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adding books from george cain's website (issue #26)
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@ -31,6 +31,7 @@ A curated list of awesome mathematics resources.
* [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)
@ -54,6 +55,8 @@ A curated list of awesome mathematics resources.
* [Numerical Analysis](#numerical-analysis)
* [Signal processing](#signal-processing)
* [Mathematics for Computer Science](#mathematics-for-computer-science)
* [Mathematical Biology](#mathematical-biology)
* [Mathematical Physics](#mathematical-physics)
* [License](#license)
<!-- END_TOC -->
@ -87,6 +90,7 @@ A curated list of awesome mathematics resources.
* [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)
@ -101,14 +105,18 @@ A curated list of awesome mathematics resources.
* [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/)
# Lecture Notes
## Foundations of Mathematics
* [Basic Concepts of Mathematics](http://www.trillia.com/zakon1.html) - Elias Zakon
### 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/)
@ -122,6 +130,9 @@ A curated list of awesome mathematics resources.
* [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
### Category Theory
@ -130,6 +141,11 @@ A curated list of awesome mathematics resources.
* [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](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
### Homotopy Type Theory
@ -150,6 +166,8 @@ A curated list of awesome mathematics resources.
* [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://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
### Algebraic Number Theory
@ -157,6 +175,7 @@ A curated list of awesome mathematics resources.
* [Introduction to Algebraic Number Theory](http://www1.spms.ntu.edu.sg/~frederique/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
@ -168,19 +187,26 @@ A curated list of awesome mathematics resources.
## 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
### Abstract Algebra
* [Introduction to Abstract Algebra](https://people.creighton.edu/~dsm33733/MTH581/Introduction%20to%20Abstract%20Algebra.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](http://www1.spms.ntu.edu.sg/~frederique/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)
* [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
### 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
@ -190,6 +216,12 @@ A curated list of awesome mathematics resources.
* [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
* [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
### Ring Theory
@ -201,6 +233,9 @@ A curated list of awesome mathematics resources.
* [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
### Lie Algebras
* [Lie Algebras](http://www.math.harvard.edu/~shlomo/docs/lie_algebras.pdf) - Shlomo Sternberg
## Combinatorics
@ -208,6 +243,7 @@ A curated list of awesome mathematics resources.
* [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
@ -218,6 +254,10 @@ A curated list of awesome mathematics resources.
## 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
### Differential Geometry
@ -226,6 +266,8 @@ A curated list of awesome mathematics resources.
* [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
### Algebraic Geometry
@ -260,14 +302,26 @@ A curated list of awesome mathematics resources.
### 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) - Jirí Lebl
* [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
### Harmonic Analysis
@ -288,6 +342,7 @@ A curated list of awesome mathematics resources.
* [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
* [Complex Analysis](http://people.math.gatech.edu/%7Ecain/winter99/complex.html) - G. Cain (Georgia Tech)
### Functional Analysis
@ -297,6 +352,9 @@ A curated list of awesome mathematics resources.
* [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
@ -310,16 +368,22 @@ A curated list of awesome mathematics resources.
### 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
### 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
@ -332,6 +396,7 @@ A curated list of awesome mathematics resources.
* [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
### Statistics
@ -345,6 +410,8 @@ A curated list of awesome mathematics resources.
* [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 Learning
@ -363,6 +430,7 @@ A curated list of awesome mathematics resources.
* [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
@ -372,6 +440,7 @@ A curated list of awesome mathematics resources.
* [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
## Signal processing
@ -384,8 +453,20 @@ A curated list of awesome mathematics resources.
## Mathematics for Computer Science
* [Mathematics for Computer Science](https://people.csail.mit.edu/meyer/mcs.pdf) - Eric Lehman, F. Thomson Leighton, Albert R. Meyer
* [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
## 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
# License