Awesome Math !Awesome (https://cdn.rawgit.com/sindresorhus/awesome/d7305f38d29fed78fa85652e3a63e154dd8e8829/media/badge.svg) (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-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)  
* **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 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/)

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)
⟡ 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/)
⟡ 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-and-stock-market-tips)
⟡ Mathcheap (https://mathcheap.xyz)
⟡ Midpoint Calculator (https://midpointcalculator.co)
⟡ Quartiles Calculator (https://quartilecalculator.net)
⟡ Corca Editor (https://corca.io/)

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)

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, 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.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.io/logic_and_proof/) -  Jeremy Avigad, Robert Y. Lewis, and Floris van Doorn
⟡ 📝 QED - an interactive textbook (https://teorth.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.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.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.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-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 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://www.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


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 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

⟡ 📝 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://www.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.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
⟡ 📝 Theory of Functions of a Real Variable (http://www.math.harvard.edu/~shlomo/docs/Real_Variables.pdf) - Shlomo Sternberg
⟡ 📝 Functional Analysis (http://spot.colorado.edu/~baggett/functional.html) - Lawerence Baggett

Measure Theory

⟡ 📝 An Introduction to Measure Theory (https://terrytao.files.wordpress.com/2012/12/gsm-126-tao5-measure-book.pdf) - Terence Tao (UCLA)
⟡ 📝 Lecture Notes on Measure Theory and Functional Analysis (http://www.mat.uniroma2.it/~cannarsa/cam_0607.pdf) - P. Cannarsa, T. D’Aprile
⟡ 📝 Lecture Notes in Measure Theory (http://www.math.chalmers.se/~borell/MeasureTheory.pdf) - Christer Borell
⟡ 📝 A Crash Course on the Lebesgue Integral and Measure Theory (http://www.gold-saucer.org/math/lebesgue/lebesgue.pdf) - Steve Cheng
⟡ 📝 Measure Theory (https://www.math.ucdavis.edu/~hunter/measure_theory/measure_notes.pdf) - John K. Hunter (University of California at Davis)
⟡ 📝 Measure and Integration (https://people.math.ethz.ch/~salamon/PREPRINTS/measure.pdf) - Dietmar A. Salamon (ETH Zürich)
⟡ 📝 Lecture notes: Measure Theory (http://www.math.ucsd.edu/~bdriver/240-00-01/Lecture_Notes/measurep.pdf) - Bruce K. Driver

Ordinary Differential Equations

⟡ 📝 Difference Equations To Differential Equations (http://www.synechism.org/wp/difference-equations-to-differential-equations/) - Dan Sloughter
⟡ 📝 Ordinary Differential Equation (https://www.math.uni-bielefeld.de/~grigor/odelec2008.pdf) - Alexander Grigorian (University of Bielefeld)
⟡ 📝 Ordinary Differential Equations: Lecture Notes (http://www.cs.bgu.ac.il/~leonid/ode_bio_files/Ionascu_LectNotes.pdf) - Eugen J. Ionascu
⟡ 📝 Ordinary Differential Equations (http://www.math.lmu.de/~philip/publications/lectureNotes/ODE.pdf) - Peter Philip
⟡ 📝 Ordinary Differential Equations (http://users.math.msu.edu/users/gnagy/teaching/ode.pdf) - Gabriel Nagy
⟡ 📝 Ordinary Differential Equations and Dynamical Systems (http://www.mat.univie.ac.at/~gerald/ftp/book-ode/ode.pdf) - Gerald Teschl
⟡ 📝 Notes on Differential Equations (http://leipper.org/manuals/zip-fill/dn-difeq-notes.pdf) - Bob Terrell
⟡ 📝 Elementary Differential Equations (http://digitalcommons.trinity.edu/mono/8/) - William F. Trench
⟡ 📝 Elementary Differential Equations With Boundary Value Problems (http://digitalcommons.trinity.edu/mono/9/) - William F. Trench
⟡ 📝 Notes on Diffy Qs: Differential Equations for Engineers (http://www.jirka.org/diffyqs/) - Jiří Lebl
⟡ 📝 Differential Equations (http://djm.cc/library/Differential_Equations_Phillips_edited.pdf) - H. B. Phillips (1922)

Partial Differential Equations

⟡ 📝 Notes on Partial Differential Equations (https://www.math.ucdavis.edu/~hunter/pdes/pde_notes.pdf) - John K. Hunter (University of California at Davis)
⟡ 📝 Partial Differential Equations: Lecture Notes (http://www.math.uni-leipzig.de/~miersemann/pdebook.pdf) - Erich Miersemann (Leipzig University)
⟡ 📝 Linear Methods of Applied Mathematics (http://www.mathphysics.com/pde/) - E. Harrell, J. Herod (Georgia Tech)


Probability and Statistics

Probability Theory

⟡ 📝 Introduction to Probability (https://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf) - Charles M. Grinstead, J. Laurie Snell
⟡ 📝 Introduction to Probability (http://vfu.bg/en/e-Learning/Math--Bertsekas_Tsitsiklis_Introduction_to_probability.pdf) - Dimitri P. Bertsekas, John N. Tsitsiklis (MIT)
⟡ 📝 A Short Introduction to Probability (http://www.maths.uq.edu.au/~kroese/asitp.pdf) - Dirk P. Kroese (University of Queensland)
⟡ 📝 Probability: Theory and Examples (https://www.math.duke.edu/~rtd/PTE/PTE4_1.pdf) - Rick Durrett
⟡ 📝 Probability and Statistics Cookbook (https://github.com/mavam/stat-cookbook/releases/download/0.2.3/stat-cookbook.pdf) - Matthias Vallentin (UC Berkeley)
⟡ 📝 The Only Probability Cheatsheet You'll Ever Need (http://www.wzchen.com/probability-cheatsheet/) - William Chen
⟡ 📝 An Introduction to Probability and Random Processes (http://www.ellerman.org/Davids-Stuff/Maths/Rota-Baclawski-Prob-Theory-79.pdf) - Gian-Carlo Rota, Kenneth Baclawski
⟡ 📝 Foundations of Constructive Probability Theory (https://arxiv.org/pdf/1906.01803.pdf) - Yuen-Kwok Chan

Statistics

⟡ 📝 Lecture Notes on Statistical Theory (http://homepages.math.uic.edu/~rgmartin/Teaching/Stat411/Notes/411notes.pdf) - Ryan Martin (University of Illinois)
⟡ 📝 Introduction to Statistics and Data Analysis for Physicists (http://www-library.desy.de/preparch/books/vstatmp_engl.pdf) - Gerhard Bohm, Günter Zech
⟡ 📝 Probability and Mathematical Statistics (http://www.iiserpune.ac.in/~ayan/MTH201/Sahoo_textbook.pdf) - Prasanna Sahoo (University of Louisville)
⟡ 📝 Lectures on Statistics (http://math.arizona.edu/~faris/stat.pdf) - William G. Faris
⟡ 📝 Statistical Theory (http://pages.pomona.edu/~ajr04747/Fall2009/Math152/Notes/Math152NotesFall09.pdf) - Adolfo J. Rumbos
⟡ 📝 Theory of Statistics (http://mason.gmu.edu/~jgentle/books/MathStat.pdf) - James E. Gentle (George Mason University)
⟡ 📝 Theory of Statistics (http://math.arizona.edu/~jwatkins/notests.pdf) - Joseph C. Watkins (University of Arizona)
⟡ 📝 Glossary of Data Modeling (https://web.archive.org/web/20130523134625/http://www.aiaccess.net/e_gm.htm) - AI Access
⟡ 📝 Statistics Papers (http://www.ats.ucla.edu/stat/papers/) - List of statistics papers curated by the Institute for Digital Research and Education (IDRE) at UCLA on methods such as bootstrap and factor invariance.
⟡ 📝 NIST Handbook of Statistical Methods (http://itl.nist.gov/div898/handbook/index.htm) - Resource on practical statistics directed towards scientists and engineers.
⟡ 📝 Concepts and Applications of Inferential Statistics (http://vassarstats.net/textbook/) - Richard Lowry
⟡ 📝 Rough set data analysis: A road to non-invasive knowledge discovery (http://www.cosc.brocku.ca/~duentsch/papers/methprimer2.html) - Ivo Düntsch, Günther Gediga
⟡ 📝 Statistical Thinking for the 21st Century (https://statsthinking21.org/) - Russell A. Poldrack
⟡ 📝 Odds and Ends: Introducing Probability & Decision with a Visual Emphasis (https://jonathanweisberg.org/vip/) - Jonathan Weisberg
⟡ 📝 Seeing Theory (https://seeing-theory.brown.edu/) - Daniel Kunin, Jingru Guo, Tyler Dae Devlin, and Daniel Xiang
⟡ 📝 Statistics Done Wrong (https://www.statisticsdonewrong.com/) - Alex Reinhart
⟡ 📝 All of Statistics: A Concise Course in Statistical Inference (https://link.springer.com/book/10.1007/978-0-387-21736-9) - Larry Wasserman

Statistical Learning

⟡ 📝 An Introduction to Statistical Learning with Applications in R (http://www-bcf.usc.edu/~gareth/ISL/ISLR%20First%20Printing.pdf) - Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani
⟡ 📝 The Elements of Statistical Learning (http://web.stanford.edu/~hastie/Papers/ESLII.pdf) - Trevor Hastie, Robert Tibshirani, Jerome Friedman
⟡ 📝 Statistical Learning Theory (https://web.stanford.edu/class/cs229t/notes.pdf) - Percy Liang
⟡ 📝 Reinforcement Learning: An Introduction (https://webdocs.cs.ualberta.ca/~sutton/book/bookdraft2016sep.pdf) - Richard S. Sutton, Andrew G. Barto

Stochastic processes

⟡ 📝 Lectures on Stochastic Processes (http://www.math.tifr.res.in/~publ/ln/tifr24.pdf) - K. Ito (Tata Institute of Fundamental Research, Bombay)
⟡ 📝 Probability and Stochastic Processes with Applications (http://www.math.harvard.edu/~knill/teaching/math144_1994/probability.pdf) - Oliver Knill (Harvard University)
⟡ 📝 Stochastic Processes (http://statweb.stanford.edu/~adembo/math-136/nnotes.pdf) - Amir Dembo (Stanford University)
⟡ 📝 Lecture Notes on Stochastic Processes (http://www.mi.fu-berlin.de/wiki/pub/CompMolBio/MarkovKetten15/stochastic_processes_2011.pdf) - Frank Noé, Bettina Keller and Jan-Hendrik Prinz (Freie Universität Berlin)
⟡ 📝 Introduction to Stochastic Processes - Lecture Notes (https://www.ma.utexas.edu/users/gordanz/notes/introduction_to_stochastic_processes.pdf) - Gordan Žitković (University of Texas)
⟡ 📝 Applied Stochastic Processes in science and engineering (https://www.math.uwaterloo.ca/~mscott/Little_Notes.pdf) - Matt Scott (University of Waterloo)
⟡ 📝 An Introduction to Stochastic Processes in Continuous Time (http://www.math.leidenuniv.nl/~spieksma/colleges/sp-master/sp-hvz1.pdf) - Flora Spieksma (Leiden University)
⟡ 📝 Markov Chains and Mixing Times (http://pages.uoregon.edu/dlevin/MARKOV/markovmixing.pdf) - David A. Levin, Yuval Peres, Elizabeth L. Wilmer
⟡ 📝 Convergence of Stochastic Processes (http://www.stat.yale.edu/~pollard/Books/1984book/pollard1984.pdf) - David Pollard


Numerical Analysis

⟡ 📝 Introduction to Numerical Analysis (http://www.math.umd.edu/~dlevy/resources/notes.pdf) - Doron Levy (University of Maryland)
⟡ 📝 A Concise Introduction to Numerical Analysis (http://www.ima.umn.edu/~arnold/597.00-01/nabook.pdf) - Douglas N. Arnold (University of Minnesota)
⟡ 📝 Numerical Analysis (http://people.cs.uchicago.edu/~ridg/newna/nalrs.pdf) - L. Ridgway Scott
⟡ 📝 Lectures In Basic Computational Numerical Analysis (https://uknowledge.uky.edu/cgi/viewcontent.cgi?article=1000&context=math_textbooks) - J. M. McDonough (University of Kentucky)
⟡ 📝 Advanced Numerical Methods and Their Applications to Industrial Problems: Adaptive Finite Element Methods (https://user.math.uni-bremen.de/schmi/SS04/YSU_Notes.pdf) - Alfred Schmidt, Arsen Narimanyan
⟡ 📝 Numerical Analysis for Engineers (https://ece.uwaterloo.ca/~dwharder/nm/) - Douglas Wilhelm Harder
⟡ 📝🎥 Advanced Linear Algebra: Foundations to Frontiers (https://www.cs.utexas.edu/users/flame/laff/alaff/frontmatter.html) - Robert van de Geijn, Margaret Myers (University of Texas at Austin)

Signal processing

⟡ 📝 Introduction to Signal Processing (http://www.ece.rutgers.edu/~orfanidi/intro2sp/orfanidis-i2sp.pdf) - Sophocles J. Orfanidis (Rutgers University)
⟡ 📝 Foundations of Signal Processing (http://www.fourierandwavelets.org/FSP_v1.1_2014.pdf) - Martin Vetterli, Jelena Kovacevic, Vivek K Goyal
⟡ 📝 An Introduction to Statistical Signal Processing (https://ee.stanford.edu/~gray/sp.pdf) - Robert M. Gray, Lee D. Davisson
⟡ 📝 Think DSP (https://greenteapress.com/wp/think-dsp/) - Allen B. Downey
⟡ 📝 Linear algebra, signal processing, and wavelets. A unified approach. (https://www.uio.no/studier/emner/matnat/math/MAT-INF2360/v15/kompendium/applinalgpython.pdf) - Øyvind Ryan (University of Oslo)


Mathematics for Computer Science

⟡ 📝 Mathematics for Computer Science (https://people.csail.mit.edu/meyer/mcs.pdf) - Eric Lehman, F. Thomson Leighton, Albert R. Meyer
⟡ 📝 Algorithms and Complexity (http://www.math.upenn.edu/%7Ewilf/AlgComp3.html) - H. Wilf
⟡ 📝 Lecture Notes on Optimization (http://people.eecs.berkeley.edu/~varaiya/papers_ps.dir/NOO.pdf) - Pravin Varaiya
⟡ 📝 Information Theory, Inference, and Learning Algorithms (http://www.inference.org.uk/mackay/itila/book.html) - David J. C. MacKay
⟡ 📝 The Chaos Textbook: Mathematics in the age of the computer (https://hypertextbook.com/chaos/) - Glenn Elert

Mathematical Biology

⟡ 📝 Mathematical Biology (http://www.math.ust.hk/~machas/mathematical-biology.pdf) - Jeffrey Chasnov

Mathematical Physics

⟡ 📝 Introduction to Continuum Mechanics (http://oaktrust.library.tamu.edu/handle/1969.1/2501) - Ray. M. Bowen
⟡ 📝 Mathematical Tools for Physics (http://www.physics.miami.edu/nearing/mathmethods/) - James Nearing
⟡ 📝 Mechanism of the Heavens (1831) (http://www.malaspina.com/etext/heavens.htm) - Mary Somerville

                                                                                                                Students Lecture Notes
⟡ Evan Chen (https://web.evanchen.cc/coursework.html) - MIT. 2012 ~ 2018. Covers Combinatorics, Number Theory, Honors Algebra, Set Theory, Real Analysis, Graph Theory, and more.
⟡ Dexter Chua (https://dec41.user.srcf.net/notes/) - Harvard. 2013 ~ 2018. Covers Analysis, Probability, Linear Algebra, Complex Analysis, Numerical Analysis, Statistics, Optimization, Algebraic Topology, Quantum Field Theory, and more.

                                                                                                                Related Awesome Lists
⟡ Theoretical Computer Science (https://github.com/mostafatouny/awesome-theoretical-computer-science)

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