-platforms) * [学会学习](#learn-to-learn) * [Youtube 系列](#youtube-series) * [工具](#tools) * [问答](#questions-and-answers) * [百科全书](#encyclopedia) * [书籍](#books) * [杂志](#magazines) * [博客](#blogs) * [会议与大会](#meetings-and-conferences) * [杂项](#misc) * [数学分支](#branches-of-mathematics) * [数学基础](#foundations-of-mathematics) * [向纯粹严谨数学过渡](#transition-to-pure-rigour-math) * [集合论](#set-theory) * [逻辑学](#logic) * [范畴论](#category-theory) * [类型论](#type-theory) * [同伦类型论](#homotopy-type-theory) * [超实数](#surreal-numbers) * [数论](#number-theory) * [代数数论](#algebraic-number-theory) * [解析数论](#analytic-number-theory) * [代数](#algebra) * [抽象代数](#abstract-algebra) * [群论](#group-theory) * [线性代数](#linear-algebra) * [环论](#ring-theory) * [伽罗瓦理论](#galois-theory) * [李代数](#lie-algebras) * [组合数学](#combinatorics) * [图论](#graph-theory) * [几何与拓扑](#geometry-and-topology) * [微分几何](#differential-geometry) * [代数几何](#algebraic-geometry) * [代数统计](#algebraic-statistics) * [拓扑](#topology) * [代数拓扑](#algebraic-topology) * [分析学](#analysis) * [实分析](#real-analysis) * [调和分析](#harmonic-analysis) * [复分析](#complex-analysis) * [泛函分析](#functional-analysis) * [测度论](#measure-theory) * [常微分方程](#ordinary-differential-equations) * [偏微分方程](#partial-differential-equations) * [混沌理论](#chaos-theory) * [概率论与数理统计](#probability-and-statistics) * [概率论](#probability-theory) * [统计学](#statistics) * [统计学习](#statistical-learning) * [随机过程](#stochastic-processes) * [数值分析](#numerical-analysis) * [信号处理](#signal-processing) * [计算机科学数学](#mathematics-for-computer-science) * [数理生物学](#mathematical-biology) * [数学物理](#mathematical-physics) * [学生课堂笔记](#students-lecture-notes) * [相关 Awesome 列表](#related-awesome-lists) * [许可协议](#license) # 通用资源 ## 学习平台 * [Khan Academy](https://www.khanacademy.org/math) * [Coursera](https://www.coursera.org/courses?query=mathematics&languages=en) * [MIT OpenCourseWare](http://ocw.mit.edu/courses/mathematics/) * [edX](https://www.edx.org/course/subject/math) * [Brilliant](https://brilliant.org/courses/#math-foundational) * [WooTube](https://misterwootube.com/) * [Mathigon](https://mathigon.org/) * [Calculus.org](http://calculus.org/) * [Ximera](https://ximera.osu.edu/) ：免费交互式数学教科书（俄亥俄州立大学） * [Almost Fun](https://www.almostfun.org/lessons/) * [Oxford Mathematics](https://www.youtube.com/c/OxfordMathematics) * [Math Academy](https://mathacademy.com/) * [Derivative Calculus Solver](https://www.derivativecalculus.com) — 专注于链式法则和替换逻辑的分步求导工具。 ## 学会学习 * [理解数学](https://github.com/nelson-brochado/understanding-math) ## Youtube 系列 * [Brandon Foltz](https://www.youtube.com/@BrandonFoltz) * [StatQuest](https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw) * [3Blue1Brown](https://www.youtube.com/@3blue1brown) * [NPTEL](https://www.youtube.com/@iit) * [Numberphile](https://www.youtube.com/@numberphile) * [PatrickJMT](https://www.youtube.com/@patrickjmt) * [Professor Leonard](https://www.youtube.com/@ProfessorLeonard) * [微积分预备 - 大学代数/三角学](https://www.youtube.com/playlist?list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP) * [微积分 1](https://www.youtube.com/playlist?list=PLF797E961509B4EB5) * [微积分 2](https://www.youtube.com/playlist?list=PLDesaqWTN6EQ2J4vgsN1HyBeRADEh4Cw-) * [微积分 3](https://www.youtube.com/playlist?list=PLDesaqWTN6ESk16YRmzuJ8f6-rnuy0Ry7) * [微分方程](https://www.youtube.com/playlist?list=PLDesaqWTN6ESPaHy2QUKVaXNZuQNxkYQ_) * [To The Point Math](https://www.youtube.com/playlist?list=PLDesaqWTN6ETc1ZwHWijCBcZ2gOvS2tTN) * [Crash Course](https://www.youtube.com/@crashcourse) * [Harvard](https://www.youtube.com/@harvard) * [MIT OpenCourseWare](https://www.youtube.com/@mitocw) * [Mathologer](https://www.youtube.com/@Mathologer) * [The Math District](https://www.youtube.com/@TheMathDistrict) * [Mathematical Monk](https://www.youtube.com/@mathematicalmonk) * [The Math Sorcerer](https://www.youtube.com/@TheMathSorcerer) ## 工具 * [Symbolab](https://www.symbolab.com/) * [Desmos](https://www.desmos.com/calculator) * [Math Words](http://www.mathwords.com/) * [Wolfram Alpha](http://www.wolframalpha.com/) * [Maxima](https://maxima.sourceforge.io/) * [Sympy](https://www.sympy.org/) * [Sagemath](http://www.sagemath.org/) * [MathFlow](https://github.com/Nonanti/MathFlow) - 具备符号计算（求导、化简、方程求解）功能的 C# 数学表达式库 * [单位转换器](https://unitconverters.net) * [GeoGebra](https://www.geogebra.org/?lang=en) * [Macaulay2](http://www2.macaulay2.com/Macaulay2/) * [Singular](https://www.singular.uni-kl.de/) * [GNU Octave](https://www.gnu.org/software/octave/) * [Magma](http://magma.maths.usyd.edu.au/magma/) * [Maple](https://www.maplesoft.com/products/Maple/) * [Matlab](https://www.mathworks.com/products/matlab.html) * [Wolfram Mathematica](https://www.wolfram.com/mathematica/) * [Free Math](https://freemathapp.org) * [xhub](https://chrome.google.com/webstore/detail/xhub/anidddebgkllnnnnjfkmjcaallemhjee) * [CopyPasteMathjax](https://www.copypastemathjax.com/) * [财务计算器](https://www.financecharts.com/pages/5724-retirement-calculators-and-stock-market-tips) * [Mathcheap](https://mathcheap.xyz) * [中点计算器](https://midpointcalculator.co) * [四分位数计算器](https://quartilecalculator.net) * [Corca Editor](https://corca.io/) * [RunMat](https://github.com/runmat-org/runmat) - 支持自动 CPU/GPU 执行的 MATLAB 语法数组数学运行时。 * [结构工程工具 (SEPCO Engineering)](https://github.com/sepcostructural/structural-engineering-tools) - 提供梁受力图、加拿大钢截面属性和压力换算的免费在线计算器。 ## 问答 * [Mathematics Stack Exchange](http://math.stackexchange.com/) * [MathOverflow](http://mathoverflow.net/) - 面向专业数学家 ## 百科全书 * [数学百科全书](https://www.encyclopediaofmath.org) * [Planetmath](http://planetmath.org/) * [ProofWiki](https://proofwiki.org/wiki/Main_Page) * [Wolfram Mathworld](http://mathworld.wolfram.com/) * [在线整数序列百科全书](https://oeis.org) - 包含许多不同整数序列的精彩汇编。由 N. J. A. Sloane 于 1964 年创立。 * 💲 [The Princeton Companion to Mathematics](https://press.princeton.edu/books/hardcover/9780691118802/the-princeton-companion-to-mathematics) - Timothy Gowers（教授，菲尔兹奖得主），June Barrow-Green（教授）和 Imre Leader（教授）。 * 💲 [Encyclopedia of Distances (4th Edition)](https://link.springer.com/book/10.1007/978-3-662-52844-0) - Michel Marie Deza, Elena Deza。 ## 书籍 * [Calculus: Basic Concepts for High Schools](https://archive.org/details/TarasovCalculus) - L.V. Tarasov * [Basics of Algebra, Topology, and Differential Calculus](http://www.cis.upenn.edu/~jean/math-basics.pdf) - Jean Gallier（宾夕法尼亚大学） * [Multivariable Calculus](http://people.math.gatech.edu/%7Ecain/notes/calculus.html) - G. Cain, J. Herod（佐治亚理工学院） * [Wikibooks](https://en.wikibooks.org/wiki/Wikibooks:Mathematics_bookshelf) * [在线数学教科书](https://people.math.gatech.edu/~cain/textbooks/onlinebooks.html) * [Beginning and Intermediate Algebra](http://www.wallace.ccfaculty.org/book/Beginning_and_Intermediate_Algebra.pdf) * [免费数学书籍](https://github.com/EbookFoundation/free-programming-books/blob/master/books/free-programming-books-subjects.md#mathematics) * [Trigonometry](http://www.mecmath.net/trig/trigbook.pdf) * [前端 Web 开发数学](https://www.manning.com/books/math-for-frontend-web-dev) * [Grokking Statistics](https://www.manning.com/books/grokking-statistics) * [人工智能背后的数学](https://www.freecodecamp.org/news/the-math-behind-artificial-intelligence-book) - Tiago Capelo Monteiro (freeCodeCamp) ## 杂志 * [Quanta Magazine](https://www.quantamagazine.org/mathematics/) - 以非专家人士易于理解的方式介绍最新的研究突破。 * [Bulletin of the American Mathematical Society](https://www.ams.org/journals/bull/all_issues.html) - 关于当代数学研究的阐述性文章，其写作方式能让非该特定主题专家的数学家也能获得启发。 * [Notices of the American Mathematical Society](http://www.ams.org/cgi-bin/notices/amsnotices.pl?article_id=fullissue&article_type=gallery&gallery_type=fullissue) - 宣传美国数学学会的活动，并以调查、报告、新闻、公告以及对行业趋势、学术界和研究的观点为特色。 * [European Mathematical Society Magazine](https://euromathsoc.org/magazine) - 该杂志发布有关会议和研讨会的公告、概述科学发展当前趋势的文章、成员学会报告以及许多其他信息类条目。 * [Mathematics Today by Institute of Mathematics and its Applications](https://ima.org.uk/publications/mathematics-today/) - 与数学相关的新闻、观点和文章，让读者随时掌握最新动态。 * [Crux Mathematicorum by Canadian Mathematical Society](https://cms.math.ca/publications/crux/) - 提供专为中学和本科水平设计的独特且具有挑战性的数学问题来源。它包含对数学竞赛有帮助的奥林匹克角。 ## 博客 * [BetterExplained](https://betterexplained.com/) - 由 Kalid Azad 维护 * [ILoveMaths](http://ilovemaths.com/) - 面向 K-12 体系 6 至 12 年级的学生 * [3blue1brown](https://www.3blue1brown.com/) - 动画数学 * [Mathsisfun](https://www.mathsisfun.com) 面向高中生及以下学生的简单、轻量级文本网站 * [MathematicsIsAScience](https://calculus123.com/wiki/Peter_Saveliev) - Peter Saveliev（美国西弗吉尼亚州亨廷顿马歇尔大学数学教授） ## 会议与大会 * [MathsJam](https://mathsjam.com/) - 每月举行的本地趣味数学/解谜聚会，以及在英国斯塔福德郡举行的年度聚会 * [Talking Maths in Public](https://talkingmathsinpublic.uk/) - 为数学传播者举办的会议，每两年举办一次，通常在英国举行 * [Bridges](https://www.bridgesmathart.org/) - 关于艺术、音乐、建筑和文化中数学联系的年度会议。2025 年的会议将在荷兰埃因霍温举行。 ## 杂项 * [维基百科上的数学领域](https://en.wikipedia.org/wiki/Areas_of_mathematics) * [Paul's Online Math Notes](http://tutorial.math.lamar.edu/) - Paul Dawkins（拉马尔大学） * [电子教科书列表](http://faculty.atu.edu/mfinan/nnotes.html) - Marcel B. Finan（阿肯色理工大学） * [Topology Atlas](http://at.yorku.ca/topology/) * [Recreations in Math](http://djm.cc/library/Recreations_in_Mathematics_Licks_edited.pdf) - H. E. Licks (1917) * [Magic Squares and Cubes](http://djm.cc/library/Magic_Squares_Cubes_Andrews_edited.pdf) - W. S. Andrews (1917) * [Convex Optimization](https://web.stanford.edu/~boyd/cvxbook/) - Stephen Boyd 和 Lieven Vandenberghe * [Fabrice Baudoin 的笔记](https://fabricebaudoin.wordpress.com/) - 包含许多主题的研究和课程笔记，包括叶状流形上的扩散、随机微积分、Dirichlet 空间中的全局分析等。 # 数学分支 **内容格式** \ 📖 书籍 \ 🎥 视频 \ 📝 讲义、幻灯片、文章、论文 ## 数学基础 ### 向纯粹严谨数学过渡 * 📝 [Basic Concepts of Mathematics](http://www.trillia.com/zakon1.html) - Elias Zakon * 📝 [Book of Proof](https://richardhammack.github.io/BookOfProof/) - Richard Hammak（弗吉尼亚联邦大学） * 📖 [How to Prove It: A Structured Approach (3rd Edition)](https://ia800501.us.archive.org/7/items/how-to-prove-it-a-structured-approach-daniel-j.-velleman/How%20to%20Prove%20It%20A%20Structured%20Approach%20%28Daniel%20J.%20Velleman%29.pdf) - Daniel J. Velleman（教授）。 ### 集合论 * 📝 [Sets, Relations, Functions](http://www.cosc.brocku.ca/~duentsch/papers/methprimer1.html) - Ivo Düntsch, Günther Gediga * 📝 [An Introduction to Set Theory](http://www.math.toronto.edu/weiss/set_theory.pdf) - William. R. Weiss * 📝 [Set Theory and Foundations of Mathematics](http://www.settheory.net/) - Sylvain Poirier * 📝 [斯坦福哲学百科全书上的集合论](http://plato.stanford.edu/entries/set-theory/) ### 逻辑学 * 📝 [Introduction to Logic](https://pdfs.semanticscholar.org/6967/f52773d9c2ccfc94658657a5761e0f00e95a.pdf) - Michael Genesereth, Eric Kao（斯坦福大学） * 📝 [An Introduction to Formal Logic](https://www.fecundity.com/codex/forallx.pdf) - P.D. Magnus（奥尔巴尼大学） * 📝 [A Problem Course in Mathematical Logic](http://euclid.trentu.ca/math/sb/pcml/pcml-16.pdf) - Stefan Bilaniuk（特伦特大学） * 📝 [Computability - An introduction to recursive function theory](http://poincare.matf.bg.ac.rs/~zarkom/Book_Math__Cutland_Computability.pdf) - Nigel Cutland（赫尔大学） * 📝 [Language, Proof, and Logic](http://homepages.uc.edu/~martinj/Symbolic_Logic/341%20Syllabus,%20Textbook,%20Handouts,%20Notes/LPL%20textbook.pdf) - Jon Barwise, John Etchemendy * 📝 [Mathematical Logic](http://www.mathematik.uni-muenchen.de/~schwicht/lectures/logic/ws03/ml.pdf) - Helmut Schwichtenberg * 📝 [Mathematical Logic](http://www.personal.psu.edu/t20/notes/logic.pdf) - Stephen G. Simpson（宾夕法尼亚州立大学） * 📝 [Formal Logic](http://maude.sip.ucm.es/~miguelpt/papers/flogic.pdf) - Miguel Palomino * 📝 [Predictive Arithmetic](https://web.math.princeton.edu/~nelson/books/pa.pdf) - Edward Nelson * 📝 [Proofs and Concepts: the fundamentals of abstract mathematics](http://people.uleth.ca/~dave.morris/books/proofs+concepts.html) - Joy Morris, Dave Morris * 📝 [Mathematical Reasoning: Writing and Proof](https://www.tedsundstrom.com/mathreasoning) - Ted Sundstrom * 📝 [Logic and Proof](http://leanprover.github.io/logic_and_proof/) - Jeremy Avigad, Robert Y. Lewis 和 Floris van Doorn * 📝 [QED - 交互式教科书](https://teorth.github.io/QED) - Terence Tao * 📝 [Open Logic Textbook](http://builds.openlogicproject.org/) - 协作编写，主要贡献者名单在[这里](https://openlogicproject.org/people/) ### 范畴论 * 📝 [Introduction to Category Theory and Categorical Logic](http://www.mathematik.tu-darmstadt.de/~streicher/CTCL.pdf) - Thomas Streicher * 📝 [An Introduction to Category Theory](http://www.cs.man.ac.uk/~hsimmons/zCATS.pdf) - Harold Simmons * 📝 [Category Theory](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.211.4754&rep=rep1&type=pdf) - Steve Awodey（卡内基梅隆大学） * 📝 [Category Theory](http://www.mathematik.uni-muenchen.de/~pareigis/Vorlesungen/04SS/Cats1.pdf) - B. Pareigis * 📝 [Category Theory for Computing Science](https://web.archive.org/web/20181221233252/http://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf) - Michael Barr, Charles Wells * 📝 [Toposes, Triples and Theories](http://www.tac.mta.ca/tac/reprints/articles/12/tr12.pdf) - Michael Barr, Charles Wells * 📝 [Abelian Categories](http://www.tac.mta.ca/tac/reprints/articles/3/tr3abs.html) - Peter Freyd * 📝 [Categories and Groupoids](http://www.tac.mta.ca/tac/reprints/articles/7/tr7abs.html) - P. J. Higgins * 📝 [Basic Concepts of Enriched Category Theory](http://www.tac.mta.ca/tac/reprints/articles/10/tr10abs.html) - G. M. Kelley * 📝 [Abstract and Concrete Categories: The Joy of Cats](http://www.tac.mta.ca/tac/reprints/articles/17/tr17abs.html) - Jiri Adamek, Horst Herrlich, George Strecker * 📝 [Seven Sketches in Compositionality: An Invitation to Applied Category Theory](http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf) - Brendan Fong 和 David I. Spivak（MIT） * 📝 [Category Theory in Context](http://www.math.jhu.edu/~eriehl/context/) - Emily Riehl（约翰霍普金斯大学） ### 类型论 * 📝 [Proofs and Types](http://www.paultaylor.eu/stable/prot.pdf) - Jean-Yves Girard * 📝 [Intuitionistic Type Theory](https://archive-pml.github.io/martin-lof/pdfs/Bibliopolis-Book-retypeset-1984.pdf) - Per Martin-Lof * 📝 [Type Theory and Functional Programming](https://www.cs.kent.ac.uk/people/staff/sjt/TTFP/) - Simon Thompson * 📝 [Programming in Martin-Lof’s Type Theory](http://www.cse.chalmers.se/research/group/logic/book/book.pdf) - Bengt Nordstrom, Kent Petersson, Jan M. Smith ### 同伦类型论 * 📝 [Homotopy Type Theory](https://hottheory.files.wordpress.com/2013/03/hott-online-611-ga1a258c.pdf) ### 超实数 * 📝 [Surreal Numbers - How two ex-students turned on to pure mathematics and found total happiness](http://www.math.harvard.edu/~knill/teaching/mathe320_2015_fall/blog15/surreal1.pdf) - D. E. Knuth * 📝 [Surreal Numbers and Games](http://web.mit.edu/sp.268/www/2010/surreal.pdf) * 📝 [Conway names, the simplicity hierarchy and the surreal number tree](http://www.ohio.edu/people/ehrlich/ConwayNames.pdf) - Philip Ehrlich ## 数论 * 📝 [Elementary Number Theory: Primes, Congruences, and Secrets](http://wstein.org/ent/ent.pdf) - William Stein * 📝 [Elementary Number Theory](http://math.utoledo.edu/~codenth/Spring_13/3200/ENT-books/Elementary_Number_Theory-Clark.pdf) - W. Edwin Clark（南佛罗里达大学） * 📝 [A Course on Number Theory](http://www.maths.qmul.ac.uk/~pjc/notes/nt.pdf) - Peter J. Cameron * 📝 [A Computational Introduction to Number Theory and Algebra](http://shoup.net/ntb/ntb-v2.pdf) - Victor Shoup * 📝 [Number Theory: A Contemporary Introduction](http://alpha.math.uga.edu/~pete/4400FULL.pdf) - Pete L. Clark * 📝 [An Introduction to the Theory of Numbers](http://www.trillia.com/moser-number.html) - Leo Moser * 📝 [Yet Another Introductory Number Theory Textbook](https://www.poritz.net/jonathan/share/yaintt/) - Jonathan A. Poritz ### 代数数论 * 📝 [Introduction to Algebraic Number Theory](https://feog.github.io/ANT10.pdf) - F. Oggier * 📝 [Algebraic Number Theory](http://www.jmilne.org/math/CourseNotes/ANT.pdf) - J.S. Milne * 📝 [Algebraic Number Theory Course Notes](http://people.math.gatech.edu/~mbaker/pdf/ANTBook.pdf) - Matthew Baker（佐治亚理工学院） * 📝 [A Course In Algebraic Number Theory](http://www.math.uiuc.edu/~r-ash/ANT.html) - Robert Ash ### 解析数论 * 📝 [Introduction to Analytic Number Theory](http://www.math.uiuc.edu/~hildebr/ant/main.pdf) - A.J. Hildebrand（伊利诺伊大学） * 📝 [Elements of Analytic Number Theory](http://math.nsc.ru/~vdovin/lectures/numth_eng.pdf) - P. S. Kolesnikov, E. P. Vdovin (Novosibirsk) * 📝 [Analytic Number Theory](http://www.mathematik.uni-muenchen.de/~forster/v/ann/annth_all.pdf) - Otto Forster（慕尼黑大学） * 📝 [Analytic Number Theory - Lecture Notes based on Davenport’s book](http://www2.math.uu.se/~astrombe/analtalt08/www_notes.pdf) - Andreas Strömbergsson ## 代数 * 📝 [A Course in Universal Algebra](http://www.math.uwaterloo.ca/~snburris/htdocs/ualg.html) - S. Burris, H.P. Sankappanavar * 📝 [A Course in Commutative Algebra](https://faculty.math.illinois.edu/~r-ash/ComAlg.html) - Robert Ash * 📝 [First Course in Algebra](http://djm.cc/library/First_Algebra_Hawkes_Luby_Touton_edited.pdf) - Herbert E. Hawkes, William A. Luby, Frank C. Touton (1910) * 📝 [Second Course in Algebra](http://djm.cc/library/Second_Algebra_Hawkes_Luby_Touton_edited.pdf) - Herbert E. Hawkes, William A. Luby, Frank C. Touton (1911) * 📝 [Algebra: An Elementary Text-Book, Part I](http://djm.cc/library/Algebra_Elementary_Text-Book_Part_I_Chrystal_edited.pdf) - G. Chrystal (1904) * 📝 [Algebra: An Elementary Text-Book, Part II](http://djm.cc/library/Algebra_Elementary_Text-Book_Part_II_Chrystal_edited02.pdf) - G. Chrystal (1900) * 📝 [Understanding Algebra](https://jamesbrennan.org/algebra) - James W. Brennan ### 抽象代数 * 📝 [Introduction to Abstract Algebra](https://zodml.org/sites/default/files/Introduction_to_Abstract_Algebra_0.pdf) - D. S. Malik, John N. Mordeson, M.K. Sen（克瑞顿大学） * 📝 [Introduction to Modern Algebra](http://aleph0.clarku.edu/~djoyce/ma225/algebra.pdf) - David Joyce（克拉克大学） * 📝 [Algebraic Methods](https://feog.github.io/AA11.pdf) - F. Oggier * 📝 [Abstract Algebra : Theory and Applications](http://abstract.ups.edu/download/aata-20150812.pdf) - Thomas W. Judson, Robert A. Beezer（奥斯汀州立大学） * 📝 [An Undergraduate Course in Abstract Algebra](http://www.maths.usyd.edu.au/u/bobh/UoS/rfwhole.pdf) - Robert Howlett * 📝 [Elements of Abstract and Linear Algebra](http://www.math.miami.edu/~ec/book) - E.H. Connell（迈阿密大学） * 📝 [Abstract Algebra: The Basic Graduate Year](http://www.math.uiuc.edu/~r-ash/Algebra.html) - Robert Ash * 📝 [Abstract Algebra: Harvard Extension（已归档）](https://web.archive.org/web/20150528171650/extension.harvard.edu/open-learning-initiative/abstract-algebra) - Benedict Gross * 📝 [Abstract Algebra: Harvard Extension 视频](https://www.youtube.com/playlist?list=PLA58AC5CABC1321A3) - Benedict Gross ### 群论 * 📝 [Notes on Group Theory](https://www2.bc.edu/mark-reeder/Groups.pdf) - Mark Reeder * 📝 [Group Theory](http://www.jmilne.org/math/CourseNotes/GT.pdf) - J.S. Milne * 📝 [Notes on Finite Group Theory](http://www.maths.qmul.ac.uk/~pjc/notes/gt.pdf) - Peter J. Cameron * 📝 [Group Theory](http://www.cns.gatech.edu/GroupTheory/index.html) - Pedrag Civitanovic ### 线性代数 * 📝 [Fundamentals of Linear Algebra](http://www.math.ubc.ca/~carrell/NB.pdf) - James B. Carrell * 📝 [Linear Algebra and Matrices](https://web.archive.org/web/20140824074655/http://mathstat.helsinki.fi/~fluch/linear_algebra_1-sp07/la1.pdf) - Martin Fluch * 📝 [Vector Space Theory](http://www.maths.usyd.edu.au/u/bobh/UoS/MATH2902/vswhole.pdf) - Robert Howlett * 📝 [Linear Algebra](http://joshua.smcvt.edu/linearalgebra) - Jim Hefferon * 📝 [MIT OpenCourseWare 线性代数课程 (18.06) Jupyter 笔记本版](https://github.com/juanklopper/MIT_OCW_Linear_Algebra_18_06) - Juan Klopper * 📝 [Elementary Linear Algebra](http://www.numbertheory.org/book/) - Keith Matthews * 📝 [A First Courses in Linear Algebra](http://linear.ups.edu/) - Rob Breezer * 📝 [Linear Algebra](https://www.math.ucdavis.edu/~linear/) - David Cherney, Tom Denton, Andrew Waldron * 📝 [Introduction to vectors and tensors, Vol 1: linear and multilinear algebra](http://oaktrust.library.tamu.edu/handle/1969.1/2502) - Ray M Bowen, C. C. Wang * 📝 [Introduction to vectors and tensors, Vol 2: vector and tensor analysis](http://oaktrust.library.tamu.edu/handle/1969.1/3609) - Ray M Bowen, C. C. Wang * 📝 [Introduction to Applied Linear Algebra](https://web.stanford.edu/~boyd/vmls/vmls.pdf) - Stephen Boyd（斯坦福大学），Lieven Vandenberghe（加州大学洛杉矶分校） * 📝 [Linear Algebra Done Wrong](https://www.math.brown.edu/~treil/papers/LADW/LADW_2017-09-04.pdf) - Sergei Treil * 📝 [Immersive Linear Algebra](http://immersivemath.com/ila/index.html) - J. Ström, K. Åström 和 T. Akenine-Möller * 📝 [Interactive Linear Algebra](https://textbooks.math.gatech.edu/ila/) - Dan Margalit 和 Joseph Rabinoff * 📝 [Linear Algebra, Infinite Dimensions, and Maple](https://people.math.gatech.edu/~herod/Hspace/Hspace.html) - James Herod * 📖 [Linear Algebra Done Right](https://linear.axler.net/) - Sheldon Axler ### 环论 * 📝 [Foundations of Module and Ring Theory](http://www.math.uni-duesseldorf.de/~wisbauer/book.pdf) - Robert Wisbauer（杜塞尔多夫大学） ### 伽罗瓦理论 * 📝 [An Introduction to Galois Theory](http://www.maths.gla.ac.uk/~ajb/dvi-ps/Galois.pdf) - Andrew Baker（格拉斯哥大学） * 📝 [Fields and Galois Theory](http://www.jmilne.org/math/CourseNotes/FT.pdf) - J.S. Milne * 📝 [Galois theory](http://homepages.warwick.ac.uk/~masda/MA3D5/Galois.pdf) - Miles Reid * 📝 [Galois Theory](https://eclass.uoa.gr/modules/document/file.php/MATH594/Stewart%20Galois%204th%20edition.pdf) - Ian Stewart * 📝 [Galois Theory](https://arxiv.org/pdf/2408.07499) — Tom Leinster（爱丁堡大学） ### 李代数 * 📝 [Lie Algebras](http://www.math.harvard.edu/~shlomo/docs/lie_algebras.pdf) - Shlomo Sternberg ## 组合数学 * 📝 [Basic Combinatorics](http://web.math.utk.edu/~wagner/papers/comb.pdf) - Carl G. Wagner（田纳西大学） * 📝 [Applied Combinatorics](http://people.math.gatech.edu/~trotter/book.pdf) - Mitchel T. Keller, William T. Trotter * 📝 [Notes on Combinatorics](http://www.maths.qmul.ac.uk/~pjc/notes/comb.pdf) - Peter J. Cameron * 📝 [Analytic Combinatorics](http://algo.inria.fr/flajolet/Publications/book.pdf) - Philippe Flajolet, Robert Sedgewick * 📝 [generatingfunctionology](http://www.math.upenn.edu/~wilf/DownldGF.html) - Herbert Wilf ### 图论 * 📝 [Graph Theory: Lecture Notes](http://www.personal.psu.edu/cxg286/Math485.pdf) - Christopher Griffin * 📝 [Graph Theory](http://www.cs.unibo.it/babaoglu/courses/cas00-01/tutorials/GraphTheory.pdf) - Reinhard Diestel * 📝 [Graph Theory : Interactive Algorithm Visualizer | Graph Theory Learning Platform](https://learngraphtheory.org/) - Hadjoudj Mohammed Islam ## 几何与拓扑 * 📝 [Fundamentals of Geometry](http://polly.phys.msu.ru/~belyaev/geometry.pdf) - Oleg A. Belyaev * 📝 [A=B](https://www.math.upenn.edu/~wilf/AeqB.html) - M. Petkovsek, H. Wilf, D. Zeilberger * 📝 [Elements](http://aleph0.clarku.edu/~djoyce/java/elements/toc.html) - Euclid * 📝 [Euclid's Elements Redux](http://starrhorse.com/euclid/) - Daniel Callahan * 📝 [Mathematical Illustrations](#encyclopedia) - Bill Casselman * 📝 [Byrne's Euclid](https://www.c82.net/euclid/) - Oliver Byrne * 📝 [Plane Geometry](http://djm.cc/library/Plane_Geometry_Wentworth_Smith_edited.pdf) - George Wentworth 和 David Eugene Smith (1913) * 📝 [Planes and Spherical Trigonometry](http://djm.cc/library/Plane_Spherical_Trigonometry_Wentworth_Smith_edited_2.pdf) - George Wentworth 和 David Eugene Smith (1915) * 📝 [Coordinate Geometry](http://djm.cc/library/Coordinate_Geometry_Fine_Thompson_edited03.pdf) - Henry Buchard Fine 和 Henry Dallas Thompson (1911) * 📝 [Analytic Geometry](http://djm.cc/library/Analytic_Geometry_Siceloff_Wentworth_Smith_edited.pdf) - Lewis Parker Siceloff, George Wentworth, David Eugene Smith (1922) ### 微分几何 * 📝 [Introduction to Differential Geometry](https://people.math.ethz.ch/~salamon/PREPRINTS/diffgeo.pdf) - Joel W. Robbin, Dietmar A. Salamon * 📝 [Notes on Differential Geometry and Lie Groups](https://www.cis.upenn.edu/~jean/gbooks/manif.html) - Jean Gallier（宾夕法尼亚大学） * 📝 [Topics in Differential Geometry](http://www.mat.univie.ac.at/~michor/dgbook.pdf) - Peter W. Michor * 📝 [Lectures on Differential Geometry](http://mysite.science.uottawa.ca/rossmann/Differential%20Geometry%20book_files/Diffgeo.pdf) - Wulf Rossmann * 📝 [An Introduction to Riemannian Geometry](http://www.matematik.lu.se/matematiklu/personal/sigma/Riemann.pdf) - Sigmundur Gudmundsson（隆德大学） * 📝 [The Geometry and Topology of Three-Manifolds](http://msri.org/publications/books/gt3m/) - W. Thurston * 📝 [Semi-Riemann Geometry and General Relativity](http://www.math.harvard.edu/~shlomo/docs/semi_riemannian_geometry.pdf) - Shlomo Sternberg * 📝 [Discrete Differential Geometry](http://www.cs.cmu.edu/~kmcrane/Projects/DDG/paper.pdf) - Keenan Crane ### 代数几何 * 📝 [A Brief Introduction to Algebraic Geometry](https://ksda.ccny.cuny.edu/PostedPapers/rickksda1107.pdf) - R.C. Churchill * 📝 [Introduction to Algebraic Geometry](http://www.math.lsa.umich.edu/~idolga/631.pdf) - Igor V. Dolgachev * 📝 [Foundations of Algebraic Geometry](http://math.stanford.edu/~vakil/216blog/FOAGjun1113public.pdf) - Ravi Vakil * 📝 [Algebraic Geometry](http://www.cis.upenn.edu/~jean/algeoms.pdf) - Jean Gallier, Stephen S. Shatz（宾夕法尼亚大学） * 📝 [Algebraic Geometry](http://www.jmilne.org/math/CourseNotes/AG.pdf) - J.S. Milne * 📝 [Algebraic Geometry](http://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2002/main.pdf) - Andreas Gathmann（凯泽斯劳滕大学） * 📝 [The Stacks Project](https://stacks.math.columbia.edu/) - 由 Aise Johan de Jong（哥伦比亚大学）维护 ### 代数统计 * 📝 [Lectures on Algebraic Statistics](https://math.berkeley.edu/~bernd/owl.pdf) - Mathias Drton, Bernd Sturmfels, Seth Sullivant * 📝 [An Introduction to Algebraic Statistics](https://www3.diism.unisi.it/~chiantini/did/00Book.pdf) - Cristiano Bocci, Luca Chiantini 和 Anthony V. Geramita * 📝 [Algebraic Statistics](https://tore.tuhh.de/dspace-cris-server/api/core/bitstreams/a0c378d5-ce8e-442a-8891-9e7f763b4279/content) - Karl-Heinz Zimmermann * 📝 [Algebraic Statistics for Computational Biology](http://yaroslavvb.com/papers/pachter-algebraic.pdf) - Pachter 和 Sturmfels。 ### 拓扑 * 📝 [General Topology](https://www.rexresearch1.com/TopologyLibrary/GeneralTopologyWillard.pdf) - Stephen Willard * 📝 [Elementary Applied Topology](https://www.math.upenn.edu/~ghrist/notes.html) - Robert Ghrist（宾夕法尼亚大学） * 📝 [Introduction to Topology](http://www.math.colostate.edu/~renzo/teaching/Topology10/Notes.pdf) * 📝 [Introduction to Topology](http://www.math.bme.hu/~kalex/Teaching/Spring10/Topology/TopNotes_Spring10.pdf) - Alex Küronya * 📝 [Introductory Topology](http://www.math.clemson.edu/~jimlb/Teaching/2009-10/Math986/Topology.pdf) - Jim L. Brown * 📝 [General Topology](http://webusers.imj-prg.fr/~pierre.schapira/lectnotes/Topo.pdf) - Pierre Schapira（巴黎第六大学） * 📝 [Elementary Topology Problem Textbook](http://www.pdmi.ras.ru/~olegviro/topoman/eng-book-nopfs.pdf) * 📝 [General Topology](http://www.math.ku.dk/~moller/e03/3gt/notes/gtnotes.pdf) - Jesper M. Møller * 📝 [Topology Topics](http://mathonline.wikidot.com/topology) ### 代数拓扑 * 📝 [Algebraic Topology](http://pi.math.cornell.edu/~hatcher/AT/AT.pdf) - Allen Hatcher * 📝 [A Concise Course in Algebraic Topology](http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf) - J. P. May * 📝 [Introduction to Algebraic Topology](http://www.math.muni.cz/~cadek/at/at.pdf) - Martin Cadek * 📝 [Algebra and Topology](http://webusers.imj-prg.fr/~pierre.schapira/lectnotes/AlTo.pdf) - Pierre Schapira（巴黎第六大学） * 📝 [Lecture Notes in Algebraic Topology](http://www.indiana.edu/~jfdavis/teaching/m623/book.pdf) - James F. Davis, Paul Kirk（印第安纳大学） * 📝 [Algebraic Topology](https://www.ma.utexas.edu/ibl1/courses/resources/12_15_07_grad_alg_top_mooremethod.pdf) - Michael Starbird * 📝 [Lecture Notes on Algebraic Topology](http://www.math.nus.edu.sg/~matwujie/ma5209.pdf) - Jie Wu ## 分析学 ### 实分析 * 📝 [MIT OpenCourseWare 微积分课程](https://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/) - G. Strang * 📝 [Elementary Calculus: An Approach Using Infinitesimals](http://www.math.wisc.edu/~keisler/calc.html) - H. Jerome Keisler 教授 * 📝 [An Introduction to Real Analysis](https://www.math.ucdavis.edu/~hunter/intro_analysis_pdf/intro_analysis.pdf) - John K. Hunter（加州大学戴维斯分校） * 📝 [Introduction to Real Analysis](http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF) - William F. Trench（三一大学，德克萨斯州） * 📝 [Basic Analysis: Introduction to Real Analysis](http://www.jirka.org/ra/realanal.pdf) - Jiří Lebl * 📝 [Elementary Real Analysis](http://prac.im.pwr.wroc.pl/~kwasnicki/pl/stuff/tbb-hyper.pdf) - Thomson, Bruckner * 📝 [Lecture Notes in Real Analysis](http://ms.mcmaster.ca/~sawyer/Publications/Real_Analysis.pdf) - Eric T. Sawyer（麦克马斯特大学） * 📝 [Real Analysis](http://math.harvard.edu/~ctm/papers/home/text/class/harvard/212a/course/course.pdf) - C. McMullen * 📝 [Real Analysis for Graduate Students](http://bass.math.uconn.edu/3rd.pdf) - Richard F. Bass * 📝 [Modern Real Analysis](http://www.math.purdue.edu/~torres/pubs/Modern-real-analysis.pdf) - William P. Ziemer（印第安纳大学） * 📝 [Mathematical Analysis Vol I](http://www.trillia.com/zakon-analysisI.html) - Elias Zakon * 📝 [Mathematical Analysis Vol II](http://www.trillia.com/zakon-analysisII.html) - Elias Zakon * 📝 [Advanced Calculus](http://www.math.harvard.edu/~shlomo/docs/Advanced_Calculus.pdf) - Lynn Loomis, Schlomo Sternberg * 📝 [ Analysis of Functions of a Single Variable](http://spot.colorado.edu/~baggett/analysis.html) - Lawerence Baggett * 📝 [The Calculus of Functions of Several Variables](http://www.synechism.org/wp/the-calculus-of-functions-of-several-variables/) - Dan Sloughter * 📝 [A ProblemText in Advanced Calculus](http://web.pdx.edu/~erdman/PTAC/problemtext_pdf.pdf) - John M. Erdman * 📝 [Calculus and Linear Algebra. Vol. 1](http://hdl.handle.net/2027/spo.5597602.0001.001) - Wilfred Kaplan, Donald J. Lewis * 📝 [Calculus and Linear Algebra. Vol. 2](https://quod.lib.umich.edu/s/spobooks/5597602.0002.001) - Wilfred Kaplan, Donald J. Lewis * 📝 [Introduction to Calculus I and II](http://www.math.odu.edu/~jhh/counter10.html) - J.H. Heinbockel * 📝 [Active Calculus](http://faculty.gvsu.edu/boelkinm/Home/Active_Calculus.html) - Matt Boelkins * 📝 [Supplements to the Exercises in Chapters 1-7 of Walter Rudin's "Principles of Mathematical Analysis"](https://math.berkeley.edu/~gbergman/ug.hndts/#Rudin) - George M. Bergman * 📝 [Calculus Made Easy](http://calculusmadeeasy.org/) - Silvanus P. Thompson (1910) * 📝 [Elements of Differential and Integral Calculus](http://djm.cc/library/Elements_Differential_Integral_Calculus_Granville_edited_2.pdf) - William Anthony Granville (1911) * 📝 [Precalculus](https://stitz-zeager.com/szprecalculus07042013.pdf) - Carl Stitz, Jeff Zeager ### 调和分析 * 📝 [Harmonic Analysis Lecture Notes](http://www.math.uiuc.edu/~laugesen/545/545Lectures.pdf) - Richard S. Laugesen（伊利诺伊大学厄巴纳-香槟分校） * 📝 [Harmonic Analysis](http://www.math.uchicago.edu/~schlag/harmonicnotes.pdf) - W. Schlag * 📝 [Lecture Notes: Fourier Transform and its Applications](https://see.stanford.edu/materials/lsoftaee261/book-fall-07.pdf) - Brad Osgood * 📝 [Fourier Analysis](http://www.reed.edu/physics/courses/Physics331.f08/pdf/Fourier.pdf) - Lucas Illing * 📝 [Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications](https://ccrma.stanford.edu/~jos/mdft) - Julius O. Smith III（斯坦福大学） ### 复分析 * 📝 [Introduction to Complex Analysis](https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/complex.pdf) - Michael Taylor * 📝 [An Introduction to Complex Analysis and Geometry](http://www.math.uiuc.edu/~jpda/jpd-complex-geometry-book-5-refs-bip.pdf) - John P. D'Angelo（伊利诺伊大学） * 📝 [A First Course in Complex Analysis](http://math.sfsu.edu/beck/papers/complex.pdf) - Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka * 📝 [A Guide to Complex Variables](http://www.math.wustl.edu/~sk/books/guide.pdf) - Steven G. Krantz * 📝 [Complex Analysis](http://www.maths.manchester.ac.uk/~cwalkden/complex-analysis/complex_analysis.pdf) - Charles Walkden * 📝 [Complex Analysis](http://www.math.ku.dk/noter/filer/koman-12.pdf) - Christian Berg * 📝 [Complex Variables](http://people.math.sc.edu/girardi/m7034/book/AshComplexVariablesWithHyperlinks.pdf) - R. B. Ash, W.P. Novinger * 📝 [Complex Analysis](http://www.maths.lth.se/matematiklu/personal/olofsson/CompHT06.pdf) - Christer Bennewitz * 📝 [Complex Analysis](https://web.archive.org/web/20150620124453/https://www.math.washington.edu/~marshall/math_536/Notes.pdf) - Donald E. Marshall * 📝 [A Concise Course in Complex Analysis and Riemann Surfaces](https://gauss.math.yale.edu/~ws442/complex.pdf) - Wilhelm Schlag * 📝 [Complex Analysis](http://people.math.gatech.edu/%7Ecain/winter99/complex.html) - G. Cain（佐治亚理工学院） * 📝 [Complex Analysis](https://complex-analysis.com/) - Juan Carlos Ponce Campuzano ### 泛函分析 * 📝 [An Introduction to Functional Analysis](https://www.math.uwaterloo.ca/~lwmarcou/notes/pmath453.pdf) - Laurent W. Marcoux（滑铁卢大学） * 📝 [Functional Analysis: Lecture Notes](http://users.math.msu.edu/users/jeffrey/920/920notes.pdf) - Jeff Schenker（密歇根州立大学） * 📝 [Functional Analysis Lecture Notes](https://archive.org/details/TB_Ward___Functional_analysis_lecture_notes) - T.B. Ward（东安格利亚大学） * 📝 [Functional Analysis](http://www.maths.lancs.ac.uk/~belton/www/notes/fa_notes.pdf) - Alexander C. R. Belton * 📝 [Topics in Real and Functional Analysis](https://www.mat.univie.ac.at/~gerald/ftp/book-fa/fa.pdf) - Gerald Teschl * 📝 [Functional Analysis](http://www2.math.ou.edu/~cremling/teaching/lecturenotes/fa-new/LN-I.pdf) - Christian Remling * 📝 [Theory of Functions of a Real Variable](http://www.math.harvard.edu/~shlomo/docs/Real_Variables.pdf) - Shlomo Sternberg * 📝 [Functional Analysis](http://spot.colorado.edu/~baggett/functional.html) - Lawerence Baggett ### 测度论 * 📝 [An Introduction to Measure Theory](https://terrytao.files.wordpress.com/2012/12/gsm-126-tao5-measure-book.pdf) - Terence Tao（加州大学洛杉矶分校） * 📝 [Lecture Notes on Measure Theory and Functional Analysis](http://www.mat.uniroma2.it/~cannarsa/cam_0607.pdf) - P. Cannarsa, T. D’Aprile * 📝 [Lecture Notes in Measure Theory](http://www.math.chalmers.se/~borell/MeasureTheory.pdf) - Christer Borell * 📝 [A Crash Course on the Lebesgue Integral and Measure Theory](http://www.gold-saucer.org/math/lebesgue/lebesgue.pdf) - Steve Cheng * 📝 [Measure Theory](https://www.math.ucdavis.edu/~hunter/measure_theory/measure_notes.pdf) - John K. Hunter（加州大学戴维斯分校） * 📝 [Measure and Integration](https://people.math.ethz.ch/~salamon/PREPRINTS/measure.pdf) - Dietmar A. Salamon（苏黎世联邦理工学院） * 📝 [Lecture notes: Measure Theory](http://www.math.ucsd.edu/~bdriver/240-00-01/Lecture_Notes/measurep.pdf) - Bruce K. Driver ### 常微分方程 * 📝 [Difference Equations To Differential Equations](http://www.synechism.org/wp/difference-equations-to-differential-equations/) - Dan Sloughter * 📝 [Ordinary Differential Equation](https://www.math.uni-bielefeld.de/~grigor/odelec2008.pdf) - Alexander Grigorian（比勒费尔德大学） * 📝 [Ordinary Differential Equations: Lecture Notes](http://www.cs.bgu.ac.il/~leonid/ode_bio_files/Ionascu_LectNotes.pdf) - Eugen J. Ionascu * 📝 [Ordinary Differential Equations](http://www.math.lmu.de/~philip/publications/lectureNotes/ODE.pdf) - Peter Philip * 📝 [Ordinary Differential Equations](http://users.math.msu.edu/users/gnagy/teaching/ode.pdf) - Gabriel Nagy * 📝 [Ordinary Differential Equations and Dynamical Systems](http://www.mat.univie.ac.at/~gerald/ftp/book-ode/ode.pdf) - Gerald Teschl * 📝 [Notes on Differential Equations](http://leipper.org/manuals/zip-fill/dn-difeq-notes.pdf) - Bob Terrell * 📝 [Elementary Differential Equations](http://digitalcommons.trinity.edu/mono/8/) - William F. Trench * 📝 [Elementary Differential Equations With Boundary Value Problems](http://digitalcommons.trinity.edu/mono/9/) - William F. Trench * 📝 [Notes on Diffy Qs: Differential Equations for Engineers](http://www.jirka.org/diffyqs/) - Jiří Lebl * 📝 [Differential Equations](http://djm.cc/library/Differential_Equations_Phillips_edited.pdf) - H. B. Phillips (1922) ### 偏微分方程 * 📝 [Notes on Partial Differential Equations](https://www.math.ucdavis.edu/~hunter/pdes/pde_notes.pdf) - K. Hunter（加州大学戴维斯分校） * 📝 [Partial Differential Equations: Lecture Notes](http://www.math.uni-leipzig.de/~miersemann/pdebook.pdf) - Erich Miersemann（莱比锡大学） * 📝 [Linear Methods of Applied Mathematics](http://www.mathphysics.com/pde/) - E. Harrell, J. Herod（佐治亚理工学院） ### 混沌理论 * 📝 [Chaos: Making a New Science](https://archive.org/details/chaosmakingnewsc0000unse) - James Gleick * 📝 [Complexity: A Guided Tour](https://archive.org/details/complexityguided0000mitc?utm_source=chatgpt.com) - Melanie Mitchell（牛津大学） ## 概率论与数理统计 ### 概率论 * 📝 [Introduction to Probability](https://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf) - Charles M. Grinstead, J. Laurie Snell * 📝 [Introduction to Probability](http://vfu.bg/en/e-Learning/Math--Bertsekas_Tsitsiklis_Introduction_to_probability.pdf) - Dimitri P. Bertsekas, John N. Tsitsiklis (MIT) * 📝 [A Short Introduction to Probability](http://www.maths.uq.edu.au/~kroese/asitp.pdf) - Dirk P. Kroese（昆士兰大学） * 📝 [Probability: Theory and Examples](https://www.math.duke.edu/~rtd/PTE/PTE4_1.pdf) - Rick Durrett * 📝 [Probability and Statistics Cookbook](https://github.com/mavam/stat-cookbook/releases/download/0.2.3/stat-cookbook.pdf) - Matthias Vallentin（加州大学伯克利分校） * 📝 [The Only Probability Cheatsheet You'll Ever Need](http://www.wzchen.com/probability-cheatsheet/) - William Chen * 📝 [An Introduction to Probability and Random Processes](http://www.ellerman.org/Davids-Stuff/Maths/Rota-Baclawski-Prob-Theory-79.pdf) - Gian-Carlo Rota, Kenneth Baclawski * 📝 [Foundations of Constructive Probability Theory](https://arxiv.org/pdf/1906.01803.pdf) - Yuen-Kwok Chan ### 统计学 * 📝 [Lecture Notes on Statistical Theory](http://homepages.math.uic.edu/~rgmartin/Teaching/Stat411/Notes/411notes.pdf) - Ryan Martin（伊利诺伊大学） * 📝 [Introduction to Statistics and Data Analysis for Physicists](http://www-library.desy.de/preparch/books/vstatmp_engl.pdf) - Gerhard Bohm, Günter Zech * 📝 [Probability and Mathematical Statistics](http://www.iiserpune.ac.in/~ayan/MTH201/Sahoo_textbook.pdf) - Prasanna Sahoo（路易斯维尔大学） * 📝 [Lectures on Statistics](http://math.arizona.edu/~faris/stat.pdf) - William G. Faris * 📝 [Statistical Theory](http://pages.pomona.edu/~ajr04747/Fall2009/Math152/Notes/Math152NotesFall09.pdf) - Adolfo J. Rumbos * 📝 [Theory of Statistics](http://mason.gmu.edu/~jgentle/books/MathStat.pdf) - James E. Gentle（乔治梅森大学） * 📝 [Theory of Statistics](http://math.arizona.edu/~jwatkins/notests.pdf) - Joseph C. Watkins（亚利桑那大学） * 📝 [Glossary of Data Modeling](https://web.archive.org/web/20130523134625/http://www.aiaccess.net/e_gm.htm) - AI Access * 📝 [Statistics Papers](http://www.ats.ucla.edu/stat/papers/) - 由加州大学洛杉矶分校数字研究与教育研究所 (IDRE) 策划的统计学论文列表，涵盖自助法和因子不变性等方法。 * 📝 [NIST Handbook of Statistical Methods](http://itl.nist.gov/div898/handbook/index.htm) - 面向科学家和工程师的实用统计学资源。 * 📝 [Concepts and Applications of Inferential Statistics](http://vassarstats.net/textbook/) - Richard Lowry * 📝 [Rough set data analysis: A road to non-invasive knowledge discovery](http://www.cosc.brocku.ca/~duentsch/papers/methprimer2.html) - Ivo Düntsch, Günther Gediga * 📝 [Statistical Thinking for the 21st Century](https://statsthinking21.org/) - Russell A. Poldrack * 📝 [Odds and Ends: Introducing Probability & Decision with a Visual Emphasis](https://jonathanweisberg.org/vip/) - Jonathan Weisberg * 📝 [Seeing Theory](https://seeing-theory.brown.edu/) - Daniel Kunin, Jingru Guo, Tyler Dae Devlin 和 Daniel Xiang * 📝 [Statistics Done Wrong](https://www.statisticsdonewrong.com/) - Alex Reinhart * 📝 [All of Statistics: A Concise Course in Statistical Inference](https://link.springer.com/book/10.1007/978-0-387-21736-9) - Larry Wasserman ### 统计学习 * 📝 [An Introduction to Statistical Learning with Applications in R](http://www-bcf.usc.edu/~gareth/ISL/ISLR%20First%20Printing.pdf) - Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani * 📝 [The Elements of Statistical Learning](http://web.stanford.edu/~hastie/Papers/ESLII.pdf) - Trevor Hastie, Robert Tibshirani, Jerome Friedman * 📝 [Statistical Learning Theory](https://web.stanford.edu/class/cs229t/notes.pdf) - Percy Liang * 📝 [Reinforcement Learning: An Introduction](https://webdocs.cs.ualberta.ca/~sutton/book/bookdraft2016sep.pdf) - Richard S. Sutton, Andrew G. Barto ### 随机过程 * 📝 [Lectures on Stochastic Processes](http://www.math.tifr.res.in/~publ/ln/tifr24.pdf) - K. Ito（塔塔基础研究所，孟买） * 📝 [Probability and Stochastic Processes with Applications](http://www.math.harvard.edu/~knill/teaching/math144_1994/probability.pdf) - Oliver Knill（哈佛大学） * 📝 [Stochastic Processes](http://statweb.stanford.edu/~adembo/math-136/nnotes.pdf) - Amir Dembo（斯坦福大学） * 📝 [Lecture Notes on Stochastic Processes](http://www.mi.fu-berlin.de/wiki/pub/CompMolBio/MarkovKetten15/stochastic_processes_2011.pdf) - Frank Noé, Bettina Keller 和 Jan-Hendrik Prinz（柏林自由大学） * 📝 [Introduction to Stochastic Processes - Lecture Notes](https://www.ma.utexas.edu/users/gordanz/notes/introduction_to_stochastic_processes.pdf) - Gordan Žitković（德克萨斯大学） * 📝 [Applied Stochastic Processes in science and engineering](https://www.math.uwaterloo.ca/~mscott/Little_Notes.pdf) - Matt Scott（滑铁卢大学） * 📝 [An Introduction to Stochastic Processes in Continuous Time](http://www.math.leidenuniv.nl/~spieksma/colleges/sp-master/sp-hvz1.pdf) - Flora Spieksma（莱顿大学） * 📝 [Markov Chains and Mixing Times](http://pages.uoregon.edu/dlevin/MARKOV/markovmixing.pdf) - David A. Levin, Yuval Peres, Elizabeth L. Wilmer * 📝 [Convergence of Stochastic Processes](http://www.stat.yale.edu/~pollard/Books/1984book/pollard1984.pdf) - David Pollard ## 数值分析 * 📝 [Introduction to Numerical Analysis](http://www.math.umd.edu/~dlevy/resources/notes.pdf) - Doron Levy（马里兰大学） * 📝 [A Concise Introduction to Numerical Analysis](http://www.ima.umn.edu/~arnold/597.00-01/nabook.pdf) - Douglas N. Arnold（明尼苏达大学） * 📝 [Numerical Analysis](http://people.cs.uchicago.edu/~ridg/newna/nalrs.pdf) - L. Ridgway Scott * 📝 [Lectures In Basic Computational Numerical Analysis](https://uknowledge.uky.edu/cgi/viewcontent.cgi?article=1000&context=math_textbooks) - J. M. McDonough（肯塔基大学） * 📝 [Advanced Numerical Methods and Their Applications to Industrial Problems: Adaptive Finite Element Methods](https://user.math.uni-bremen.de/schmi/SS04/YSU_Notes.pdf) - Alfred Schmidt, Arsen Narimanyan * 📝 [Numerical Analysis for Engineers](https://ece.uwaterloo.ca/~dwharder/nm/) - Douglas Wilhelm Harder * 📝🎥 [Advanced Linear Algebra: Foundations to Frontiers](https://www.cs.utexas.edu/users/flame/laff/alaff/frontmatter.html) - Robert van de Geijn, Margaret Myers（德克萨斯大学奥斯汀分校） ## 信号处理 * 📝 [Introduction to Signal Processing](http://www.ece.rutgers.edu/~orfanidi/intro2sp/orfanidis-i2sp.pdf) - Sophocles J. Orfanidis（罗格斯大学） * 📝 [Foundations of Signal Processing](http://www.fourierandwavelets.org/FSP_v1.1_2014.pdf) - Martin Vetterli, Jelena Kovacevic, Vivek K Goyal * 📝 [An Introduction to Statistical Signal Processing](https://ee.stanford.edu/~gray/sp.pdf) - Robert M. Gray, Lee D. Davisson * 📝 [Think DSP](https://greenteapress.com/wp/think-dsp/) - Allen B. Downey * 📝 [Linear algebra, signal processing, and wavelets. A unified approach.](https://www.uio.no/studier/emner/matnat/math/MAT-INF2360/v15/kompendium/applinalgpython.pdf) - Øyvind Ryan（奥斯陆大学） ## 计算机科学数学 * 📝 [Mathematics for Computer Science](https://people.csail.mit.edu/meyer/mcs.pdf) - Eric Lehman, F. Thomson Leighton, Albert R. Meyer * 📝 [Algorithms and Complexity](http://www.math.upenn.edu/%7Ewilf/AlgComp3.html) - H. Wilf * 📝 [Lecture Notes on Optimization](http://people.eecs.berkeley.edu/~varaiya/papers_ps.dir/NOO.pdf) - Pravin Varaiya * 📝 [Information Theory, Inference, and Learning Algorithms](http://www.inference.org.uk/mackay/itila/book.html) - David J. C. MacKay * 📝 [The Chaos Textbook: Mathematics in the age of the computer](https://hypertextbook.com/chaos/) - Glenn Elert ## 数理生物学 * 📝 [Mathematical Biology](http://www.math.ust.hk/~machas/mathematical-biology.pdf) - Jeffrey Chasnov ## 数学物理 * 📝 [Introduction to Continuum Mechanics](http://oaktrust.library.tamu.edu/handle/1969.1/2501) - Ray. M. Bowen * 📝 [Mathematical Tools for Physics](http://www.physics.miami.edu/nearing/mathmethods/) - James Nearing * 📝 [Mechanism of the Heavens (1831)](http://www.malaspina.com/etext/heavens.htm) - Mary Somerville # 学生课堂笔记 * [Evan Chen](https://web.evanchen.cc/coursework.html) - MIT。2012 ~ 2018。涵盖组合数学、数论、荣誉代数、集合论、实分析、图论等。 * [Dexter Chua](https://dec41.user.srcf.net/notes/) - 哈佛大学。2013 ~ 2018。涵盖分析学、概率论、线性代数、复分析、数值分析、统计学、优化、代数拓扑、量子场论等。 # 相关 Awesome 列表 * [理论计算机科学](https://github.com/mostafatouny/awesome-theoretical-computer-science) # 许可协议 [](http://creativecommons.org/publicdomain/zero/1.0/) 在法律允许的范围内，[Cyrille Rossant](http://cyrille.rossant.net) 已放弃本作品的所有版权及相关或邻接权利。

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