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@ -15,6 +15,7 @@ A curated list of awesome mathematics resources.
* [Questions and Answers](#questions-and-answers)
* [Encyclopedia](#encyclopedia)
* [Books](#books)
* [Magazines](#magazines)
* [Blogs](#blogs)
* [Misc](#misc)
* [Lecture Notes](#lecture-notes)
@ -41,6 +42,7 @@ A curated list of awesome mathematics resources.
* [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)
@ -62,6 +64,7 @@ A curated list of awesome mathematics resources.
* [Mathematical Biology](#mathematical-biology)
* [Mathematical Physics](#mathematical-physics)
* [Students Lecture Notes](#students-lecture-notes)
* [Related Awesome Lists](#related-awesome-lists)
* [License](#license)
<!-- END_TOC -->
@ -78,6 +81,10 @@ A curated list of awesome mathematics resources.
* [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)
* [MathRelay](https://www.mathrelay.com/)
* [Almost Fun](https://www.almostfun.org/lessons/)
* [Oxford Mathematics](https://www.youtube.com/c/OxfordMathematics)
## Learn to Learn
@ -85,13 +92,24 @@ A curated list of awesome mathematics resources.
## Youtube Series
* [Brandon Foltz](https://www.youtube.com/user/BCFoltz/playlists?view=1&sort=da&flow=grid)
* [3blue1brown](https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw/playlists)
* [NPTEL](https://www.youtube.com/watch?v=VVYLpmKRfQ8&list=PL6C92B335BD4238AB)
* [Prof. Leonard](https://www.youtube.com/watch?v=9FtHB7V14Fo&list=PL5102DFDC6790F3D0)
* [Crash Course](https://www.youtube.com/watch?v=zouPoc49xbk&list=PL8dPuuaLjXtNM_Y-bUAhblSAdWRnmBUcr)
* [Harvard](https://www.youtube.com/watch?v=KbB0FjPg0mw&list=PL2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo)
* [MIT](https://www.youtube.com/watch?v=VPZD_aij8H0&list=PLUl4u3cNGP60uVBMaoNERc6knT_MgPKS0)
* [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)
## Tools
@ -102,7 +120,7 @@ A curated list of awesome mathematics resources.
* [Maxima](https://maxima.sourceforge.io/)
* [Sympy](https://www.sympy.org/)
* [Sagemath](http://www.sagemath.org/)
* [Unit Converter](https://unitconverter.net)
* [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/)
@ -112,6 +130,8 @@ A curated list of awesome mathematics resources.
* [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/)
## Questions and Answers
@ -124,6 +144,7 @@ A curated list of awesome mathematics resources.
* [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.
## Books
@ -133,15 +154,24 @@ A curated list of awesome mathematics resources.
* [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/free-programming-books.md#mathematics)
* [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 light weight site for students upto highschool
* [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)
## Misc
@ -152,6 +182,7 @@ A curated list of awesome mathematics resources.
* [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.
# Lecture Notes
@ -172,6 +203,7 @@ A curated list of awesome mathematics resources.
* [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)
@ -211,7 +243,6 @@ A curated list of awesome mathematics resources.
### 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
* [An Introduction to Surreal Numbers](https://www.whitman.edu/Documents/Academics/Mathematics/Grimm.pdf) - Gretchen Grimm
* [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
@ -224,8 +255,7 @@ A curated list of awesome mathematics resources.
* [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 Introductary Number Theory Textbook](https://www.poritz.net/jonathan/share/yaintt/) - Jonathan A. Poritz
* [Elementary Number Theory](https://napocaro.files.wordpress.com/2015/02/david_m-_burton_elementary_number_theory_sixth_bookfi-org.pdf) - David M. Burton
* [Yet Another Introductory Number Theory Textbook](https://www.poritz.net/jonathan/share/yaintt/) - Jonathan A. Poritz
### Algebraic Number Theory
@ -278,9 +308,7 @@ A curated list of awesome mathematics resources.
* [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
* [Linear Algebra](http://www.calpoly.edu/~jborzell/Courses/Year%2010-11/Fall%202010/Petersen-Linear_Algebra-Math_306.pdf) - Peter Petersen
* [MIT OpenCourseWare Lectures on Linear Algebra (18.06) as Jupyter Notebooks](https://github.com/juanklopper/MIT_OCW_Linear_Algebra_18_06) - Juan Klopper
* [Linear Algebra](http://joshua.smcvt.edu/linalg.html) - Jim Hefferon
* [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
@ -343,10 +371,11 @@ A curated list of awesome mathematics resources.
* [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](http://www.sci.ccny.cuny.edu/~ksda/PostedPapers/rickksda1107.pdf) - R.C. Churchill
* [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)
@ -354,6 +383,12 @@ A curated list of awesome mathematics resources.
* [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)
@ -424,7 +459,7 @@ A curated list of awesome mathematics resources.
* [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](http://www.math.uchicago.edu/~schlag/bookweb.pdf) - Wilhelm Schlag
* [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
@ -441,7 +476,7 @@ A curated list of awesome mathematics resources.
### Measure Theory
* [An Introduction to Measure Theory](https://terrytao.files.wordpress.com/2011/01/measure-book1.pdf) - Terence Tao (UCLA)
* [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
@ -525,12 +560,12 @@ A curated list of awesome mathematics resources.
## Numerical Analysis
* [Introduction to Numerical Analysis](http://www.math.umd.edu/~dlevy/books/na.pdf) - Doron Levy (University of Maryland)
* [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](http://www.engr.uky.edu/~acfd/egr537-lctrs.pdf) - J. M. McDonough (University of Kentucky)
* [Advanced Numerical Methods and Their Applications to Industrial Problems: Adaptive Finite Element Methods](http://www.math.uni-bremen.de/~schmidt/SS04/YSU_Notes.pdf) - Alfred Schmidt, Arsen Narimanyan
* [Numerical Analysis for Engineers](https://ece.uwaterloo.ca/~dwharder/NumericalAnalysis/) - Douglas Wilhelm Harder
* [Numerical Analysis for Engineers](https://ece.uwaterloo.ca/~dwharder/nm/) - Douglas Wilhelm Harder
## Signal processing
@ -564,6 +599,9 @@ A curated list of awesome mathematics resources.
* [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)
# License
[![CC0](http://i.creativecommons.org/p/zero/1.0/88x31.png)](http://creativecommons.org/publicdomain/zero/1.0/)