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--- visibility: public --- # Math **repo:** [rossant/awesome-math](https://github.com/rossant/awesome-math) **category:** [[theory|Theory]] **related:** [[data-science|Data Science]] · [[algorithms|Algorithms]] --- # Awesome Math [](https://github.com/sindresorhus/awesome) A curated list of awesome mathematics resources. All resources are freely available except those with a 💲 icon. # Contents * [Contents](#contents) * [General Resources](#general-resources) * [Learning Platforms](#[learning](/@harrisonqian/awesome/wiki/programming-languages/learning)-platforms) * [Learn to Learn](#learn-to-learn) * [Youtube Series](#youtube-series) * [Tools](#tools) * [Questions and Answers](#questions-and-answers) * [Encyclopedia](#encyclopedia) * [Books](#books) * [Magazines](#magazines) * [Blogs](#blogs) * [Meetings and Conferences](#meetings-and-conferences) * [Misc](#misc) * [Branches of Mathematics](#branches-of-mathematics) * [Foundations of Mathematics](#foundations-of-mathematics) * [Transition To Pure Rigour Math](#transition-to-pure-rigour-math) * [Set Theory](#set-theory) * [Logic](#logic) * [Category Theory](#category-theory) * [Type Theory](#type-theory) * [Homotopy Type Theory](#homotopy-type-theory) * [Surreal Numbers](#surreal-numbers) * [Number Theory](#number-theory) * [Algebraic Number Theory](#algebraic-number-theory) * [Analytic Number Theory](#analytic-number-theory) * [Algebra](#algebra) * [Abstract Algebra](#abstract-algebra) * [Group Theory](#group-theory) * [Linear Algebra](#linear-algebra) * [Ring Theory](#ring-theory) * [Galois Theory](#galois-theory) * [Lie Algebras](#lie-algebras) * [Combinatorics](#combinatorics) * [Graph Theory](#graph-theory) * [Geometry and Topology](#geometry-and-topology) * [Differential Geometry](#differential-geometry) * [Algebraic Geometry](#algebraic-geometry) * [Algebraic Statistics](#algebraic-statistics) * [Topology](#topology) * [Algebraic Topology](#algebraic-topology) * [Analysis](#analysis) * [Real Analysis](#real-analysis) * [Harmonic Analysis](#harmonic-analysis) * [Complex Analysis](#complex-analysis) * [Functional Analysis](#functional-analysis) * [Measure Theory](#measure-theory) * [Ordinary Differential Equations](#ordinary-differential-equations) * [Partial Differential Equations](#partial-differential-equations) * [Chaos Theory](#chaos-theory) * [Probability and Statistics](#probability-and-statistics) * [Probability Theory](#probability-theory) * [Statistics](#statistics) * [Statistical Learning](#statistical-learning) * [Stochastic processes](#stochastic-processes) * [Numerical Analysis](#numerical-analysis) * [Signal processing](#signal-processing) * [Mathematics for Computer Science](#mathematics-for-computer-science) * [Mathematical Biology](#mathematical-biology) * [Mathematical Physics](#mathematical-physics) * [Students Lecture Notes](#students-lecture-notes) * [Related [Awesome](/@harrisonqian/awesome/wiki/miscellaneous/awesome) Lists](#related-awesome-lists) * [License](#license) # General Resources ## Learning Platforms * [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/) : free interactive mathematics textbooks (Ohio State University) * [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) — A step-by-step differentiation tool focusing on the chain rule and substitution logic. ## Learn to Learn * [Understanding Mathematics](https://github.com/nelson-brochado/understanding-math) ## Youtube Series * [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) * [Precalculus - College Algebra/Trigonometry](https://www.youtube.com/playlist?list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP) * [Calculus 1](https://www.youtube.com/playlist?list=PLF797E961509B4EB5) * [Calculus 2](https://www.youtube.com/playlist?list=PLDesaqWTN6EQ2J4vgsN1HyBeRADEh4Cw-) * [Calculus 3](https://www.youtube.com/playlist?list=PLDesaqWTN6ESk16YRmzuJ8f6-rnuy0Ry7) * [Differential Equations](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) ## Tools * [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) - C# math expression library with symbolic computation (differentiation, simplification, equation solving) * [Unit Converter](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/) * [Finance calculators](https://www.financecharts.com/pages/5724-retirement-[calculators](/@harrisonqian/awesome/wiki/miscellaneous/calculators)-and-stock-market-tips) * [Mathcheap](https://mathcheap.xyz) * [Midpoint Calculator](https://midpointcalculator.co) * [Quartiles Calculator](https://quartilecalculator.net) * [Corca Editor](https://corca.io/) * [RunMat](https://github.com/runmat-org/runmat) - Runtime for MATLAB-syntax array math with automatic CPU/GPU execution. * [Structural Engineering Tools (SEPCO Engineering)](https://github.com/sepcostructural/structural-engineering-tools) - Free online [calculators](/@harrisonqian/awesome/wiki/miscellaneous/calculators) for beam diagrams, Canadian steel section properties, and pressure conversions. ## Questions and Answers * [Mathematics Stack Exchange](http://math.stackexchange.com/) * [MathOverflow](http://mathoverflow.net/) - for professional mathematicians ## Encyclopedia * [Encyclopedia of Mathematics](https://www.encyclopediaofmath.org) * [Planetmath](http://planetmath.org/) * [ProofWiki](https://proofwiki.org/wiki/Main_Page) * [Wolfram Mathworld](http://mathworld.wolfram.com/) * [The On-Line Encyclopedia of Integer Sequences](https://oeis.org) - Great compendium of many different integer sequences. Founded 1964 by N. J. A. Sloane. * 💲 [The Princeton Companion to Mathematics](https://press.princeton.edu/books/hardcover/9780691118802/the-princeton-companion-to-mathematics) - Timothy Gowers (Professor, Fields medallist), June Barrow-Green (Professor), and Imre Leader (Professor). * 💲 [Encyclopedia of Distances (4th Edition)](https://link.springer.com/book/10.1007/978-3-662-52844-0) - Michel Marie Deza, Elena Deza. ## Books * [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 (University of Pennsylvania) * [Multivariable Calculus](http://people.math.gatech.edu/%7Ecain/notes/calculus.html) - G. Cain, J. Herod (Georgia Tech) * [Wikibooks](https://en.wikibooks.org/wiki/Wikibooks:Mathematics_bookshelf) * [Online Mathematics Textbooks](https://people.math.gatech.edu/~cain/textbooks/onlinebooks.html) * [Beginning and Intermediate Algebra](http://www.wallace.ccfaculty.org/book/Beginning_and_Intermediate_Algebra.pdf) * [Free Mathematics Books](https://github.com/EbookFoundation/free-programming-books/blob/master/books/free-programming-books-subjects.md#mathematics) * [Trigonometry](http://www.mecmath.net/trig/trigbook.pdf) * [Math for Frontend Web Dev](https://www.manning.com/books/math-for-frontend-web-dev) * [Grokking Statistics](https://www.manning.com/books/grokking-statistics) * [The Math Behind Artificial Intelligence](https://www.freecodecamp.org/news/the-math-behind-artificial-intelligence-book) - Tiago Capelo Monteiro (freeCodeCamp) ## Magazines * [Quanta Magazine](https://www.quantamagazine.org/mathematics/) - Features latest research breakthroughs in an accessible style for non-experts. * [Bulletin of the American Mathematical Society](https://www.ams.org/journals/bull/all_issues.html) - Expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. * [Notices of the American Mathematical Society](http://www.ams.org/cgi-bin/notices/amsnotices.pl?article_id=fullissue&article_type=gallery&gallery_type=fullissue) - Publicizes activities of the Society and features surveys, reports, news, announcements, and opinions on industry trends, academia, and research. * [European Mathematical Society Magazine](https://euromathsoc.org/magazine) - The Magazine features announcements about meetings and conferences, articles outlining current trends in scientific development, reports on member societies, and many other informational items. * [Mathematics Today by Institute of Mathematics and its Applications](https://ima.org.uk/publications/mathematics-today/) - News, opinions, and articles related to mathematics, so the reader stays updated. * [Crux Mathematicorum by Canadian Mathematical Society](https://cms.math.ca/publications/crux/) - source of unique and challenging mathematical problems designed for the secondary and undergraduate levels. It includes an Olympiad Corner which is helpful for math competitions. ## Blogs * [BetterExplained](https://betterexplained.com/) - Maintained by Kalid Azad * [ILoveMaths](http://ilovemaths.com/) - For grades 6 thru 12 in K-12 system * [3blue1brown](https://www.3blue1brown.com/) - Animated Maths * [Mathsisfun](https://www.mathsisfun.com) simple text lightweight site for students up to highschool * [MathematicsIsAScience](https://calculus123.com/wiki/Peter_Saveliev) - Peter Saveliev (Professor of mathematics at Marshall University, Huntington WV, USA) ## Meetings and Conferences * [MathsJam](https://mathsjam.com/) - monthly local recreational maths/puzzle meetups and an annual gathering in Staffordshire, England * [Talking Maths in Public](https://talkingmathsinpublic.uk/) - a conference for maths communicators, running every two years, usually in the UK * [Bridges](https://www.bridgesmathart.org/) - an annual conference on mathematical connections in art, [music](/@harrisonqian/awesome/wiki/media/music), architecture, and culture. The 2025 meeting is in Eindhoven, Netherlands. ## Misc * [Areas of mathematics on Wikipedia](https://en.wikipedia.org/wiki/Areas_of_mathematics) * [Paul's Online Math Notes](http://tutorial.math.lamar.edu/) - Paul Dawkins (Lamar University) * [List of electronic textbooks](http://faculty.atu.edu/mfinan/nnotes.html) - Marcel B. Finan (Arkansas Tech University) * [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 and Lieven Vandenberghe * [Fabrice Baudoin's Notes](https://fabricebaudoin.wordpress.com/) - Both research and lecture notes on many topics, Including Diffusions on foliated manifold, Stochastic Calculus, Global analysis in Dirichlet spaces, and more. # Branches of Mathematics **Content Format** \ 📖 Books \ 🎥 Videos \ 📝 Lecture notes, slides, articles, papers ## Foundations of Mathematics ### Transition To Pure Rigour Math * 📝 [Basic Concepts of Mathematics](http://www.trillia.com/zakon1.html) - Elias Zakon * 📝 [Book of Proof](https://richardhammack.[github](/@harrisonqian/awesome/wiki/development-environment/github).io/BookOfProof/) - Richard Hammak (Virginia Commonwealth University) * 📖 [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 (Professor). ### Set Theory * 📝 [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 A. R. Weiss * 📝 [Set Theory and Foundations of Mathematics](http://www.settheory.net/) - Sylvain Poirier * 📝 [Set Theory on the Stanford Encyclopedia of Philosophy](http://plato.stanford.edu/entries/set-theory/) ### Logic * 📝 [Introduction to Logic](https://pdfs.semanticscholar.org/6967/f52773d9c2ccfc94658657a5761e0f00e95a.pdf) - Michael Genesereth, Eric Kao (Stanford University) * 📝 [An Introduction to Formal Logic](https://www.fecundity.com/codex/forallx.pdf) - P.D. Magnus (University at Albany) * 📝 [A Problem Course in Mathematical Logic](http://euclid.trentu.ca/math/sb/pcml/pcml-16.pdf) - Stefan Bilaniuk (Trent University) * 📝 [Computability - An introduction to recursive function theory](http://poincare.matf.bg.ac.rs/~zarkom/Book_Math__Cutland_Computability.pdf) - Nigel Cutland (University of Hull) * 📝 [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 (Pennsylvania State University) * 📝 [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](/@harrisonqian/awesome/wiki/development-environment/github).io/logic_and_proof/) - Jeremy Avigad, Robert Y. Lewis, and Floris van Doorn * 📝 [QED - an interactive textbook](https://teorth.[github](/@harrisonqian/awesome/wiki/development-environment/github).io/QED) - Terence Tao * 📝 [Open Logic Textbook](http://builds.openlogicproject.org/) - collaborative effort, main contributors listed [here](https://openlogicproject.org/people/) ### Category Theory * 📝 [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 (Carnegie Mellon University) * 📝 [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 and David I. Spivak (MIT) * 📝 [Category Theory in Context](http://www.math.jhu.edu/~eriehl/context/) - Emily Riehl (John Hopkins University) ### Type Theory * 📝 [Proofs and Types](http://www.paultaylor.eu/stable/prot.pdf) - Jean-Yves Girard * 📝 [Intuitionistic Type Theory](https://archive-pml.[github](/@harrisonqian/awesome/wiki/development-environment/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 ### Homotopy Type Theory * 📝 [Homotopy Type Theory](https://hottheory.files.wordpress.com/2013/03/hott-online-611-ga1a258c.pdf) ### Surreal Numbers * 📝 [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 ## Number Theory * 📝 [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 (University of South Florida) * 📝 [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 ### Algebraic Number Theory * 📝 [Introduction to Algebraic Number Theory](https://feog.[github](/@harrisonqian/awesome/wiki/development-environment/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 (Georgia Tech) * 📝 [A Course In Algebraic Number Theory](http://www.math.uiuc.edu/~r-ash/ANT.html) - Robert Ash ### Analytic Number Theory * 📝 [Introduction to Analytic Number Theory](http://www.math.uiuc.edu/~hildebr/ant/main.pdf) - A.J. Hildebrand (University of Illinois) * 📝 [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 (LMU Munich) * 📝 [Analytic Number Theory - Lecture Notes based on Davenport’s book](http://www2.math.uu.se/~astrombe/analtalt08/www_notes.pdf) - Andreas Strömbergsson ## Algebra * 📝 [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 ### Abstract Algebra * 📝 [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 (Creighton University) * 📝 [Introduction to Modern Algebra](http://aleph0.clarku.edu/~djoyce/ma225/algebra.pdf) - David Joyce (Clark University) * 📝 [Algebraic Methods](https://feog.[github](/@harrisonqian/awesome/wiki/development-environment/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 (Austin State University) * 📝 [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 (University of Miami) * 📝 [Abstract Algebra: The Basic Graduate Year](http://www.math.uiuc.edu/~r-ash/Algebra.html) - Robert Ash * 📝 [Abstract Algebra: Harvard Extension (Archived)](https://web.archive.org/web/20150528171650/extension.harvard.edu/open-[learning](/@harrisonqian/awesome/wiki/programming-languages/learning)-initiative/abstract-algebra) - Benedict Gross * 📝 [Abstract Algebra: Harvard Extension Videos](https://www.youtube.com/playlist?list=PLA58AC5CABC1321A3) - Benedict Gross ### Group Theory * 📝 [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 ### Linear Algebra * 📝 [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 Lectures on Linear Algebra (18.06) as [Jupyter](/@harrisonqian/awesome/wiki/miscellaneous/jupyter) Notebooks](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 (Stanford University), Lieven Vandenberghe (UCLA) * 📝 [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, and T. Akenine-Möller * 📝 [Interactive Linear Algebra](https://textbooks.math.gatech.edu/ila/) - Dan Margalit and 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 ### Ring Theory * 📝 [Foundations of Module and Ring Theory](http://www.math.uni-duesseldorf.de/~wisbauer/book.pdf) - Robert Wisbauer (University of Düsseldorf) ### Galois Theory * 📝 [An Introduction to Galois Theory](http://www.maths.gla.ac.uk/~ajb/dvi-ps/Galois.pdf) - Andrew Baker (University of Glasgow) * 📝 [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 (University of Edinburgh) ### Lie Algebras * 📝 [Lie Algebras](http://www.math.harvard.edu/~shlomo/docs/lie_algebras.pdf) - Shlomo Sternberg ## Combinatorics * 📝 [Basic Combinatorics](http://web.math.utk.edu/~wagner/papers/comb.pdf) - Carl G. Wagner (University of Tennessee) * 📝 [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 ### Graph Theory * 📝 [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](/@harrisonqian/awesome/wiki/programming-languages/learning) Platform](https://learngraphtheory.org/) - Hadjoudj Mohammed Islam ## Geometry and Topology * 📝 [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](http://www.math.ubc.ca/~cass/graphics/manual/) - 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 and David Eugene Smith (1913) * 📝 [Planes and Spherical Trigonometry](http://djm.cc/library/Plane_Spherical_Trigonometry_Wentworth_Smith_edited_2.pdf) - George Wentworth and David Eugene Smith (1915) * 📝 [Coordinate Geometry](http://djm.cc/library/Coordinate_Geometry_Fine_Thompson_edited03.pdf) - Henry Buchard Fine and 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) ### Differential Geometry * 📝 [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 (University of Pennsylvania) * 📝 [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 (Lund University) * 📝 [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 ### Algebraic Geometry * 📝 [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 (University of Pennsylvania) * 📝 [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 (University of Kaiserslautern) * 📝 [The [Stacks](/@harrisonqian/awesome/wiki/miscellaneous/stacks) Project](https://stacks.math.columbia.edu/) - Maintained by Aise Johan de Jong (Columbia) ### Algebraic Statistics * 📝 [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 and 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, and Sturmfels. ### Topology * 📝 [General Topology](https://www.rexresearch1.com/TopologyLibrary/GeneralTopologyWillard.pdf) - Stephen Willard * 📝 [Elementary Applied Topology](https://www.math.upenn.edu/~ghrist/notes.html) - Robert Ghrist (UPenn) * 📝 [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 (Paris VI University) * 📝 [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) ### Algebraic Topology * 📝 [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 (Paris VI University) * 📝 [Lecture Notes in Algebraic Topology](http://www.indiana.edu/~jfdavis/teaching/m623/book.pdf) - James F. Davis, Paul Kirk (Indiana University) * 📝 [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 ## Analysis ### Real Analysis * 📝 [MIT OpenCourseWare Lectures on Calculus](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) - Professor H. Jerome Keisler * 📝 [An Introduction to Real Analysis](https://www.math.ucdavis.edu/~hunter/intro_analysis_pdf/intro_analysis.pdf) - John K. Hunter (University of California at Davis) * 📝 [Introduction to Real Analysis](http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF) - William F. Trench (Trinity University, Texas) * 📝 [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](/@harrisonqian/awesome/wiki/development-environment/hyper).pdf) - Thomson, Bruckner * 📝 [Lecture Notes in Real Analysis](http://ms.mcmaster.ca/~sawyer/Publications/Real_Analysis.pdf) - Eric T. Sawyer (McMaster University) * 📝 [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 (Indiana University) * 📝 [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 ### Harmonic Analysis * 📝 [Harmonic Analysis Lecture Notes](http://www.math.uiuc.edu/~laugesen/545/545Lectures.pdf) - Richard S. Laugesen (University of Illinois at Urbana–Champaign) * 📝 [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 (Stanford University) ### Complex Analysis * 📝 [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 (University of Illinois) * 📝 [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 (Georgia Tech) * 📝 [Complex Analysis](https://complex-analysis.com/) - Juan Carlos Ponce Campuzano ### Functional Analysis * 📝 [An Introduction to Functional Analysis](https://www.math.uwaterloo.ca/~lwmarcou/notes/pmath453.pdf) - Laurent W. Marcoux (University of Waterloo) * 📝 [Functional Analysis: Lecture Notes](http://users.math.msu.edu/users/jeffrey/920/920notes.pdf) - Jeff Schenker (Michigan State University) * 📝 [Functional Analysis Lecture Notes](https://archive.org/details/TB_Ward___Functional_analysis_lecture_notes) - T.B. Ward (University of East Anglia) * 📝 [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 --- *truncated — [full list on GitHub](https://github.com/rossant/awesome-math)*