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<h1 id="awesome-math-awesome">Awesome Math <a
href="https://github.com/sindresorhus/awesome"><img
src="https://cdn.rawgit.com/sindresorhus/awesome/d7305f38d29fed78fa85652e3a63e154dd8e8829/media/badge.svg"
alt="Awesome" /></a></h1>
<p>A curated list of awesome mathematics resources.</p>
<p>All resources are freely available except those with a 💲 icon.</p>
<h1 id="contents">Contents</h1>
<!-- START_TOC -->
<ul>
<li><a href="#contents">Contents</a></li>
<li><a href="#general-resources">General Resources</a>
<ul>
<li><a href="#learning-platforms">Learning Platforms</a></li>
<li><a href="#learn-to-learn">Learn to Learn</a></li>
<li><a href="#youtube-series">Youtube Series</a></li>
<li><a href="#tools">Tools</a></li>
<li><a href="#questions-and-answers">Questions and Answers</a></li>
<li><a href="#encyclopedia">Encyclopedia</a></li>
<li><a href="#books">Books</a></li>
<li><a href="#magazines">Magazines</a></li>
<li><a href="#blogs">Blogs</a></li>
<li><a href="#misc">Misc</a></li>
</ul></li>
<li><a href="#branches-of-mathematics">Branches of Mathematics</a>
<ul>
<li><a href="#foundations-of-mathematics">Foundations of Mathematics</a>
<ul>
<li><a href="#transition-to-pure-rigour-math">Transition To Pure Rigour
Math</a></li>
<li><a href="#set-theory">Set Theory</a></li>
<li><a href="#logic">Logic</a></li>
<li><a href="#category-theory">Category Theory</a></li>
<li><a href="#type-theory">Type Theory</a></li>
<li><a href="#homotopy-type-theory">Homotopy Type Theory</a></li>
<li><a href="#surreal-numbers">Surreal Numbers</a></li>
</ul></li>
<li><a href="#number-theory">Number Theory</a>
<ul>
<li><a href="#algebraic-number-theory">Algebraic Number Theory</a></li>
<li><a href="#analytic-number-theory">Analytic Number Theory</a></li>
</ul></li>
<li><a href="#algebra">Algebra</a>
<ul>
<li><a href="#abstract-algebra">Abstract Algebra</a></li>
<li><a href="#group-theory">Group Theory</a></li>
<li><a href="#linear-algebra">Linear Algebra</a></li>
<li><a href="#ring-theory">Ring Theory</a></li>
<li><a href="#galois-theory">Galois Theory</a></li>
<li><a href="#lie-algebras">Lie Algebras</a></li>
</ul></li>
<li><a href="#combinatorics">Combinatorics</a>
<ul>
<li><a href="#graph-theory">Graph Theory</a></li>
</ul></li>
<li><a href="#geometry-and-topology">Geometry and Topology</a>
<ul>
<li><a href="#differential-geometry">Differential Geometry</a></li>
<li><a href="#algebraic-geometry">Algebraic Geometry</a></li>
<li><a href="#algebraic-statistics">Algebraic Statistics</a></li>
<li><a href="#topology">Topology</a></li>
<li><a href="#algebraic-topology">Algebraic Topology</a></li>
</ul></li>
<li><a href="#analysis">Analysis</a>
<ul>
<li><a href="#real-analysis">Real Analysis</a></li>
<li><a href="#harmonic-analysis">Harmonic Analysis</a></li>
<li><a href="#complex-analysis">Complex Analysis</a></li>
<li><a href="#functional-analysis">Functional Analysis</a></li>
<li><a href="#measure-theory">Measure Theory</a></li>
<li><a href="#ordinary-differential-equations">Ordinary Differential
Equations</a></li>
<li><a href="#partial-differential-equations">Partial Differential
Equations</a></li>
</ul></li>
<li><a href="#probability-and-statistics">Probability and Statistics</a>
<ul>
<li><a href="#probability-theory">Probability Theory</a></li>
<li><a href="#statistics">Statistics</a></li>
<li><a href="#statistical-learning">Statistical Learning</a></li>
<li><a href="#stochastic-processes">Stochastic processes</a></li>
</ul></li>
<li><a href="#numerical-analysis">Numerical Analysis</a></li>
<li><a href="#signal-processing">Signal processing</a></li>
<li><a href="#mathematics-for-computer-science">Mathematics for Computer
Science</a></li>
<li><a href="#mathematical-biology">Mathematical Biology</a></li>
<li><a href="#mathematical-physics">Mathematical Physics</a></li>
</ul></li>
<li><a href="#students-lecture-notes">Students Lecture Notes</a></li>
<li><a href="#related-awesome-lists">Related Awesome Lists</a></li>
<li><a href="#license">License</a></li>
</ul>
<!-- END_TOC -->
<h1 id="general-resources">General Resources</h1>
<h2 id="learning-platforms">Learning Platforms</h2>
<ul>
<li><a href="https://www.khanacademy.org/math">Khan Academy</a></li>
<li><a
href="https://www.coursera.org/courses?query=mathematics&amp;languages=en">Coursera</a></li>
<li><a href="http://ocw.mit.edu/courses/mathematics/">MIT
OpenCourseWare</a></li>
<li><a href="https://www.edx.org/course/subject/math">edX</a></li>
<li><a
href="https://brilliant.org/courses/#math-foundational">Brilliant</a></li>
<li><a href="https://misterwootube.com/">WooTube</a></li>
<li><a href="https://mathigon.org/">Mathigon</a></li>
<li><a href="http://calculus.org/">Calculus.org</a></li>
<li><a href="https://ximera.osu.edu/">Ximera</a> : free interactive
mathematics textbooks (Ohio State University)</li>
<li><a href="https://www.mathrelay.com/">MathRelay</a></li>
<li><a href="https://www.almostfun.org/lessons/">Almost Fun</a></li>
<li><a href="https://www.youtube.com/c/OxfordMathematics">Oxford
Mathematics</a></li>
</ul>
<h2 id="learn-to-learn">Learn to Learn</h2>
<ul>
<li><a
href="https://github.com/nelson-brochado/understanding-math">Understanding
Mathematics</a></li>
</ul>
<h2 id="youtube-series">Youtube Series</h2>
<ul>
<li><a href="https://www.youtube.com/@BrandonFoltz">Brandon
Foltz</a></li>
<li><a
href="https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw">StatQuest</a></li>
<li><a href="https://www.youtube.com/@3blue1brown">3Blue1Brown</a></li>
<li><a href="https://www.youtube.com/@iit">NPTEL</a></li>
<li><a href="https://www.youtube.com/@patrickjmt">PatrickJMT</a></li>
<li><a href="https://www.youtube.com/@ProfessorLeonard">Professor
Leonard</a>
<ul>
<li><a
href="https://www.youtube.com/playlist?list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP">Precalculus
- College Algebra/Trigonometry</a></li>
<li><a
href="https://www.youtube.com/playlist?list=PLF797E961509B4EB5">Calculus
1</a></li>
<li><a
href="https://www.youtube.com/playlist?list=PLDesaqWTN6EQ2J4vgsN1HyBeRADEh4Cw-">Calculus
2</a></li>
<li><a
href="https://www.youtube.com/playlist?list=PLDesaqWTN6ESk16YRmzuJ8f6-rnuy0Ry7">Calculus
3</a></li>
<li><a
href="https://www.youtube.com/playlist?list=PLDesaqWTN6ESPaHy2QUKVaXNZuQNxkYQ_">Differential
Equations</a></li>
<li><a
href="https://www.youtube.com/playlist?list=PLDesaqWTN6ETc1ZwHWijCBcZ2gOvS2tTN">To
The Point Math</a></li>
</ul></li>
<li><a href="https://www.youtube.com/@crashcourse">Crash Course</a></li>
<li><a href="https://www.youtube.com/@harvard">Harvard</a></li>
<li><a href="https://www.youtube.com/@mitocw">MIT
OpenCourseWare</a></li>
<li><a href="https://www.youtube.com/@Mathologer">Mathologer</a></li>
<li><a href="https://www.youtube.com/@TheMathDistrict">The Math
District</a></li>
<li><a href="https://www.youtube.com/@mathematicalmonk">Mathematical
Monk</a></li>
</ul>
<h2 id="tools">Tools</h2>
<ul>
<li><a href="https://www.symbolab.com/">Symbolab</a></li>
<li><a href="https://www.desmos.com/calculator">Desmos</a></li>
<li><a href="http://www.mathwords.com/">Math Words</a></li>
<li><a href="http://www.wolframalpha.com/">Wolfram Alpha</a></li>
<li><a href="https://maxima.sourceforge.io/">Maxima</a></li>
<li><a href="https://www.sympy.org/">Sympy</a></li>
<li><a href="http://www.sagemath.org/">Sagemath</a></li>
<li><a href="https://unitconverters.net">Unit Converter</a></li>
<li><a href="https://www.geogebra.org/?lang=en">GeoGebra</a></li>
<li><a href="http://www2.macaulay2.com/Macaulay2/">Macaulay2</a></li>
<li><a href="https://www.singular.uni-kl.de/">Singular</a></li>
<li><a href="https://www.gnu.org/software/octave/">GNU Octave</a></li>
<li><a href="http://magma.maths.usyd.edu.au/magma/">Magma</a></li>
<li><a href="https://www.maplesoft.com/products/Maple/">Maple</a></li>
<li><a
href="https://www.mathworks.com/products/matlab.html">Matlab</a></li>
<li><a href="https://www.wolfram.com/mathematica/">Wolfram
Mathematica</a></li>
<li><a href="https://freemathapp.org">Free Math</a></li>
<li><a
href="https://chrome.google.com/webstore/detail/xhub/anidddebgkllnnnnjfkmjcaallemhjee">xhub</a></li>
<li><a
href="https://www.copypastemathjax.com/">CopyPasteMathjax</a></li>
</ul>
<h2 id="questions-and-answers">Questions and Answers</h2>
<ul>
<li><a href="http://math.stackexchange.com/">Mathematics Stack
Exchange</a></li>
<li><a href="http://mathoverflow.net/">MathOverflow</a> - for
professional mathematicians</li>
</ul>
<h2 id="encyclopedia">Encyclopedia</h2>
<ul>
<li><a href="https://www.encyclopediaofmath.org">Encyclopedia of
Mathematics</a></li>
<li><a href="http://planetmath.org/">Planetmath</a></li>
<li><a href="https://proofwiki.org/wiki/Main_Page">ProofWiki</a></li>
<li><a href="http://mathworld.wolfram.com/">Wolfram Mathworld</a></li>
<li><a href="https://oeis.org">The On-Line Encyclopedia of Integer
Sequences</a> - Great compendium of many different integer sequences.
Founded 1964 by N. J. A. Sloane.</li>
<li>💲 <a
href="https://press.princeton.edu/books/hardcover/9780691118802/the-princeton-companion-to-mathematics">The
Princeton Companion to Mathematics</a> - Timothy Gowers (Professor,
Fields medallist), June Barrow-Green (Professor), and Imre Leader
(Professor).</li>
<li>💲 <a
href="https://link.springer.com/book/10.1007/978-3-662-52844-0">Encyclopedia
of Distances (4th Edition)</a> - Michel Marie Deza, Elena Deza.</li>
</ul>
<h2 id="books">Books</h2>
<ul>
<li><a href="https://archive.org/details/TarasovCalculus">Calculus:
Basic Concepts for High Schools</a> - L.V. Tarasov</li>
<li><a href="http://www.cis.upenn.edu/~jean/math-basics.pdf">Basics of
Algebra, Topology, and Differential Calculus</a> - Jean Gallier
(University of Pennsylvania)</li>
<li><a
href="http://people.math.gatech.edu/%7Ecain/notes/calculus.html">Multivariable
Calculus</a> - G. Cain, J. Herod (Georgia Tech)</li>
<li><a
href="https://en.wikibooks.org/wiki/Wikibooks:Mathematics_bookshelf">Wikibooks</a></li>
<li><a
href="https://people.math.gatech.edu/~cain/textbooks/onlinebooks.html">Online
Mathematics Textbooks</a></li>
<li><a
href="http://www.wallace.ccfaculty.org/book/Beginning_and_Intermediate_Algebra.pdf">Beginning
and Intermediate Algebra</a></li>
<li><a
href="https://github.com/EbookFoundation/free-programming-books/blob/master/books/free-programming-books-subjects.md#mathematics">Free
Mathematics Books</a></li>
<li><a
href="http://www.mecmath.net/trig/trigbook.pdf">Trigonometry</a></li>
</ul>
<h2 id="magazines">Magazines</h2>
<ul>
<li><a href="https://www.quantamagazine.org/mathematics/">Quanta
Magazine</a> - Features latest research breakthroughs in an accessible
style for non-experts.</li>
<li><a href="https://www.ams.org/journals/bull/all_issues.html">Bulletin
of the American Mathematical Society</a> - Expository articles on
contemporary mathematical research, written in a way that gives insight
to mathematicians who may not be experts in the particular topic.</li>
<li><a
href="http://www.ams.org/cgi-bin/notices/amsnotices.pl?article_id=fullissue&amp;article_type=gallery&amp;gallery_type=fullissue">Notices
of the American Mathematical Society</a> - Publicizes activities of the
Society and features surveys, reports, news, announcements, and opinions
on industry trends, academia, and research.</li>
<li><a href="https://euromathsoc.org/magazine">European Mathematical
Society Magazine</a> - The Magazine features announcements about
meetings and conferences, articles outlining current trends in
scientific development, reports on member societies, and many other
informational items.</li>
<li><a
href="https://ima.org.uk/publications/mathematics-today/">Mathematics
Today by Institute of Mathematics and its Applications</a> - News,
opinions, and articles related to mathematics, so the reader stays
updated.</li>
<li><a href="https://cms.math.ca/publications/crux/">Crux Mathematicorum
by Canadian Mathematical Society</a> - 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.</li>
</ul>
<h2 id="blogs">Blogs</h2>
<ul>
<li><a href="https://betterexplained.com/">BetterExplained</a> -
Maintained by Kalid Azad</li>
<li><a href="http://ilovemaths.com/">ILoveMaths</a> - For grades 6 thru
12 in K-12 system</li>
<li><a href="https://www.3blue1brown.com/">3blue1brown</a> - Animated
Maths</li>
<li><a href="https://www.mathsisfun.com">Mathsisfun</a> simple text
lightweight site for students up to highschool</li>
<li><a
href="https://calculus123.com/wiki/Peter_Saveliev">MathematicsIsAScience</a>
- Peter Saveliev (Professor of mathematics at Marshall University,
Huntington WV, USA)</li>
</ul>
<h2 id="misc">Misc</h2>
<ul>
<li><a href="https://en.wikipedia.org/wiki/Areas_of_mathematics">Areas
of mathematics on Wikipedia</a></li>
<li><a href="http://tutorial.math.lamar.edu/">Paul’s Online Math
Notes</a> - Paul Dawkins (Lamar University)</li>
<li><a href="http://faculty.atu.edu/mfinan/nnotes.html">List of
electronic textbooks</a> - Marcel B. Finan (Arkansas Tech
University)</li>
<li><a href="http://at.yorku.ca/topology/">Topology Atlas</a></li>
<li><a
href="http://djm.cc/library/Recreations_in_Mathematics_Licks_edited.pdf">Recreations
in Math</a> - H. E. Licks (1917)</li>
<li><a
href="http://djm.cc/library/Magic_Squares_Cubes_Andrews_edited.pdf">Magic
Squares and Cubes</a> - W. S. Andrews (1917)</li>
<li><a href="https://web.stanford.edu/~boyd/cvxbook/">Convex
Optimization</a> - Stephen Boyd and Lieven Vandenberghe</li>
<li><a href="https://fabricebaudoin.wordpress.com/">Fabrice Baudoin’s
Notes</a> - Both research and lecture notes on many topics, Including
Diffusions on foliated manifold, Stochastic Calculus, Global analysis in
Dirichlet spaces, and more.</li>
</ul>
<h1 id="branches-of-mathematics">Branches of Mathematics</h1>
<p><strong>Content Format</strong><br />
📖 Books<br />
🎥 Videos<br />
📝 Lecture notes, slides, articles, papers</p>
<h2 id="foundations-of-mathematics">Foundations of Mathematics</h2>
<h3 id="transition-to-pure-rigour-math">Transition To Pure Rigour
Math</h3>
<ul>
<li>📝 <a href="http://www.trillia.com/zakon1.html">Basic Concepts of
Mathematics</a> - Elias Zakon</li>
<li>📝 <a href="https://www.people.vcu.edu/~rhammack/BookOfProof/">Book
of Proof</a> - Richard Hammak (Virginia Commonwealth University)</li>
<li>📖💲 <a
href="https://www.cambridge.org/highereducation/books/how-to-prove-it/6D2965D625C6836CD4A785A2C843B3DA">How
to Prove It: A Structured Approach (3rd Edition)</a> - Daniel J.
Velleman (Professor).</li>
</ul>
<h3 id="set-theory">Set Theory</h3>
<ul>
<li>📝 <a
href="http://www.cosc.brocku.ca/~duentsch/papers/methprimer1.html">Sets,
Relations, Functions</a> - Ivo Düntsch, Günther Gediga</li>
<li>📝 <a href="http://www.math.toronto.edu/weiss/set_theory.pdf">An
Introduction to Set Theory</a> - William A. R. Weiss</li>
<li>📝 <a href="http://www.settheory.net/">Set Theory and Foundations of
Mathematics</a> - Sylvain Poirier</li>
<li>📝 <a href="http://plato.stanford.edu/entries/set-theory/">Set
Theory on the Stanford Encyclopedia of Philosophy</a></li>
</ul>
<h3 id="logic">Logic</h3>
<ul>
<li>📝 <a
href="https://pdfs.semanticscholar.org/6967/f52773d9c2ccfc94658657a5761e0f00e95a.pdf">Introduction
to Logic</a> - Michael Genesereth, Eric Kao (Stanford University)</li>
<li>📝 <a href="https://www.fecundity.com/codex/forallx.pdf">An
Introduction to Formal Logic</a> - P.D. Magnus (University at
Albany)</li>
<li>📝 <a href="http://euclid.trentu.ca/math/sb/pcml/pcml-16.pdf">A
Problem Course in Mathematical Logic</a> - Stefan Bilaniuk (Trent
University)</li>
<li>📝 <a
href="http://poincare.matf.bg.ac.rs/~zarkom/Book_Math__Cutland_Computability.pdf">Computability
- An introduction to recursive function theory</a> - Nigel Cutland
(University of Hull)</li>
<li>📝 <a
href="http://homepages.uc.edu/~martinj/Symbolic_Logic/341%20Syllabus,%20Textbook,%20Handouts,%20Notes/LPL%20textbook.pdf">Language,
Proof, and Logic</a> - Jon Barwise, John Etchemendy</li>
<li>📝 <a
href="http://www.mathematik.uni-muenchen.de/~schwicht/lectures/logic/ws03/ml.pdf">Mathematical
Logic</a> - Helmut Schwichtenberg</li>
<li>📝 <a
href="http://www.personal.psu.edu/t20/notes/logic.pdf">Mathematical
Logic</a> - Stephen G. Simpson (Pennsylvania State University)</li>
<li>📝 <a
href="http://maude.sip.ucm.es/~miguelpt/papers/flogic.pdf">Formal
Logic</a> - Miguel Palomino</li>
<li>📝 <a
href="https://web.math.princeton.edu/~nelson/books/pa.pdf">Predictive
Arithmetic</a> - Edward Nelson</li>
<li>📝 <a
href="http://people.uleth.ca/~dave.morris/books/proofs+concepts.html">Proofs
and Concepts: the fundamentals of abstract mathematics</a> - Joy Morris,
Dave Morris</li>
<li>📝 <a href="https://www.tedsundstrom.com/mathreasoning">Mathematical
Reasoning: Writing and Proof</a> - Ted Sundstrom</li>
<li>📝 <a href="http://leanprover.github.io/logic_and_proof/">Logic and
Proof</a> - Jeremy Avigad, Robert Y. Lewis, and Floris van Doorn</li>
<li>📝 <a href="https://teorth.github.io/QED">QED - an interactive
textbook</a> - Terence Tao</li>
<li>📝 <a href="http://builds.openlogicproject.org/">Open Logic
Textbook</a> - collaborative effort, main contributors listed <a
href="https://openlogicproject.org/people/">here</a></li>
</ul>
<h3 id="category-theory">Category Theory</h3>
<ul>
<li>📝 <a
href="http://www.mathematik.tu-darmstadt.de/~streicher/CTCL.pdf">Introduction
to Category Theory and Categorical Logic</a> - Thomas Streicher</li>
<li>📝 <a href="http://www.cs.man.ac.uk/~hsimmons/zCATS.pdf">An
Introduction to Category Theory</a> - Harold Simmons</li>
<li>📝 <a
href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.211.4754&amp;rep=rep1&amp;type=pdf">Category
Theory</a> - Steve Awodey (Carnegie Mellon University)</li>
<li>📝 <a
href="http://www.mathematik.uni-muenchen.de/~pareigis/Vorlesungen/04SS/Cats1.pdf">Category
Theory</a> - B. Pareigis</li>
<li>📝 <a
href="https://web.archive.org/web/20181221233252/http://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf">Category
Theory for Computing Science</a> - Michael Barr, Charles Wells</li>
<li>📝 <a
href="http://www.tac.mta.ca/tac/reprints/articles/12/tr12.pdf">Toposes,
Triples and Theories</a> - Michael Barr, Charles Wells</li>
<li>📝 <a
href="http://www.tac.mta.ca/tac/reprints/articles/3/tr3abs.html">Abelian
Categories</a> - Peter Freyd</li>
<li>📝 <a
href="http://www.tac.mta.ca/tac/reprints/articles/7/tr7abs.html">Categories
and Groupoids</a> - P. J. Higgins</li>
<li>📝 <a
href="http://www.tac.mta.ca/tac/reprints/articles/10/tr10abs.html">Basic
Concepts of Enriched Category Theory</a> - G. M. Kelley</li>
<li>📝 <a
href="http://www.tac.mta.ca/tac/reprints/articles/17/tr17abs.html">Abstract
and Concrete Categories: The Joy of Cats</a> - Jiri Adamek, Horst
Herrlich, George Strecker</li>
<li>📝 <a
href="http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf">Seven
Sketches in Compositionality: An Invitation to Applied Category
Theory</a> - Brendan Fong and David I. Spivak (MIT)</li>
<li>📝 <a href="http://www.math.jhu.edu/~eriehl/context/">Category
Theory in Context</a> - Emily Riehl (John Hopkins University)</li>
</ul>
<h3 id="type-theory">Type Theory</h3>
<ul>
<li>📝 <a href="http://www.paultaylor.eu/stable/prot.pdf">Proofs and
Types</a> - Jean-Yves Girard</li>
<li>📝 <a
href="https://archive-pml.github.io/martin-lof/pdfs/Bibliopolis-Book-retypeset-1984.pdf">Intuitionistic
Type Theory</a> - Per Martin-Lof</li>
<li>📝 <a href="https://www.cs.kent.ac.uk/people/staff/sjt/TTFP/">Type
Theory and Functional Programming</a> - Simon Thompson</li>
<li>📝 <a
href="http://www.cse.chalmers.se/research/group/logic/book/book.pdf">Programming
in Martin-Lof’s Type Theory</a> - Bengt Nordstrom, Kent Petersson, Jan
M. Smith</li>
</ul>
<h3 id="homotopy-type-theory">Homotopy Type Theory</h3>
<ul>
<li>📝 <a
href="https://hottheory.files.wordpress.com/2013/03/hott-online-611-ga1a258c.pdf">Homotopy
Type Theory</a></li>
</ul>
<h3 id="surreal-numbers">Surreal Numbers</h3>
<ul>
<li>📝 <a
href="http://www.math.harvard.edu/~knill/teaching/mathe320_2015_fall/blog15/surreal1.pdf">Surreal
Numbers - How two ex-students turned on to pure mathematics and found
total happiness</a> - D. E. Knuth</li>
<li>📝 <a href="http://web.mit.edu/sp.268/www/2010/surreal.pdf">Surreal
Numbers and Games</a></li>
<li>📝 <a
href="http://www.ohio.edu/people/ehrlich/ConwayNames.pdf">Conway names,
the simplicity hierarchy and the surreal number tree</a> - Philip
Ehrlich</li>
</ul>
<h2 id="number-theory">Number Theory</h2>
<ul>
<li>📝 <a href="http://wstein.org/ent/ent.pdf">Elementary Number Theory:
Primes, Congruences, and Secrets</a> - William Stein</li>
<li>📝 <a
href="http://math.utoledo.edu/~codenth/Spring_13/3200/ENT-books/Elementary_Number_Theory-Clark.pdf">Elementary
Number Theory</a> - W. Edwin Clark (University of South Florida)</li>
<li>📝 <a href="http://www.maths.qmul.ac.uk/~pjc/notes/nt.pdf">A Course
on Number Theory</a> - Peter J. Cameron</li>
<li>📝 <a href="http://shoup.net/ntb/ntb-v2.pdf">A Computational
Introduction to Number Theory and Algebra</a> - Victor Shoup</li>
<li>📝 <a href="http://alpha.math.uga.edu/~pete/4400FULL.pdf">Number
Theory: A Contemporary Introduction</a> - Pete L. Clark</li>
<li>📝 <a href="http://www.trillia.com/moser-number.html">An
Introduction to the Theory of Numbers</a> - Leo Moser</li>
<li>📝 <a href="https://www.poritz.net/jonathan/share/yaintt/">Yet
Another Introductory Number Theory Textbook</a> - Jonathan A.
Poritz</li>
</ul>
<h3 id="algebraic-number-theory">Algebraic Number Theory</h3>
<ul>
<li>📝 <a
href="http://www1.spms.ntu.edu.sg/~frederique/ANT10.pdf">Introduction to
Algebraic Number Theory</a></li>
<li>📝 <a
href="http://www1.spms.ntu.edu.sg/~frederique/ANT10.pdf">Introduction to
Algebraic Number Theory</a> - F. Oggier</li>
<li>📝 <a
href="http://www.jmilne.org/math/CourseNotes/ANT.pdf">Algebraic Number
Theory</a> - J.S. Milne</li>
<li>📝 <a
href="http://people.math.gatech.edu/~mbaker/pdf/ANTBook.pdf">Algebraic
Number Theory Course Notes</a> - Matthew Baker (Georgia Tech)</li>
<li>📝 <a href="http://www.math.uiuc.edu/~r-ash/ANT.html">A Course In
Algebraic Number Theory</a> - Robert Ash</li>
</ul>
<h3 id="analytic-number-theory">Analytic Number Theory</h3>
<ul>
<li>📝 <a
href="http://www.math.uiuc.edu/~hildebr/ant/main.pdf">Introduction to
Analytic Number Theory</a> - A.J. Hildebrand (University of
Illinois)</li>
<li>📝 <a
href="http://math.nsc.ru/~vdovin/lectures/numth_eng.pdf">Elements of
Analytic Number Theory</a> - P. S. Kolesnikov, E. P. Vdovin
(Novosibirsk)</li>
<li>📝 <a
href="http://www.mathematik.uni-muenchen.de/~forster/v/ann/annth_all.pdf">Analytic
Number Theory</a> - Otto Forster (LMU Munich)</li>
<li>📝 <a
href="http://www2.math.uu.se/~astrombe/analtalt08/www_notes.pdf">Analytic
Number Theory - Lecture Notes based on Davenport’s book</a> - Andreas
Strömbergsson</li>
</ul>
<h2 id="algebra">Algebra</h2>
<ul>
<li>📝 <a
href="http://www.math.uwaterloo.ca/~snburris/htdocs/ualg.html">A Course
in Universal Algebra</a> - S. Burris, H.P. Sankappanavar</li>
<li>📝 <a href="https://faculty.math.illinois.edu/~r-ash/ComAlg.html">A
Course in Commutative Algebra</a> - Robert Ash</li>
<li>📝 <a
href="http://djm.cc/library/First_Algebra_Hawkes_Luby_Touton_edited.pdf">First
Course in Algebra</a> - Herbert E. Hawkes, William A. Luby, Frank C.
Touton (1910)</li>
<li>📝 <a
href="http://djm.cc/library/Second_Algebra_Hawkes_Luby_Touton_edited.pdf">Second
Course in Algebra</a> - Herbert E. Hawkes, William A. Luby, Frank C.
Touton (1911)</li>
<li>📝 <a
href="http://djm.cc/library/Algebra_Elementary_Text-Book_Part_I_Chrystal_edited.pdf">Algebra:
An Elementary Text-Book, Part I</a> - G. Chrystal (1904)</li>
<li>📝 <a
href="http://djm.cc/library/Algebra_Elementary_Text-Book_Part_II_Chrystal_edited02.pdf">Algebra:
An Elementary Text-Book, Part II</a> - G. Chrystal (1900)</li>
<li>📝 <a href="https://jamesbrennan.org/algebra">Understanding
Algebra</a> - James W. Brennan</li>
</ul>
<h3 id="abstract-algebra">Abstract Algebra</h3>
<ul>
<li>📝 <a
href="https://zodml.org/sites/default/files/Introduction_to_Abstract_Algebra_0.pdf">Introduction
to Abstract Algebra</a> - D. S. Malik, John N. Mordeson, M.K. Sen
(Creighton University)</li>
<li>📝 <a
href="http://aleph0.clarku.edu/~djoyce/ma225/algebra.pdf">Introduction
to Modern Algebra</a> - David Joyce (Clark University)</li>
<li>📝 <a
href="http://www1.spms.ntu.edu.sg/~frederique/AA11.pdf">Algebraic
Methods</a> - F. Oggier</li>
<li>📝 <a
href="http://abstract.ups.edu/download/aata-20150812.pdf">Abstract
Algebra : Theory and Applications</a> - Thomas W. Judson, Robert A.
Beezer (Austin State University)</li>
<li>📝 <a href="http://www.maths.usyd.edu.au/u/bobh/UoS/rfwhole.pdf">An
Undergraduate Course in Abstract Algebra</a> - Robert Howlett</li>
<li>📝 <a href="http://www.math.miami.edu/~ec/book">Elements of Abstract
and Linear Algebra</a> - E.H. Connell (University of Miami)</li>
<li>📝 <a href="http://www.math.uiuc.edu/~r-ash/Algebra.html">Abstract
Algebra: The Basic Graduate Year</a> - Robert Ash</li>
<li>📝 <a
href="https://web.archive.org/web/20150528171650/extension.harvard.edu/open-learning-initiative/abstract-algebra">Abstract
Algebra: Harvard Extension (Archived)</a> - Benedict Gross</li>
<li>📝 <a
href="https://www.youtube.com/playlist?list=PLA58AC5CABC1321A3">Abstract
Algebra: Harvard Extension Videos</a> - Benedict Gross</li>
</ul>
<h3 id="group-theory">Group Theory</h3>
<ul>
<li>📝 <a href="https://www2.bc.edu/mark-reeder/Groups.pdf">Notes on
Group Theory</a> - Mark Reeder</li>
<li>📝 <a href="http://www.jmilne.org/math/CourseNotes/GT.pdf">Group
Theory</a> - J.S. Milne</li>
<li>📝 <a href="http://www.maths.qmul.ac.uk/~pjc/notes/gt.pdf">Notes on
Finite Group Theory</a> - Peter J. Cameron</li>
<li>📝 <a href="http://www.cns.gatech.edu/GroupTheory/index.html">Group
Theory</a> - Pedrag Civitanovic</li>
</ul>
<h3 id="linear-algebra">Linear Algebra</h3>
<ul>
<li>📝 <a href="http://www.math.ubc.ca/~carrell/NB.pdf">Fundamentals of
Linear Algebra</a> - James B. Carrell</li>
<li>📝 <a
href="https://web.archive.org/web/20140824074655/http://mathstat.helsinki.fi/~fluch/linear_algebra_1-sp07/la1.pdf">Linear
Algebra and Matrices</a> - Martin Fluch</li>
<li>📝 <a
href="http://www.maths.usyd.edu.au/u/bobh/UoS/MATH2902/vswhole.pdf">Vector
Space Theory</a> - Robert Howlett</li>
<li>📝 <a href="http://joshua.smcvt.edu/linearalgebra">Linear
Algebra</a> - Jim Hefferon</li>
<li>📝 <a
href="https://github.com/juanklopper/MIT_OCW_Linear_Algebra_18_06">MIT
OpenCourseWare Lectures on Linear Algebra (18.06) as Jupyter
Notebooks</a> - Juan Klopper</li>
<li>📝 <a href="http://www.numbertheory.org/book/">Elementary Linear
Algebra</a> - Keith Matthews</li>
<li>📝 <a href="http://linear.ups.edu/">A First Courses in Linear
Algebra</a> - Rob Breezer</li>
<li>📝 <a href="https://www.math.ucdavis.edu/~linear/">Linear
Algebra</a> - David Cherney, Tom Denton, Andrew Waldron</li>
<li>📝 <a
href="http://oaktrust.library.tamu.edu/handle/1969.1/2502">Introduction
to vectors and tensors, Vol 1: linear and multilinear algebra</a> - Ray
M Bowen, C. C. Wang</li>
<li>📝 <a
href="http://oaktrust.library.tamu.edu/handle/1969.1/3609">Introduction
to vectors and tensors, Vol 2: vector and tensor analysis</a> - Ray M
Bowen, C. C. Wang</li>
<li>📝 <a
href="https://web.stanford.edu/~boyd/vmls/vmls.pdf">Introduction to
Applied Linear Algebra</a> - Stephen Boyd (Stanford University), Lieven
Vandenberghe (UCLA)</li>
<li>📝 <a
href="https://www.math.brown.edu/~treil/papers/LADW/LADW_2017-09-04.pdf">Linear
Algebra Done Wrong</a> - Sergei Treil</li>
<li>📝 <a href="http://immersivemath.com/ila/index.html">Immersive
Linear Algebra</a> - J. Ström, K. Åström, and T. Akenine-Möller</li>
<li>📝 <a href="https://textbooks.math.gatech.edu/ila/">Interactive
Linear Algebra</a> - Dan Margalit and Joseph Rabinoff</li>
<li>📝 <a
href="https://people.math.gatech.edu/~herod/Hspace/Hspace.html">Linear
Algebra, Infinite Dimensions, and Maple</a> - James Herod</li>
</ul>
<h3 id="ring-theory">Ring Theory</h3>
<ul>
<li>📝 <a
href="http://www.math.uni-duesseldorf.de/~wisbauer/book.pdf">Foundations
of Module and Ring Theory</a> - Robert Wisbauer (University of
Düsseldorf)</li>
</ul>
<h3 id="galois-theory">Galois Theory</h3>
<ul>
<li>📝 <a href="http://www.maths.gla.ac.uk/~ajb/dvi-ps/Galois.pdf">An
Introduction to Galois Theory</a> - Andrew Baker (University of
Glasgow)</li>
<li>📝 <a href="http://www.jmilne.org/math/CourseNotes/FT.pdf">Fields
and Galois Theory</a> - J.S. Milne</li>
<li>📝 <a
href="http://homepages.warwick.ac.uk/~masda/MA3D5/Galois.pdf">Galois
theory</a> - Miles Reid</li>
<li>📝 <a
href="https://math.illinoisstate.edu/schebol/teaching/407-14-files/Stewart-galois_theory.pdf">Galois
Theory</a> - Ian Stewart</li>
</ul>
<h3 id="lie-algebras">Lie Algebras</h3>
<ul>
<li>📝 <a
href="http://www.math.harvard.edu/~shlomo/docs/lie_algebras.pdf">Lie
Algebras</a> - Shlomo Sternberg</li>
</ul>
<h2 id="combinatorics">Combinatorics</h2>
<ul>
<li>📝 <a href="http://www.math.utk.edu/~wagner/papers/comb.pdf">Basic
Combinatorics</a> - Carl G. Wagner (University of Tennessee)</li>
<li>📝 <a href="http://people.math.gatech.edu/~trotter/book.pdf">Applied
Combinatorics</a> - Mitchel T. Keller, William T. Trotter</li>
<li>📝 <a href="http://www.maths.qmul.ac.uk/~pjc/notes/comb.pdf">Notes
on Combinatorics</a> - Peter J. Cameron</li>
<li>📝 <a
href="http://algo.inria.fr/flajolet/Publications/book.pdf">Analytic
Combinatorics</a> - Philippe Flajolet, Robert Sedgewick</li>
<li>📝 <a
href="http://www.math.upenn.edu/~wilf/DownldGF.html">generatingfunctionology</a>
- Herbert Wilf</li>
</ul>
<h3 id="graph-theory">Graph Theory</h3>
<ul>
<li>📝 <a href="http://www.personal.psu.edu/cxg286/Math485.pdf">Graph
Theory: Lecture Notes</a> - Christopher Griffin</li>
<li>📝 <a
href="http://www.cs.unibo.it/babaoglu/courses/cas00-01/tutorials/GraphTheory.pdf">Graph
Theory</a> - Reinhard Diestel</li>
</ul>
<h2 id="geometry-and-topology">Geometry and Topology</h2>
<ul>
<li>📝 <a
href="http://polly.phys.msu.ru/~belyaev/geometry.pdf">Fundamentals of
Geometry</a> - Oleg A. Belyaev</li>
<li>📝 <a href="https://www.math.upenn.edu/~wilf/AeqB.html">A=B</a> - M.
Petkovsek, H. Wilf, D. Zeilberger</li>
<li>📝 <a
href="http://aleph0.clarku.edu/~djoyce/java/elements/toc.html">Elements</a>
- Euclid</li>
<li>📝 <a href="http://starrhorse.com/euclid/">Euclid’s Elements
Redux</a> - Daniel Callahan</li>
<li>📝 <a
href="http://www.math.ubc.ca/~cass/graphics/manual/">Mathematical
Illustrations</a> - Bill Casselman</li>
<li>📝 <a href="https://www.c82.net/euclid/">Byrne’s Euclid</a> - Oliver
Byrne</li>
<li>📝 <a
href="http://djm.cc/library/Plane_Geometry_Wentworth_Smith_edited.pdf">Plane
Geometry</a> - George Wentworth and David Eugene Smith (1913)</li>
<li>📝 <a
href="http://djm.cc/library/Plane_Spherical_Trigonometry_Wentworth_Smith_edited_2.pdf">Planes
and Spherical Trigonometry</a> - George Wentworth and David Eugene Smith
(1915)</li>
<li>📝 <a
href="http://djm.cc/library/Coordinate_Geometry_Fine_Thompson_edited03.pdf">Coordinate
Geometry</a> - Henry Buchard Fine and Henry Dallas Thompson (1911)</li>
<li>📝 <a
href="http://djm.cc/library/Analytic_Geometry_Siceloff_Wentworth_Smith_edited.pdf">Analytic
Geometry</a> - Lewis Parker Siceloff, George Wentworth, David Eugene
Smith (1922)</li>
</ul>
<h3 id="differential-geometry">Differential Geometry</h3>
<ul>
<li>📝 <a
href="https://people.math.ethz.ch/~salamon/PREPRINTS/diffgeo.pdf">Introduction
to Differential Geometry</a> - Joel W. Robbin, Dietmar A. Salamon</li>
<li>📝 <a href="http://www.seas.upenn.edu/~jean/diffgeom.pdf">Notes on
Differential Geometry and Lie Groups</a> - Jean Gallier (University of
Pennsylvania)</li>
<li>📝 <a href="http://www.mat.univie.ac.at/~michor/dgbook.pdf">Topics
in Differential Geometry</a> - Peter W. Michor</li>
<li>📝 <a
href="http://mysite.science.uottawa.ca/rossmann/Differential%20Geometry%20book_files/Diffgeo.pdf">Lectures
on Differential Geometry</a> - Wulf Rossmann</li>
<li>📝 <a
href="http://www.matematik.lu.se/matematiklu/personal/sigma/Riemann.pdf">An
Introduction to Riemannian Geometry</a> - Sigmundur Gudmundsson (Lund
University)</li>
<li>📝 <a href="http://msri.org/publications/books/gt3m/">The Geometry
and Topology of Three-Manifolds</a> - W. Thurston</li>
<li>📝 <a
href="http://www.math.harvard.edu/~shlomo/docs/semi_riemannian_geometry.pdf">Semi-Riemann
Geometry and General Relativity</a> - Shlomo Sternberg</li>
<li>📝 <a
href="http://www.cs.cmu.edu/~kmcrane/Projects/DDG/paper.pdf">Discrete
Differential Geometry</a> - Keenan Crane</li>
</ul>
<h3 id="algebraic-geometry">Algebraic Geometry</h3>
<ul>
<li>📝 <a
href="https://ksda.ccny.cuny.edu/PostedPapers/rickksda1107.pdf">A Brief
Introduction to Algebraic Geometry</a> - R.C. Churchill</li>
<li>📝 <a
href="http://www.math.lsa.umich.edu/~idolga/631.pdf">Introduction to
Algebraic Geometry</a> - Igor V. Dolgachev</li>
<li>📝 <a
href="http://math.stanford.edu/~vakil/216blog/FOAGjun1113public.pdf">Foundations
of Algebraic Geometry</a> - Ravi Vakil</li>
<li>📝 <a href="http://www.cis.upenn.edu/~jean/algeoms.pdf">Algebraic
Geometry</a> - Jean Gallier, Stephen S. Shatz (University of
Pennsylvania)</li>
<li>📝 <a href="http://www.jmilne.org/math/CourseNotes/AG.pdf">Algebraic
Geometry</a> - J.S. Milne</li>
<li>📝 <a
href="http://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2002/main.pdf">Algebraic
Geometry</a> - Andreas Gathmann (University of Kaiserslautern)</li>
<li>📝 <a href="https://stacks.math.columbia.edu/">The Stacks
Project</a> - Maintained by Aise Johan de Jong (Columbia)</li>
</ul>
<h3 id="algebraic-statistics">Algebraic Statistics</h3>
<ul>
<li>📝 <a href="https://math.berkeley.edu/~bernd/owl.pdf">Lectures on
Algebraic Statistics</a> - Mathias Drton, Bernd Sturmfels, Seth
Sullivant</li>
<li>📝 <a
href="https://www3.diism.unisi.it/~chiantini/did/00Book.pdf">An
Introduction to Algebraic Statistics</a> - Cristiano Bocci, Luca
Chiantini and Anthony V. Geramita</li>
<li>📝 <a
href="https://tore.tuhh.de/dspace-cris-server/api/core/bitstreams/a0c378d5-ce8e-442a-8891-9e7f763b4279/content">Algebraic
Statistics</a> - Karl-Heinz Zimmermann</li>
<li>📝 <a
href="http://yaroslavvb.com/papers/pachter-algebraic.pdf">Algebraic
Statistics for Computational Biology</a> - Pachter, and Sturmfels.</li>
</ul>
<h3 id="topology">Topology</h3>
<ul>
<li>📝 <a
href="https://www.math.upenn.edu/~ghrist/notes.html">Elementary Applied
Topology</a> - Robert Ghrist (UPenn)</li>
<li>📝 <a
href="http://www.math.colostate.edu/~renzo/teaching/Topology10/Notes.pdf">Introduction
to Topology</a></li>
<li>📝 <a
href="http://www.math.bme.hu/~kalex/Teaching/Spring10/Topology/TopNotes_Spring10.pdf">Introduction
to Topology</a> - Alex Küronya</li>
<li>📝 <a
href="http://www.math.clemson.edu/~jimlb/Teaching/2009-10/Math986/Topology.pdf">Introductory
Topology</a> - Jim L. Brown</li>
<li>📝 <a
href="http://webusers.imj-prg.fr/~pierre.schapira/lectnotes/Topo.pdf">General
Topology</a> - Pierre Schapira (Paris VI University)</li>
<li>📝 <a
href="http://www.pdmi.ras.ru/~olegviro/topoman/eng-book-nopfs.pdf">Elementary
Topology Problem Textbook</a></li>
<li>📝 <a
href="http://www.math.ku.dk/~moller/e03/3gt/notes/gtnotes.pdf">General
Topology</a> - Jesper M. Møller</li>
<li>📝 <a href="http://mathonline.wikidot.com/topology">Topology
Topics</a></li>
</ul>
<h3 id="algebraic-topology">Algebraic Topology</h3>
<ul>
<li>📝 <a
href="http://www.math.cornell.edu/~hatcher/AT/AT.pdf">Algebraic
Topology</a> - Allen Hatcher</li>
<li>📝 <a
href="http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf">A
Concise Course in Algebraic Topology</a> - J. P. May</li>
<li>📝 <a href="http://www.math.muni.cz/~cadek/at/at.pdf">Introduction
to Algebraic Topology</a> - Martin Cadek</li>
<li>📝 <a
href="http://webusers.imj-prg.fr/~pierre.schapira/lectnotes/AlTo.pdf">Algebra
and Topology</a> - Pierre Schapira (Paris VI University)</li>
<li>📝 <a
href="http://www.indiana.edu/~jfdavis/teaching/m623/book.pdf">Lecture
Notes in Algebraic Topology</a> - James F. Davis, Paul Kirk (Indiana
University)</li>
<li>📝 <a
href="https://www.ma.utexas.edu/ibl1/courses/resources/12_15_07_grad_alg_top_mooremethod.pdf">Algebraic
Topology</a> - Michael Starbird</li>
<li>📝 <a href="http://www.math.nus.edu.sg/~matwujie/ma5209.pdf">Lecture
Notes on Algebraic Topology</a> - Jie Wu</li>
</ul>
<h2 id="analysis">Analysis</h2>
<h3 id="real-analysis">Real Analysis</h3>
<ul>
<li>📝 <a
href="https://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/">MIT
OpenCourseWare Lectures on Calculus</a> - G. Strang</li>
<li>📝 <a href="http://www.math.wisc.edu/~keisler/calc.html">Elementary
Calculus: An Approach Using Infinitesimals</a> - Professor H. Jerome
Keisler</li>
<li>📝 <a
href="https://www.math.ucdavis.edu/~hunter/intro_analysis_pdf/intro_analysis.pdf">An
Introduction to Real Analysis</a> - John K. Hunter (University of
California at Davis)</li>
<li>📝 <a
href="http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF">Introduction
to Real Analysis</a> - William F. Trench (Trinity University,
Texas)</li>
<li>📝 <a href="http://www.jirka.org/ra/realanal.pdf">Basic Analysis:
Introduction to Real Analysis</a> - Jiří Lebl</li>
<li>📝 <a
href="http://prac.im.pwr.wroc.pl/~kwasnicki/pl/stuff/tbb-hyper.pdf">Elementary
Real Analysis</a> - Thomson, Bruckner</li>
<li>📝 <a
href="http://ms.mcmaster.ca/~sawyer/Publications/Real_Analysis.pdf">Lecture
Notes in Real Analysis</a> - Eric T. Sawyer (McMaster University)</li>
<li>📝 <a
href="http://math.harvard.edu/~ctm/papers/home/text/class/harvard/212a/course/course.pdf">Real
Analysis</a> - C. McMullen</li>
<li>📝 <a href="http://bass.math.uconn.edu/3rd.pdf">Real Analysis for
Graduate Students</a> - Richard F. Bass</li>
<li>📝 <a
href="http://www.math.purdue.edu/~torres/pubs/Modern-real-analysis.pdf">Modern
Real Analysis</a> - William P. Ziemer (Indiana University)</li>
<li>📝 <a
href="http://www.trillia.com/zakon-analysisI.html">Mathematical Analysis
Vol I</a> - Elias Zakon</li>
<li>📝 <a
href="http://www.trillia.com/zakon-analysisII.html">Mathematical
Analysis Vol II</a> - Elias Zakon</li>
<li>📝 <a
href="http://www.math.harvard.edu/~shlomo/docs/Advanced_Calculus.pdf">Advanced
Calculus</a> - Lynn Loomis, Schlomo Sternberg</li>
<li>📝 <a
href="http://spot.colorado.edu/~baggett/analysis.html">Analysis of
Functions of a Single Variable</a> - Lawerence Baggett</li>
<li>📝 <a
href="http://www.synechism.org/wp/the-calculus-of-functions-of-several-variables/">The
Calculus of Functions of Several Variables</a> - Dan Sloughter</li>
<li>📝 <a href="http://web.pdx.edu/~erdman/PTAC/problemtext_pdf.pdf">A
ProblemText in Advanced Calculus</a> - John M. Erdman</li>
<li>📝 <a
href="http://hdl.handle.net/2027/spo.5597602.0001.001">Calculus and
Linear Algebra. Vol. 1</a> - Wilfred Kaplan, Donald J. Lewis</li>
<li>📝 <a
href="https://quod.lib.umich.edu/s/spobooks/5597602.0002.001">Calculus
and Linear Algebra. Vol. 2</a> - Wilfred Kaplan, Donald J. Lewis</li>
<li>📝 <a
href="http://www.math.odu.edu/~jhh/counter10.html">Introduction to
Calculus I and II</a> - J.H. Heinbockel</li>
<li>📝 <a
href="http://faculty.gvsu.edu/boelkinm/Home/Active_Calculus.html">Active
Calculus</a> - Matt Boelkins</li>
<li>📝 <a
href="https://math.berkeley.edu/~gbergman/ug.hndts/#Rudin">Supplements
to the Exercises in Chapters 1-7 of Walter Rudin’s “Principles of
Mathematical Analysis”</a> - George M. Bergman</li>
<li>📝 <a href="http://calculusmadeeasy.org/">Calculus Made Easy</a> -
Silvanus P. Thompson (1910)</li>
<li>📝 <a
href="http://djm.cc/library/Elements_Differential_Integral_Calculus_Granville_edited_2.pdf">Elements
of Differential and Integral Calculus</a> - William Anthony Granville
(1911)</li>
<li>📝 <a
href="https://stitz-zeager.com/szprecalculus07042013.pdf">Precalculus</a>
- Carl Stitz, Jeff Zeager</li>
</ul>
<h3 id="harmonic-analysis">Harmonic Analysis</h3>
<ul>
<li>📝 <a
href="http://www.math.uiuc.edu/~laugesen/545/545Lectures.pdf">Harmonic
Analysis Lecture Notes</a> - Richard S. Laugesen (University of Illinois
at Urbana–Champaign)</li>
<li>📝 <a
href="http://www.math.uchicago.edu/~schlag/harmonicnotes.pdf">Harmonic
Analysis</a> - W. Schlag</li>
<li>📝 <a
href="https://see.stanford.edu/materials/lsoftaee261/book-fall-07.pdf">Lecture
Notes: Fourier Transform and its Applications</a> - Brad Osgood</li>
<li>📝 <a
href="http://www.reed.edu/physics/courses/Physics331.f08/pdf/Fourier.pdf">Fourier
Analysis</a> - Lucas Illing</li>
<li>📝 <a href="https://ccrma.stanford.edu/~jos/mdft">Mathematics of the
Discrete Fourier Transform (DFT) with Audio Applications</a> - Julius O.
Smith III (Stanford University)</li>
</ul>
<h3 id="complex-analysis">Complex Analysis</h3>
<ul>
<li>📝 <a
href="https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/complex.pdf">Introduction
to Complex Analysis</a> - Michael Taylor</li>
<li>📝 <a
href="http://www.math.uiuc.edu/~jpda/jpd-complex-geometry-book-5-refs-bip.pdf">An
Introduction to Complex Analysis and Geometry</a> - John P. D’Angelo
(University of Illinois)</li>
<li>📝 <a href="http://math.sfsu.edu/beck/papers/complex.pdf">A First
Course in Complex Analysis</a> - Matthias Beck, Gerald Marchesi, Dennis
Pixton, Lucas Sabalka</li>
<li>📝 <a href="http://www.math.wustl.edu/~sk/books/guide.pdf">A Guide
to Complex Variables</a> - Steven G. Krantz</li>
<li>📝 <a
href="http://www.maths.manchester.ac.uk/~cwalkden/complex-analysis/complex_analysis.pdf">Complex
Analysis</a> - Charles Walkden</li>
<li>📝 <a href="http://www.math.ku.dk/noter/filer/koman-12.pdf">Complex
Analysis</a> - Christian Berg</li>
<li>📝 <a
href="http://people.math.sc.edu/girardi/m7034/book/AshComplexVariablesWithHyperlinks.pdf">Complex
Variables</a> - R. B. Ash, W.P. Novinger</li>
<li>📝 <a
href="http://www.maths.lth.se/matematiklu/personal/olofsson/CompHT06.pdf">Complex
Analysis</a> - Christer Bennewitz</li>
<li>📝 <a
href="https://web.archive.org/web/20150620124453/https://www.math.washington.edu/~marshall/math_536/Notes.pdf">Complex
Analysis</a> - Donald E. Marshall</li>
<li>📝 <a href="https://gauss.math.yale.edu/~ws442/complex.pdf">A
Concise Course in Complex Analysis and Riemann Surfaces</a> - Wilhelm
Schlag</li>
<li>📝 <a
href="http://people.math.gatech.edu/%7Ecain/winter99/complex.html">Complex
Analysis</a> - G. Cain (Georgia Tech)</li>
<li>📝 <a href="https://complex-analysis.com/">Complex Analysis</a> -
Juan Carlos Ponce Campuzano</li>
</ul>
<h3 id="functional-analysis">Functional Analysis</h3>
<ul>
<li>📝 <a
href="https://www.math.uwaterloo.ca/~lwmarcou/notes/pmath453.pdf">An
Introduction to Functional Analysis</a> - Laurent W. Marcoux (University
of Waterloo)</li>
<li>📝 <a
href="http://users.math.msu.edu/users/jeffrey/920/920notes.pdf">Functional
Analysis: Lecture Notes</a> - Jeff Schenker (Michigan State
University)</li>
<li>📝 <a
href="https://archive.org/details/TB_Ward___Functional_analysis_lecture_notes">Functional
Analysis Lecture Notes</a> - T.B. Ward (University of East Anglia)</li>
<li>📝 <a
href="http://www.maths.lancs.ac.uk/~belton/www/notes/fa_notes.pdf">Functional
Analysis</a> - Alexander C. R. Belton</li>
<li>📝 <a
href="https://www.mat.univie.ac.at/~gerald/ftp/book-fa/fa.pdf">Topics in
Real and Functional Analysis</a> - Gerald Teschl</li>
<li>📝 <a
href="http://www2.math.ou.edu/~cremling/teaching/lecturenotes/fa-new/LN-I.pdf">Functional
Analysis</a> - Christian Remling</li>
<li>📝 <a
href="http://www.math.harvard.edu/~shlomo/docs/Real_Variables.pdf">Theory
of Functions of a Real Variable</a> - Shlomo Sternberg</li>
<li>📝 <a
href="http://spot.colorado.edu/~baggett/functional.html">Functional
Analysis</a> - Lawerence Baggett</li>
</ul>
<h3 id="measure-theory">Measure Theory</h3>
<ul>
<li>📝 <a
href="https://terrytao.files.wordpress.com/2012/12/gsm-126-tao5-measure-book.pdf">An
Introduction to Measure Theory</a> - Terence Tao (UCLA)</li>
<li>📝 <a
href="http://www.mat.uniroma2.it/~cannarsa/cam_0607.pdf">Lecture Notes
on Measure Theory and Functional Analysis</a> - P. Cannarsa, T.
D’Aprile</li>
<li>📝 <a
href="http://www.math.chalmers.se/~borell/MeasureTheory.pdf">Lecture
Notes in Measure Theory</a> - Christer Borell</li>
<li>📝 <a href="http://www.gold-saucer.org/math/lebesgue/lebesgue.pdf">A
Crash Course on the Lebesgue Integral and Measure Theory</a> - Steve
Cheng</li>
<li>📝 <a
href="https://www.math.ucdavis.edu/~hunter/measure_theory/measure_notes.pdf">Measure
Theory</a> - John K. Hunter (University of California at Davis)</li>
<li>📝 <a
href="https://people.math.ethz.ch/~salamon/PREPRINTS/measure.pdf">Measure
and Integration</a> - Dietmar A. Salamon (ETH Zürich)</li>
<li>📝 <a
href="http://www.math.ucsd.edu/~bdriver/240-00-01/Lecture_Notes/measurep.pdf">Lecture
notes: Measure Theory</a> - Bruce K. Driver</li>
</ul>
<h3 id="ordinary-differential-equations">Ordinary Differential
Equations</h3>
<ul>
<li>📝 <a
href="http://www.synechism.org/wp/difference-equations-to-differential-equations/">Difference
Equations To Differential Equations</a> - Dan Sloughter</li>
<li>📝 <a
href="https://www.math.uni-bielefeld.de/~grigor/odelec2008.pdf">Ordinary
Differential Equation</a> - Alexander Grigorian (University of
Bielefeld)</li>
<li>📝 <a
href="http://www.cs.bgu.ac.il/~leonid/ode_bio_files/Ionascu_LectNotes.pdf">Ordinary
Differential Equations: Lecture Notes</a> - Eugen J. Ionascu</li>
<li>📝 <a
href="http://www.math.lmu.de/~philip/publications/lectureNotes/ODE.pdf">Ordinary
Differential Equations</a> - Peter Philip</li>
<li>📝 <a
href="http://users.math.msu.edu/users/gnagy/teaching/ode.pdf">Ordinary
Differential Equations</a> - Gabriel Nagy</li>
<li>📝 <a
href="http://www.mat.univie.ac.at/~gerald/ftp/book-ode/ode.pdf">Ordinary
Differential Equations and Dynamical Systems</a> - Gerald Teschl</li>
<li>📝 <a
href="http://leipper.org/manuals/zip-fill/dn-difeq-notes.pdf">Notes on
Differential Equations</a> - Bob Terrell</li>
<li>📝 <a href="http://digitalcommons.trinity.edu/mono/8/">Elementary
Differential Equations</a> - William F. Trench</li>
<li>📝 <a href="http://digitalcommons.trinity.edu/mono/9/">Elementary
Differential Equations With Boundary Value Problems</a> - William F.
Trench</li>
<li>📝 <a href="http://www.jirka.org/diffyqs/">Notes on Diffy Qs:
Differential Equations for Engineers</a> - Jiří Lebl</li>
<li>📝 <a
href="http://djm.cc/library/Differential_Equations_Phillips_edited.pdf">Differential
Equations</a> - H. B. Phillips (1922)</li>
</ul>
<h3 id="partial-differential-equations">Partial Differential
Equations</h3>
<ul>
<li>📝 <a
href="https://www.math.ucdavis.edu/~hunter/pdes/pde_notes.pdf">Notes on
Partial Differential Equations</a> - John K. Hunter (University of
California at Davis)</li>
<li>📝 <a
href="http://www.math.uni-leipzig.de/~miersemann/pdebook.pdf">Partial
Differential Equations: Lecture Notes</a> - Erich Miersemann (Leipzig
University)</li>
<li>📝 <a href="http://www.mathphysics.com/pde/">Linear Methods of
Applied Mathematics</a> - E. Harrell, J. Herod (Georgia Tech)</li>
</ul>
<h2 id="probability-and-statistics">Probability and Statistics</h2>
<h3 id="probability-theory">Probability Theory</h3>
<ul>
<li>📝 <a
href="https://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf">Introduction
to Probability</a> - Charles M. Grinstead, J. Laurie Snell</li>
<li>📝 <a
href="http://vfu.bg/en/e-Learning/Math--Bertsekas_Tsitsiklis_Introduction_to_probability.pdf">Introduction
to Probability</a> - Dimitri P. Bertsekas, John N. Tsitsiklis (MIT)</li>
<li>📝 <a href="http://www.maths.uq.edu.au/~kroese/asitp.pdf">A Short
Introduction to Probability</a> - Dirk P. Kroese (University of
Queensland)</li>
<li>📝 <a
href="https://www.math.duke.edu/~rtd/PTE/PTE4_1.pdf">Probability: Theory
and Examples</a> - Rick Durrett</li>
<li>📝 <a
href="https://github.com/mavam/stat-cookbook/releases/download/0.2.3/stat-cookbook.pdf">Probability
and Statistics Cookbook</a> - Matthias Vallentin (UC Berkeley)</li>
<li>📝 <a href="http://www.wzchen.com/probability-cheatsheet/">The Only
Probability Cheatsheet You’ll Ever Need</a> - William Chen</li>
<li>📝 <a
href="http://www.ellerman.org/Davids-Stuff/Maths/Rota-Baclawski-Prob-Theory-79.pdf">An
Introduction to Probability and Random Processes</a> - Gian-Carlo Rota,
Kenneth Baclawski</li>
<li>📝 <a href="https://arxiv.org/pdf/1906.01803.pdf">Foundations of
Constructive Probability Theory</a> - Yuen-Kwok Chan</li>
</ul>
<h3 id="statistics">Statistics</h3>
<ul>
<li>📝 <a
href="http://homepages.math.uic.edu/~rgmartin/Teaching/Stat411/Notes/411notes.pdf">Lecture
Notes on Statistical Theory</a> - Ryan Martin (University of
Illinois)</li>
<li>📝 <a
href="http://www-library.desy.de/preparch/books/vstatmp_engl.pdf">Introduction
to Statistics and Data Analysis for Physicists</a> - Gerhard Bohm,
Günter Zech</li>
<li>📝 <a
href="http://www.iiserpune.ac.in/~ayan/MTH201/Sahoo_textbook.pdf">Probability
and Mathematical Statistics</a> - Prasanna Sahoo (University of
Louisville)</li>
<li>📝 <a href="http://math.arizona.edu/~faris/stat.pdf">Lectures on
Statistics</a> - William G. Faris</li>
<li>📝 <a
href="http://pages.pomona.edu/~ajr04747/Fall2009/Math152/Notes/Math152NotesFall09.pdf">Statistical
Theory</a> - Adolfo J. Rumbos</li>
<li>📝 <a href="http://mason.gmu.edu/~jgentle/books/MathStat.pdf">Theory
of Statistics</a> - James E. Gentle (George Mason University)</li>
<li>📝 <a href="http://math.arizona.edu/~jwatkins/notests.pdf">Theory of
Statistics</a> - Joseph C. Watkins (University of Arizona)</li>
<li>📝 <a
href="https://web.archive.org/web/20130523134625/http://www.aiaccess.net/e_gm.htm">Glossary
of Data Modeling</a> - AI Access</li>
<li>📝 <a href="http://www.ats.ucla.edu/stat/papers/">Statistics
Papers</a> - List of statistics papers curated by the Institute for
Digital Research and Education (IDRE) at UCLA on methods such as
bootstrap and factor invariance.</li>
<li>📝 <a href="http://itl.nist.gov/div898/handbook/index.htm">NIST
Handbook of Statistical Methods</a> - Resource on practical statistics
directed towards scientists and engineers.</li>
<li>📝 <a href="http://vassarstats.net/textbook/">Concepts and
Applications of Inferential Statistics</a> - Richard Lowry</li>
<li>📝 <a
href="http://www.cosc.brocku.ca/~duentsch/papers/methprimer2.html">Rough
set data analysis: A road to non-invasive knowledge discovery</a> - Ivo
Düntsch, Günther Gediga</li>
<li>📝 <a href="https://statsthinking21.org/">Statistical Thinking for
the 21st Century</a> - Russell A. Poldrack</li>
<li>📝 <a href="https://jonathanweisberg.org/vip/">Odds and Ends:
Introducing Probability &amp; Decision with a Visual Emphasis</a> -
Jonathan Weisberg</li>
<li>📝 <a href="https://seeing-theory.brown.edu/">Seeing Theory</a> -
Daniel Kunin, Jingru Guo, Tyler Dae Devlin, and Daniel Xiang</li>
<li>📝 <a href="https://www.statisticsdonewrong.com/">Statistics Done
Wrong</a> - Alex Reinhart</li>
<li>📝 <a
href="https://link.springer.com/book/10.1007/978-0-387-21736-9">All of
Statistics: A Concise Course in Statistical Inference</a> - Larry
Wasserman</li>
</ul>
<h3 id="statistical-learning">Statistical Learning</h3>
<ul>
<li>📝 <a
href="http://www-bcf.usc.edu/~gareth/ISL/ISLR%20First%20Printing.pdf">An
Introduction to Statistical Learning with Applications in R</a> - Gareth
James, Daniela Witten, Trevor Hastie, Robert Tibshirani</li>
<li>📝 <a href="http://web.stanford.edu/~hastie/Papers/ESLII.pdf">The
Elements of Statistical Learning</a> - Trevor Hastie, Robert Tibshirani,
Jerome Friedman</li>
<li>📝 <a
href="https://web.stanford.edu/class/cs229t/notes.pdf">Statistical
Learning Theory</a> - Percy Liang</li>
<li>📝 <a
href="https://webdocs.cs.ualberta.ca/~sutton/book/bookdraft2016sep.pdf">Reinforcement
Learning: An Introduction</a> - Richard S. Sutton, Andrew G. Barto</li>
</ul>
<h3 id="stochastic-processes">Stochastic processes</h3>
<ul>
<li>📝 <a
href="http://www.math.tifr.res.in/~publ/ln/tifr24.pdf">Lectures on
Stochastic Processes</a> - K. Ito (Tata Institute of Fundamental
Research, Bombay)</li>
<li>📝 <a
href="http://www.math.harvard.edu/~knill/teaching/math144_1994/probability.pdf">Probability
and Stochastic Processes with Applications</a> - Oliver Knill (Harvard
University)</li>
<li>📝 <a
href="http://statweb.stanford.edu/~adembo/math-136/nnotes.pdf">Stochastic
Processes</a> - Amir Dembo (Stanford University)</li>
<li>📝 <a
href="http://www.mi.fu-berlin.de/wiki/pub/CompMolBio/MarkovKetten15/stochastic_processes_2011.pdf">Lecture
Notes on Stochastic Processes</a> - Frank Noé, Bettina Keller and
Jan-Hendrik Prinz (Freie Universität Berlin)</li>
<li>📝 <a
href="https://www.ma.utexas.edu/users/gordanz/notes/introduction_to_stochastic_processes.pdf">Introduction
to Stochastic Processes - Lecture Notes</a> - Gordan Žitković
(University of Texas)</li>
<li>📝 <a
href="https://www.math.uwaterloo.ca/~mscott/Little_Notes.pdf">Applied
Stochastic Processes in science and engineering</a> - Matt Scott
(University of Waterloo)</li>
<li>📝 <a
href="http://www.math.leidenuniv.nl/~spieksma/colleges/sp-master/sp-hvz1.pdf">An
Introduction to Stochastic Processes in Continuous Time</a> - Flora
Spieksma (Leiden University)</li>
<li>📝 <a
href="http://pages.uoregon.edu/dlevin/MARKOV/markovmixing.pdf">Markov
Chains and Mixing Times</a> - David A. Levin, Yuval Peres, Elizabeth L.
Wilmer</li>
<li>📝 <a
href="http://www.stat.yale.edu/~pollard/Books/1984book/pollard1984.pdf">Convergence
of Stochastic Processes</a> - David Pollard</li>
</ul>
<h2 id="numerical-analysis">Numerical Analysis</h2>
<ul>
<li>📝 <a
href="http://www.math.umd.edu/~dlevy/resources/notes.pdf">Introduction
to Numerical Analysis</a> - Doron Levy (University of Maryland)</li>
<li>📝 <a href="http://www.ima.umn.edu/~arnold/597.00-01/nabook.pdf">A
Concise Introduction to Numerical Analysis</a> - Douglas N. Arnold
(University of Minnesota)</li>
<li>📝 <a
href="http://people.cs.uchicago.edu/~ridg/newna/nalrs.pdf">Numerical
Analysis</a> - L. Ridgway Scott</li>
<li>📝 <a
href="https://uknowledge.uky.edu/cgi/viewcontent.cgi?article=1000&amp;context=math_textbooks">Lectures
In Basic Computational Numerical Analysis</a> - J. M. McDonough
(University of Kentucky)</li>
<li>📝 <a
href="https://user.math.uni-bremen.de/schmi/SS04/YSU_Notes.pdf">Advanced
Numerical Methods and Their Applications to Industrial Problems:
Adaptive Finite Element Methods</a> - Alfred Schmidt, Arsen
Narimanyan</li>
<li>📝 <a href="https://ece.uwaterloo.ca/~dwharder/nm/">Numerical
Analysis for Engineers</a> - Douglas Wilhelm Harder</li>
<li>📝🎥 <a
href="https://www.cs.utexas.edu/users/flame/laff/alaff/frontmatter.html">Advanced
Linear Algebra: Foundations to Frontiers</a> - Robert van de Geijn,
Margaret Myers (University of Texas at Austin)</li>
</ul>
<h2 id="signal-processing">Signal processing</h2>
<ul>
<li>📝 <a
href="http://www.ece.rutgers.edu/~orfanidi/intro2sp/orfanidis-i2sp.pdf">Introduction
to Signal Processing</a> - Sophocles J. Orfanidis (Rutgers
University)</li>
<li>📝 <a
href="http://www.fourierandwavelets.org/FSP_v1.1_2014.pdf">Foundations
of Signal Processing</a> - Martin Vetterli, Jelena Kovacevic, Vivek K
Goyal</li>
<li>📝 <a href="https://ee.stanford.edu/~gray/sp.pdf">An Introduction to
Statistical Signal Processing</a> - Robert M. Gray, Lee D. Davisson</li>
<li>📝 <a href="https://greenteapress.com/wp/think-dsp/">Think DSP</a> -
Allen B. Downey</li>
<li>📝 <a
href="https://www.uio.no/studier/emner/matnat/math/MAT-INF2360/v15/kompendium/applinalgpython.pdf">Linear
algebra, signal processing, and wavelets. A unified approach.</a> -
Øyvind Ryan (University of Oslo)</li>
</ul>
<h2 id="mathematics-for-computer-science">Mathematics for Computer
Science</h2>
<ul>
<li>📝 <a href="https://people.csail.mit.edu/meyer/mcs.pdf">Mathematics
for Computer Science</a> - Eric Lehman, F. Thomson Leighton, Albert R.
Meyer</li>
<li>📝 <a
href="http://www.math.upenn.edu/%7Ewilf/AlgComp3.html">Algorithms and
Complexity</a> - H. Wilf</li>
<li>📝 <a
href="http://people.eecs.berkeley.edu/~varaiya/papers_ps.dir/NOO.pdf">Lecture
Notes on Optimization</a> - Pravin Varaiya</li>
<li>📝 <a
href="http://www.inference.org.uk/mackay/itila/book.html">Information
Theory, Inference, and Learning Algorithms</a> - David J. C. MacKay</li>
<li>📝 <a href="https://hypertextbook.com/chaos/">The Chaos Textbook:
Mathematics in the age of the computer</a> - Glenn Elert</li>
</ul>
<h2 id="mathematical-biology">Mathematical Biology</h2>
<ul>
<li>📝 <a
href="http://www.math.ust.hk/~machas/mathematical-biology.pdf">Mathematical
Biology</a> - Jeffrey Chasnov</li>
</ul>
<h2 id="mathematical-physics">Mathematical Physics</h2>
<ul>
<li>📝 <a
href="http://oaktrust.library.tamu.edu/handle/1969.1/2501">Introduction
to Continuum Mechanics</a> - Ray. M. Bowen</li>
<li>📝 <a
href="http://www.physics.miami.edu/nearing/mathmethods/">Mathematical
Tools for Physics</a> - James Nearing</li>
<li>📝 <a href="http://www.malaspina.com/etext/heavens.htm">Mechanism of
the Heavens (1831)</a> - Mary Somerville</li>
</ul>
<h1 id="students-lecture-notes">Students Lecture Notes</h1>
<ul>
<li><a href="https://web.evanchen.cc/coursework.html">Evan Chen</a> -
MIT. 2012 ~ 2018. Covers Combinatorics, Number Theory, Honors Algebra,
Set Theory, Real Analysis, Graph Theory, and more.</li>
<li><a href="https://dec41.user.srcf.net/notes/">Dexter Chua</a> -
Harvard. 2013 ~ 2018. Covers Analysis, Probability, Linear Algebra,
Complex Analysis, Numerical Analysis, Statistics, Optimization,
Algebraic Topology, Quantum Field Theory, and more.</li>
</ul>
<h1 id="related-awesome-lists">Related Awesome Lists</h1>
<ul>
<li><a
href="https://github.com/mostafatouny/awesome-theoretical-computer-science">Theoretical
Computer Science</a></li>
</ul>
<h1 id="license">License</h1>
<p><a href="http://creativecommons.org/publicdomain/zero/1.0/"><img
src="http://i.creativecommons.org/p/zero/1.0/88x31.png"
alt="CC0" /></a></p>
<p>To the extent possible under law, <a
href="http://cyrille.rossant.net">Cyrille Rossant</a> has waived all
copyright and related or neighboring rights to this work.</p>
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