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Algebra I

Geometry

Trigonometry

Calculus

Advanced Probability and Statistics

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500 textbooks are available on the E-book Directory

Algebra

• A First Book in Algebra, by Wallace C. Boyden
• Theory of Groups of Finite Order, by William Burnside
• On the study and difficulties of mathematics, by Augustus De Morgan
• First Course in the Theory of Equations, by Leonard E. Dickson
• Condensation of Determinants, by Lewis Carroll
• The Number-System of Algebra (2nd edition), by Henry B. Fine
• Lectures on Elementary Mathematics, by J. L. Lagrange
• A Review of Algebra, by Romeyn Henry Rivenburg
• An Introduction to Nonassociative Algebras, by Richard D. Schafer
• The First Steps in Algebra, by G. A. Wentworth

Number Theory

• The Theory of Numbers, by R. D. Carmichael
• Diophantine Analysis, by R. D. Carmichael
• Essays on the Theory of Numbers, by Richard Dedekind
• Some Famous Problems of the Theory of Numbers and in Particular Waring?s Problem

Combinatorics

• Topics on Tournaments, by John W. Moon

Calculus, Real Analysis, Fourier Series

• A Course of Pure Mathematics, by G. H. Hardy
• Calculus Made Easy, by Silvanus P. Thompson
• The Integration of Functions of a Single Variable, by G. H. Hardy
• An Elementary Treatise on Fourier?s Series and Spherical, Cylindrical, and Ellipsoidal Harmonics, by William Elwood Byerly
• Elementary Illustrations of the Differential and Integral Calculus, by De Morgan
• Introduction to Infinitesimal Analysis; Functions of One Real Variable, by Lennes et al.
• Hyperbolic Functions, by James McMahon

Complex Analysis, Elliptic Functions

• On Riemann?s Theory of Algebraic Functions and their Integrals, by Felix Klein

Euclidean and Non-Euclidean Geometry

• Euclid?s Book on Divisions of Figures, by Archibald, Euclid, Fibonacci, and Woepcke
• Geometrical Solutions Derived from Mechanics; a Treatise of Archimedes
• Conic Sections: Treated Geometrically, by W. H. Besant
• The Elements of non-Euclidean Geometry, by Julian Lowell Coolidge
• The Foundations of Geometry, by David Hilbert
• Solid Geometry with Problems and Applications by N. J. Lennes et al.
• Non-Euclidean Geometry, by Henry Parker Manning
• Plane Geometry, by G. A. Wentworth

Trigonometry, Technical Drawing

• Elements of Plane Trigonometry, by Hugh Blackburn
• How to Draw a Straight Line: A Lecture on Linkages, by A. B. Kempe
• Spherical Trigonometry: For the Use of Colleges and Schools, by I. Todhunter

Differential, Projective, and Synthetic Geometry

• General Investigations of Curved Surfaces of 1827 and 1825, by Carl Friedrich Gauss
• An Elementary Course in Synthetic Projective Geometry by Lehmer, Derrick Norman

Quaternions

• A Primer of Quaternions, by Arthur S. Hathaway
• Utility of Quaternions in Physics, by Alexander McAulay
• Vector Analysis and Quaternions, by Alexander Macfarlane

Probability

• A Treatise on Probability, by John Maynard Keynes
• Chance and Luck, by Richard A. Proctor

Elementary mathematics, Analysis,Lebesgue Integrals ..

• Basic Concepts of Mathematics by Elias Zakon
• Mathematical Analysis I by Elias Zakon
• Calculus by Gilbert Strang
• MEASURE THEORY Vol1 by David H. Fremlin
• MEASURE THEORY Vol2 by David H. Fremlin
• MEASURE THEORY Vol3 by David H. Fremlin
• MEASURE THEORY Vol4 by David H. Fremlin
• Real Analysis for Engineers by Erhan Cinlar, and Robert J. Vanderbei
• Measure Theory and Integration by Vitali Liskevich
• The Matrix Cookbook by Kaare Brandt Petersen
• Classical Geometry and Low-Dimensional Topology by Danny Calegari
• Basic algebra and trigonometry by Thomas Ward
• First Year Mathematics by William Chen
• Multivariable Calculus by George Cain, and James Herod
• Complex Analysis by George Cain
• Linear Algebra by Jim Hefferon
• Elementary Linear Algebra by Keith Matthews
• A First Course in Linear Algebra by Robert A. Beezer
• Complex Analysis by Douglas N. Arnold
• Set Theoretic Real Analysis by Krzysztof Ciesielski
• Expository notes in The finite reflection groups by Daniel Allcock
• Classical Geometry by Danny Calegari
• Difference Equations to Differential Equations by Dan Sloughter
• Course of linear algebra and multidimensional geometry by Ruslan Sharipov
• Examples, Lecture Notes and Specimen Exam Questions and Natural Sciences Tripos
• Calculus project by Michael Livshits
• The Octonions by John C. Baez
• Advanced Calculus by Shlomo Sternberg
• Whitman Calculus by David Guichard
• Olympiad Inequalities by Thomas J. Mildorf
• Elementary Real Analysis by Andrew M. Bruckner, Brian S. Thomson, and Judith B. Bruckner
• Precalculus (Electronic version annually updated.) by David H. Collingwood, and K. David Prince
• Understanding Calculus by Faraz Hussain [new]
• A ProblemText in Advanced Calculus by John M. Erdman [new]

Mathematical Logic and Set theory

• Mathematical Logic ? an Introduction by Michal Walicki
• Set theory by Peter G. Dixon
• Mathematical Logic by Stephen G. Simpson
• Foundations of Mathematics by Stephen G. Simpson
• Model Theory by Stephen G. Simpson
• A Problem Course in Mathematical Logic by Stefan Bilaniuk
• Computability and Incompleteness by Jeremy Avigad
• Complete proofs of Gdel?s Incompleteness Theorems by Byunghan Kim
• Fundamentals of Model Theory by William Weiss, and Cherie D?Mello
• Logic for Everyone by Robert A. Herrmann
• Proofs and Concepts by Dave Witte Morris, and Joy Morris [new]

Discrete Math

• Lecture Notes on Discrete Mathematics by Lszl Lovsz

Number Theory

Introductory Number Theory

• An Introduction to the Theory of Numbers by Leo Moser
• Number Theory Notes for students at IMO level by Naoki Sato
• Elementary Number Theory by William Edwin Clark
• Lecture notes on elementary number theory by Bruce Ikenaga
• Exercises with solutions on elementary number theory by Nigel Byott
• Elementary Number Theory by Michael Filaseta

p-adic numbers

• Lecture notes on p-adic numbers by Andrew Baker

Arithmetic Geometry

• Open Questions in Arithmetic Algebraic Geometry by Alice Silverberg

Fermat?s Last Theorem

• William Hammond?s Fermat Archive
• Review of Alf van der Poorten?s Notes on Fermat?s Last Theorem by Andrew Granville

Algebraic Number Theory

• Survey of Euclidean Number Fields by Franz Lemmermeyer
• A Computational Introduction to Number Theory and Algebra by Victor Shoup
• A Course In Algebraic Number Theory by Robert B. Ash
• Elementary and algebraic number theory by Ivan Fesenko
• Algebraic Number Theory by Jim Milne
• Algebraic Number Theory by Robin Chapman
• Invitation to higher local fields by Ivan Fesenko, and Masato Kurihara
• Euclidean Number Fields by Franz Lemmermeyer
• Algebra and Number Theory by Andrew Baker
• Elementary Number Theory by William A. Stein
• Notes for Dick Gross? Algebraic Number Theory Course by S. Sather-Wagstaff
• Algebraic Number Theory & Introduction to Automorphic L-functions by Ching-Li Chai
• Algebraic Number Theory by Jerome William Hoffmann
• Introduction to Number Theory by Franz Lemmermeyer

Analytic Number Theory

• Course notes for analytic number theory by Graham Everest
• Distribution of Prime Numbers by William Chen
• Introduction to Analytic Number Theory by Noam Elkies

Algebra, Algebraic Geometry

Algebra, Abstract

• Workbook in Higher Algebra by David Surowski
• Differential Algebra by Joseph Fels Ritt
• Structure and Representations of Jordan Algebras by Nathan Jacobson
• A Course in Universal Algebra by Stanley N. Burris, and H.P. Sankappanavar
• An Invitation to General Algebra and Universal Constructions by George M. Bergman
• Varieties of Lattices by Peter Jipsen, and Henry Rose
• Lectures on Matrices by Joseph Henry Maclagen Wedderburn
• Elementary Abstract Algebra by Edwin Clark
• Intro to Abstract Algebra by Paul Garrett
• Elements of Abstract and Linear Algebra by Edwin H. Connell
• Abstract Algebra:The Basic Graduate Year by Robert Ash
• A Course In Commutative Algebra by Robert Ash
• Notes for geometric group theory course by John R. Stallings
• Advanced Linear Algebra lecture notes (with real algorithm for the real Jordan form) by Keith Matthews
• Commutative algebra by Ivan Fesenko
• Abstract Algebra ? Number Theory, Group Theory, Galois Theory by Daviidd Wilkins
• Abstract group theory by Chuck Miller
• The Classification of the Finite Simple Groups by Daniel Gorenstein, Richard Lyons, and Ronald Solomon
• Group Characters, Symmetric Functions, and the Hecke Algebra by David M. Goldschmidt
• Finite Groups and their Representations by Andrew Baker
• Classical Groups by Peter Cameron
• Galois theory by Miles Reid
• Toeplitz and Circulant Matrices by Robert M. Gray
• Homogeneous spaces and equivariant embeddings by Dmitri A. Timashev
• Algebra: Abstract and Concrete by Frederick M. Goodman
• Commutative Algebra, Algebraic Geometry, Number theory, Field Theory, Galois Theory by Sudhir R. Ghorpade
• Fundamental Problems in Algorithmic Algebra by Chee Yap
• Braid groups and Galois theory by Frazer Jarvis
• A. N. Whitehead?s Geometric Algebra by Stephen Blake
• Commutator Theory for Congruence Modular Varieties by Ralph Freese, and Ralph McKenzie
• Constructive Aspects of the Inverse Galois Problem by A. Ledet, and N. Yui, and C. Jensen
• Publications and prepublications about braids

Algebraic Geometry

• Determinantal rings by Winfried Bruns, and Udo Vetter
• Algebraic geometry and projective differential geometry by Joseph M. Landsberg
• Introduction to Algebraic Geometry by Igor V. Dolgachev
• Algebraic Geometry by J.S. Milne
• Modular forms by Igor Dolgachev
• Complex analytic and algebraic geometry by Jean-Pierre Demailly
• Introduction to Algebraic Geometry by Yuriy Drozd
• Algebraic Curves by Hendrik L. Lenstra
• Algebraic Geometry, Toric Varieties, Galois Theory by David A. Cox
• Quasi-projective Moduli for Polarized Manifolds by Eckart Viehweg
• Lectures on Vanishing Theorems by Eckart Viehweg, and Hlne Esnault
• Introduction to Algebraic Geometry by Ravi Vakil
• Resolution of Singularities by Jnos Kollr
• Eleven books on geometry, topology, and algebra by Andrew Ranicki

Elliptic Curves

• Elliptic curves by Miles Reid
• Elliptic Curves by Jim Milne
• Modular curves by Bas Edixhoven
• Expository articles ? Computing rational points on curves, Elliptic curves by Bjorn Poonen

Category Theory

• Mixed Motives by Marc Levine
• Toposes, Triples and Theories by Michael Barr, and Charles Wells
• Abstract and Concrete Categories by J. Adamek, H. Herrlich, and G. Strecker
• A Gentle Introduction to Category Theory by Maarten M.Fokkinga
• Introduction to The Theory of Categories by David Madore
• Higher-Dimensional Categories: an illustrated guide book by Eugenia Cheng, and Aaron Lauda
• Higher Operads, Higher Categories by Tom Leinster

Lie Algebras

• Algebraic Groups and Discontinuous Subgroups by Armand Borel, and George D. Mostow
• Theory of representations etc by Claudio Procesi
• Semisimple Lie Algebras and their Representations by Robert N. Cahn
• Lie Algebras by Shlomo Sternberg

Topology

• Textbook in Problems on Elementary Topology by O.Ya.Viro, O.A.Ivanov, V.M.Kharlamov, and N.Y.Netsvetaev
• Topology Course by Aisling McCluskey, and Brian McMaster
• Topology by Thomas Ward
• Foliations and the topology of 3-manifolds by Danny Calegari

Algebraic Topology

• Algebraic Topology by Allen Hatcher
• Cohomology, Connections, Curvature and Characteristic Classes by David Mond
• Introduction to Characteritic Classes and Index Theory by Jean-Pierre Schneiders
• Algebraic Topology by Solomon Lefschetz
• Abstract group theory and topology articles by Walter Neumann

K-Theory

• An introduction to algebraic K-theory by Charles Weibel

Knots

• Knots Knotes by J. D. Roberts
• Vassiliev invariants and combinatorial structures by Sergei V. Duzhin
• Introduction to Vassiliev knot invariants by Sergei V. Duzhin, and Sergei Chmutov
• History of Knot Theory by Andrew Ranicki
• Knot Theory by Swatee Naik
• Knot theory from Vandermonde to Jones by Jozef H. Przytycki

Analysis

• Homeomorphisms in Analysis by Casper Goffman, Togo Nishiura, and Daniel Waterman
• Why the Boundary of a Round Drop Becomes a Curve of Order Four by A. N. Varchenko, and P. I. Etingof
• Lectures on Entire Functions by B. Ya. Levin
• Constructive Real Numbers and Constructive Function Spaces by N. A. Sanin
• Complex Variables by W.P. Novinger, and Robert B. Ash
• Foundations of Nonstandard Analysis by Erland Gadde
• Analytic functions by Stanislaw Saks, and Antoni Zygmund
• Theory of Functions of real variable by Shlomo Sternberg
• Real Analysis by Andrew M. Bruckner, Brian S. Thomson, and Judith B. Bruckner
• Introduction to Real Analysis by William F. Trench [new]

Functional Analysis

Functional Analysis

• Functional Analysis by Douglas N. Arnold
• Functional Analysis by Paul Garrett
• Functional Analysis by Thomas Ward
• Functional Analysis and Semi-Groups by Einar Hille, and Ralph S. Phillips
• The Convenient Setting of Global Analysis by Andreas Kriegl, and Peter W. Michor
• Hilbert Space Methods for Partial Differential Equations by Ralph E. Showalter
• Monotone Operators in Banach Space and Nonlinear Partial Differential Equations by Ralph E. Showalter
• Harmonic Analysis and Partial Differential Equations by Bjrn E.J. Dahlberg, and Carlos E. Kenig
• Functional Analysis by Thomas Ward
• Harmonic Function Theory by Sheldon Axler, Paul Bourdon, and Wade Ramey
• An Introduction to C*-Algebras by Pierre de la Harpe, and Vaughan Jones
• Functional Analysis by Peter G. Dixon
• Introduction to Microlocal Analysis by Richard Melrose
• Bernoulli Periodic Functions by Miguel Lerma
• Holomorphic Methods in Analysis and Mathematical Physics by Brian C. Hall

Differential Equations

• Nonlinear Analysis and Ordinary Differential Equations by Klaus Schmitt
• Ordinary Differential Equations and Dynamical Systems by Gerald Teschl
• Ordinary Differential Equations by Sheldon Newhouse
• Partial Differential Equations of Mathematical Physics by William W. Symes
• Analytic differential equations by Yulij Ilyashenko, and Sergei Yakovenko
• Exterior Differential Systems and Euler-Lagrange Partial Differential Equations by Robert L. Bryant, Phillip A. Griffiths, and Daniel A. Grossman
• Monograph on quasilinear partial differential equations by Marco Squassina
• Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations by Lloyd N. Trefethen
• Notes on Diffy Qs: Differential Equations for Engineers by Ji? Lebl [new]

Geometry

Differential Geometry

• Introduction to Tensor Calculus and Continuum Mechanics by John H. Heinbockel
• Topics in Differential Geometry by Peter W. Michor
• Natural operations in differential geometry by Peter W. Michor, Ivan Kolar, and Jan Slovak
• Intrinsic Geometry of Surfaces by A. D. Aleksandrov, and V. A. Zalgaller
• An Introduction to Riemannian Geometry by Sigmundur Gudmundsson, and Lund University
• Riemann Surfaces, Dynamics and Geometry by Curtis McMullen
• Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem by Peter B. Gilkey
• Differentiable Manifolds by Mariusz Wodzicki
• Differential Geometry by Sergei Yakovenko
• Symplectic Geometry with and Eye Toward Combinatorics by Sue Tolman
• Differential Geometry and Physics by Gabriel Lugo
• Differential geometry reconstructed by Alan U. Kennington
• Course of Differential Geometry by Ruslan Sharipov
• The Geometrization of Physics by Richard S. Palais
• Projective Geometry, Geometry of Surfaces, Differentiable Manifolds by Nigel Hitchin
• Vector Bundles and an Introduction to Gauge Theory by Steven Bradlow, Hung-Jen Hsu, and Chris Willett
• Twistor Geometry and Gauge Theory by Martin Wolf
• Complex Geometry of Nature and General Relativity by Giampiero Esposito
• Geometric Asymptotics by Victor Guillemin, and Shlomo Sternberg
• Projective Geometry by Balzs Csiks
• Differential Geometry by Balzs Csiks
• Projective and Polar Spaceas by Peter Cameron
• Transformation groups for begginers by S. V. Duzhin, and B. D. Tcherbotarevsky
• An Introduction to Differentiable Manifolds and Riemannian Geometry by William M. Boothby

Mathematical Physics

Dynamics

• Mechanism of the Heavens (1831), by Mary Somerville by Russell McNeil
• Dynamical Systems by George D. Birkhoff
• Dynamics in One Complex Variable: Introductory Lectures by John Milnor
• Geometrical theory of dynamical systems by Nils Berglun
• Introduction to Statics and Dynamics by Andy Ruina, and Rudra Prata

Entropy

• Entropy on the World Wide Web
• Entropy of Compact Group Automorphisms by Thomas Ward
• Valuations and Hyperbolicity in Dynamics by Thomas Ward
• Effective Hamiltonians and averaging for Hamiltonian dynamics by Lawrence Craig Evans
• Entropy and Partial Differential Equations by Lawrence Craig Evans
• CLASSICAL AND QUANTUM CHAOS by Predrag Cvitanovic?, Roberto Artuso, Ronnie Mainieri, Gregor Tanner, Gbor Vattay, Niall Whelan, and Andreas Wirzba
• Dynamical systems by Shlomo Sternberg

Quantum Mechanics

• Mathematical Methods in Quantum Mechanics by Gerald Teschl
• Quantum Mechanics by Klaus Schulten
• Foundations of Quantum Mechanics & Quantum Information by M.B. Plenio
• Quantum Geometry and more by Micho Durdevich
• Quantum Probability Theory by Miklos Redei, and Stephen J. Summers

Quantum Field Theory

• Comprehensive textbook on quantum (and classical) field theory by Warren Siegel
• Quantum Field Theory by Ben Simons
• Mathematical ideas and notions of quantum field theory by Pavel Etingof
• Introduction to Algebraic and Constructive Quantum Field Theory by Irving E. Segal, Zhengfang Zhou, and John C. Baez
• Quantum Field Theory program at IAS by Irving E. Segal, Zhengfang Zhou, and John C. Baez
• Graduate textbooks: Field Theory, Relativity, Superspace, Strings by Warren Siegel
• What is String Theory by Joseph Polchinski
• Fluctuating Geometries in Statistical Mechanics and Field Theory
• Operator Algebras and Quantum Statistical Mechanics, Vol I by Ola Bratteli
• Operator Algebras and Quantum Statistical Mechanics, Vol II by Ola Bratteli
• D-Brane Primer by Clifford V. Johnson
• Introduction to Superstring Theory by Elias Kiritsis
• Algebraic Quantum Field Theory by Hans Halvorson, and Michael Mueger

Condensed Matter

• Worked examples in the Geometry of Crystals by HKDH Bhadeshia
• Introduction to Solid-State Physics; Many-Body Theory by Chetan Nayak
• Many-Body Physics by Piers Coleman
• Theory of Superconductivity by Helmut Eschrig
• High-Temperature Superconductivity by Peter Hirschfeld
• Solid State Physics by Peter Hirschfeld
• Complex Surphaces in Materials Science
• Photonic Crystals: Molding the Flow of Light by John D. Joannopoulos, Steven G. Johnson, Joshua N. Winn, and Robert D. Meade

Special and General Relativity

• General Relativity, Nonlinear PDEs, etc by Sergiu Klainerman
• Special Relativity and Geometry by C. E. Harle, and R. Bianconi
• Differential Geometry (and Relativity) by Bob Gardner
• General Relativity and Quantum Cosmology by Sean M. Carroll
• Public lectures by Stephen Hawking and Roger Penrose

Physics

• Essential Physics 1 by Frank Firk
• Introduction to Groups, Invariants & Particles by Frank W.K. Firk
• Classical Electrodynamics by Bo Thid
• Classical electrodynamics and theory of relativity by Ruslan Sharipov
• Electromagnetic Theory and Computation: A Topological Approach by Paul W. Gross, and P. Robert Kotiuga
• MOTION MOUNTAIN TEXTBOOK Hiking beyond space and time along the concepts of modern physics by Christoph Schiller
• Fundamentals of Thermodynamics by J. Karl Johnson
• Non-Equilibrium Statistical Mechanics by Klaus Schulten
• Course in Electrodynamics by Franz Wegner
• Light and Matter by Ben Crowell
• Order-of-magnitude-physics by Sanjoy Mahajan
• Physical Applications of Geometric Algebra by Anthony Lasenby, and Chris Doran
• Group Theory: Lie?s, Tracks, And Exceptional Groups by Predrag Cvitanovic?
• An Elementary Introduction to Groups and Representations by Brian C. Hall
• Geometric Models for Noncommutative Algebras by A. Cannas da Silva, and A. Weinstein
• Differential Forms in Electromagnetic Theory by Richard H. Selfridge, David V. Arnold, and Karl F. Warnick
• Lectures on integration of several variables by Michael Adler
• Methods of Mathematical Physics by Mark Trodden
• Further Mathematical Methods by Niels Walet
• Computational Physics by Angus MacKinnon
• Zeno meets modern science by Zurab K. Silagadze
• Feynman?s derivation of Maxwell equations and extra dimensions by Zurab K. Silagadze
• TeV scale gravity, mirror universe, and ? dinosaurs by Zurab K. Silagadze
• Quick introduction to tensor analysis by Ruslan Sharipov
• Traveling Wave Solutions of Parabolic Systems by Aizik I. Volpert, Vitaly A. Volpert, and Vladimir A. Volpert

Probability Theory

• Introduction to Probability by Charles Grinstead, and J. Laurie Snell
• Probability Tutorials by Noel Vaillant
• Probability Theory: The Logic of Science by Edwin Thompson Jaynes
• Probability Theory As Extended Logic by Larry Bretthorst
• Introduction to Probability by Oliver Knill
• Random Walks and Diffusion by Martin Z. Bazant
• Reversible Markov Chains and Random Walks on Graphs by David Aldous, and Jim Fill
• An Invitation to Sample Paths of Brownian Motion by Yuval Peres
• Notes on probability theory by Hendrik W. Lenstra, Jr.
• An introduction to stochastic differential equations by Lawrence Craig Evans
• Stochastic Calculus by Alan Bain
• Probability Theory by S.R.S.Varadhan
• Statistics by S.R.S.Varadhan
• Stochastic Processes by S.R.S.Varadhan
• Stochastic Differential Equations by Thomas G. Kurtz
• Stochastic Integration and Stochastic Differential Equations by Klaus Bichteler
• Probability, Random Processes, and Ergodic Properties by Robert M. Gray

Applied Mathematics

• Derivations of Applied Mathematics by Thaddeus H. Black
• Linear Methods of Applied Mathematics by Evans Harrell, and James Herod
• Linear Algebra, Infinite Dimensions, and Maple by James Herod
• generatingfunctionology by Herbert Wilf
• Algorithms and Complexity by Herbert S. Wilf
• A=B by Herbert Wilf, Marko Petkovsek, and Doron Zeilberger
• Applied Math Textbook by Sean Mauch
• Mathematical Tools for Physics by James Nearing
• Applied Mathematics by Peter J. Olver, and Chehrzad Shakiban
• Surveys in Combinatorics
• Computational Complexity: A Conceptual Perspective by Oded Goldreich
• Papers on Combinatorial Enumeration and Asymptotics by Andrew Odlyzko
• Hyperplane Arrangements by Richard Stanley
• Introduction to Statistical Signal Processing by R.M. Gray, and L.D. Davisson
• Applied Abstract Algebra by David Joyner, Richard Kreminski, and Joann Turisco

Numerical Analysis

• Numerical Analysis by Lucio Tavernini
• Finite Element Method/Boundry Element Method by Peter Hunter
• Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods by Richard Barrett, Michael Berry, Tony F. Chan, James Demmel, June Donato, Jack Dongarra, Victor Eijkhout, Roldan Pozo, Charles Romine, and Henk van der Vorst
• Numerical Analysis at the University of Cambridge
• Numerical Mathematics and Scientific Computation by Germund Dahlquist, and ke Bjrck
• The Boundary Element Method in Acoustics by Stephen Kirkup
• Computational geometry, mesh generation, numerical methods by Jonathan Shewchuk
• Numerical Analysis by Steven Elliot Pav
• Convex Optimization by Stephen Boyd, and Lieven Vandenberghe
• Optimization by Pravin Varaiya

Information Theory

• Information Theory, Inference and Learning Algorithms by David J. C. MacKay
• A Short Course in Information Theory by David J. C. MacKay
• Primer on Information Theory by Thomas Schneider
• Several books (not only Information Theory) by Gregory J. Chaitin

Financial mathematics

• Applied Quantitative Finance by W. Hrdle, T. Kleinow, and G. Stahl
• Measure theory, Probability, Stochastic calculus, General theory of processes, Financial mathematics by Rich Bass
• Structural Analysis of Discrete Data and Econometric Applications by Charles F. Manski, and Daniel L. McFadden
• Essential Principles of Economics by Roger McCain
• Game theory examples by Roger McCain
• Discrete Time Finance by Christian Ewald
• Mathematical Finance: Introduction to Continuous Time Financial Market Models by Christian Ewald
• Games, Fixed Points and Mathematical Economics by Christian Ewald

Game Theory

• Gametheory.net
• Determinacy in infinite games by Jindrich Zapletal

Cryptography

• Handbook of Applied Cryptography by Alfred J. Menezes, Paul C. van Oorschot, and Scott A. Vanstone
• Foundations of Cryptography, Vol 1 by Oded Goldreich
• Foundations of Cryptography, Vol 2 by Oded Goldreich
• Cryptography by S. Goldwasser, and M. Bellare
• Introduction to Modern Cryptography by Mihir Bellare, and Phillip Rogaway
• Cryptography and Cryptanalysis by Anna Lysyanskaya
• Modern Cryptography by Mihir Bellare and Phillip Rogaway
• Cryptography and Cryptanalysis by Glenn Durfee
• Coding Theory and Cryptography: From Enigma and Geheimschreiber to Quantum Theory by David Joyner

Miscellanea

• Mathematics under the Microscope by Alexandre Borovik
• What is and what will be: Integrating spirituality and science by Paul Budnik

Fractals

• Fractals in the Plane ? the Ergodic Theory Methods by F. Przytycki, and M. Urbanski
• Conformal Dynamics by Curt McMullen
• Fractals by P. G. Dixon

Graph Theory

• Graph Theory with Applications by J.A. Bondy, and U.S.R. Murty
• Graph Theory by Reinhard Diestel

• Interactive Graph theory tutorials by Chris K. Caldwell

Coxeter groups

• Miscellaneous facts about Coxeter groups by Robert B. Howlett
• Buildings, BN-pairs, Hecke algebras, classical groups by Paul Garrett

Nielsen Fixed Point Theory

• Nielsen fixed point theory, Geometric group theory by Ross Geoghegan

Permutation Puzzles

• Mathematics of Rubik?s cube by David Joyner

Springer Math Books

A Classical Introduction to Modern Number Theory,Kenneth IrelandMichael Rosen

A Classical Introduction to Modern Number Theory,Kenneth IrelandMichael Rosen

A Course in Arithmetic,Jean-Pierre Serre

A Course in Computational Algebraic Number Theory,Henri Cohen

A Course in Differential Geometry,Wilhelm Klingenberg

A Course in Functional Analysis,John B. Conway

A Course in Homological Algebra,P. J. HiltonU. Stammbach

A Course in Homological Algebra,Peter J. HiltonUrs Stammbach

A Course in Mathematical Logic,Yu. I. Manin

A Course in Number Theory and Cryptography,Neal Koblitz

A Course in Number Theory and Cryptography,Neal Koblitz

A Course in Simple-Homotopy Theory,Marshall M. Cohen

A Course in p-adic Analysis,Alain M. Robert

A Course in the Theory of Groups,Derek J. S. Robinson

A Course in the Theory of Groups,Derek J. S. Robinson

A Course on Borel Sets,S. M. Srivastava

A Course on Borel Sets,S. M. Srivastava

A First Course in Noncommutative Rings,T. Y. Lam

A First Course in Noncommutative Rings,T. Y. Lam

A Hilbert Space Problem Book,P. R. Halmos

A Hilbert Space Problem Book,Paul R. Halmos

A Short Course on Spectral Theory,William Arveson

Additive Number Theory,Melvyn B. Nathanson

Advanced Linear Algebra,Steven Roman

Advanced Mathematical Analysis,Richard Beals

Advanced Topics in Computational Number Theory,Henri Cohen

Advanced Topics in the Arithmetic of Elliptic Curves,Joseph H. Silverman

Algebra,Serge Lang

Algebra,Thomas W. Hungerford

Algebra,William A. AdkinsSteven H. Weintraub

Algebraic Functions and Projective Curves,David M. Goldschmidt

Algebraic Geometry,Joe Harris

Algebraic Geometry,Robin Hartshorne

Algebraic Graph Theory,Chris GodsilGordon Royle

Algebraic Groups and Class Fields,Jean-Pierre Serre

Algebraic K-Theory and Its Applications,Jonathan Rosenberg

Algebraic Number Theory,Serge Lang

Algebraic Number Theory,Serge Lang

Algebraic Theories,Ernest G. Manes

Algebraic Topology,William Fulton

An Algebraic Introduction to Mathematical Logic,Donald W. BarnesJohn M. Mack

An Introduction to Algebraic Topology,Joseph J. Rotman

An Introduction to Analysis,Arlen BrownCarl Pearcy

An Introduction to Banach Space Theory,Robert E. Megginson

An Introduction to Convex Polytopes,Arne Brondsted

An Introduction to Knot Theory,W. B. Raymond Lickorish

An Introduction to Riemann-Finsler Geometry,D. BaoS.-S. ChernZ. Shen

An Introduction to the Theory of Groups,Joseph J. Rotman

An Invitation to C*-Algebras,William Arveson

Analysis Now,Gert K. Pedersen

Analysis for Applied Mathematics,Ward Cheney

Analytic Number Theory,Donald J. Newman

Applications of Lie Groups to Differential Equations,Peter J. Olver

Associative Algebras,Richard S. Pierce

Axiomatic Set Theory,Gaisi TakeutiWilson M. Zaring

Banach Algebra Techniques in Operator Theory,Ronald G. Douglas

Banach Algebras and Several Complex Variables,John Wermer

Basic Homological Algebra,M. Scott Osborne

Basic Theory of Algebraic Groups and Lie Algebras,Gerhard P. Hochschild

Brownian Motion and Stochastic Calculus,Ioannis KaratzasSteven E. Shreve

Brownian Motion and Stochastic Calculus,Ioannis KaratzasSteven E. Shreve

Categories for the Working Mathematician,Saunders Mac Lane

Categories for the Working Mathematician,Saunders Mac Lane

Classical Descriptive Set Theory,Alexander S. Kechris

Classical Topics in Complex Function Theory,Reinhold Remmert

Classical Topology and Combinatorial Group Theory,Dr. John Stillwell

Classical Topology and Combinatorial Group Theory,John Stillwell

Cohomology of Groups,Kenneth S. Brown

Combinatorial Convexity and Algebraic Geometry,Gunter Ewald

Combinatorics with Emphasis on the Theory of Graphs,Jack E. GraverMark E. Watkins

Commutative Algebra,David Eisenbud

Commutative Algebra,Oscar ZariskiPierre Samuel

Complex Analysis,Serge Lang

Complex Analysis,Serge Lang

Complex Analysis,Serge Lang

Complex Variables,Carlos A. BerensteinRoger Gay

Computability,Douglas S. Bridges

Convex Polytopes,Volker KaibelVictor KleeGunter M. Ziegler

Cyclotomic Fields I and II,Serge Lang

Cyclotomic Fields II,Serge Lang

Cyclotomic Fields,Dr. Serge Lang

Denumerable Markov Chains,John G. KemenyJ. Laurie SnellAnthony W. Knapp

Differential Analysis on Complex Manifolds,R. O. Wells Jr.

Differential Forms in Algebraic Topology,Raoul BottLoring W. Tu

Differential Geometry: Manifolds, Curves, and Surfaces,Marcel BergerBernard Gostiaux

Differential Topology,Morris W. Hirsch

Differential and Riemannian Manifolds,Serge Lang

Diophantine Geometry,Marc HindryJoseph H. Silverman

Elementary Algebraic Geometry,Dr. Keith Kendig

Elementary Methods in Number Theory,Melvyn B. Nathanson

Elements of Functional Analysis,Francis HirschGilles Lacombe

Elements of Homotopy Theory,George W. Whitehead Professor Emeritus

Elliptic Curves,Dale Husemoller

Elliptic Curves,Dale Husemoller

Elliptic Functions,Serge Lang

Fibre Bundles,Dale Husemoller

Fibre Bundles,Dale Husemoller

Field Theory,Steven Roman

Field and Galois Theory,Patrick Morandi

Finite Reflection Groups,L. C. GroveC. T. Benson

Foundations of Differentiable Manifolds and Lie Groups,Frank W. Warner

Foundations of Hyperbolic Manifolds,John G. Ratcliffe

Foundations of Real and Abstract Analysis,Douglas S. Bridges

Fourier Analysis and Its Applications,S. AxlerF. W. GehringK. A. Ribet

Fourier Analysis on Number Fields,Dinakar RamakrishnanRobert J. Valenza

Fourier Series,R. E. Edwards

Fourier Series,R. E. Edwards

From Holomorphic Functions to Complex Manifolds,Klaus FritzscheHans Grauert

Functions of One Complex Variable I,John B. Conway

Functions of One Complex Variable II,John B. Conway

Functions of One Complex Variable,John B. Conway

Fundamentals of Differential Geometry,Serge Lang

Galois Theory,Jean-Pierre Escofier

General Relativity for Mathematicians,Dr. Rainer K. SachsDr. Hung-Hsi Wu

Geometric Functional Analysis and its Applications,Richard B. Holmes

Geometric Topology in Dimensions 2 and 3,Edwin E. Moise

Graph Theory,Bela Bollobas

Grobner Bases,Thomas BeckerVolker Weispfenning

Groups and Representations,J. L. AlperinRowen B. Bell

Harmonic Analysis on Semigroups,Christian BergJens Peter Reus ChristensenPaul Ressel

Harmonic Function Theory,Sheldon AxlerPaul BourdonWade Ramey

Harmonic Function Theory,Sheldon AxlerPaul BourdonWade Ramey

Holomorphic Functions and Integral Representations in Several Complex Variables,R. Michael Range

Homology Theory,James W. Vick

Integration and Probability,Paul Malliavin

Introduction to Affine Group Schemes,William C. Waterhouse

Introduction to Algebraic and Abelian Functions,Serge Lang

Introduction to Axiomatic Set Theory,Gaisi TakeutiWilson M. Zaring

Introduction to Axiomatic Set Theory,Gaisi TakeutiWilson M. Zaring

Introduction to Coding Theory,J. H. van Lint

Introduction to Coding Theory,J. H. van Lint

Introduction to Coding Theory,J. H. van Lint

Introduction to Cyclotomic Fields,Lawrence C. Washington

Introduction to Cyclotomic Fields,Lawrence C. Washington

Introduction to Elliptic Curves and Modular Forms,Neal Koblitz

Introduction to Elliptic Curves and Modular Forms,Neal Koblitz

Introduction to Knot Theory,Richard H. CrowellRalph H. Fox

Introduction to Lie Algebras and Representation Theory,James E. Humphreys

Introduction to Operator Theory I,Arlen BrownCarl Pearcy

Introduction to Smooth Manifolds,John M. Lee

Introduction to Topological Manifolds,John M. Lee

Lectures in Abstract Algebra I,Nathan Jacobson

Lectures in Abstract Algebra,Nathan Jacobson

Lectures in Abstract Algebra,Nathan Jacobson

Lectures on Discrete Geometry,Jiri Matousek

Lectures on Modules and Rings,T. Y. Lam

Lectures on Polytopes,Gunter M. Ziegler

Lectures on Riemann Surfaces,Otto Forster

Lectures on the Hyperreals,Robert Goldblatt

Lectures on the Theory of Algebraic Numbers,Erich Hecke

Lie Groups,Daniel Bump

Lie Groups, Lie Algebras, and Representations,Brian C. Hall

?Lie Groups, Lie Algebras and Their Representations?

Linear Algebra,Werner Greub

Linear Algebraic Groups,Armand Borel

Linear Algebraic Groups,James E. Humphreys

Linear Geometry,K. W. GruenbergA. J. Weir

Linear Operators in Hilbert Spaces,Joachim Weidmann

Linear Representations of Finite Groups,Jean-Pierre Serre

Linear Topological Spaces,John L. KelleyIsaac NamiokaW. F. Donoghue Jr.Kenneth R. LucasB. J. PettisEbbe Thue PoulsenG. Baley PriceWendy RobertsonW. R. ScottKennan T. Smith

Local Fields,Jean-Pierre Serre

Mathematical Logic,J. Donald Monk

Mathematical Methods of Classical Mechanics,V. I. Arnold

Mathematical Methods of Classical Mechanics,V. I. Arnold

Matrices,Denis Serre

Matrix Analysis,Rajendra Bhatia

Measure Theory,J. L. Doob

Measure Theory,Paul R. Halmos

Measure and Category,John C. Oxtoby

Measure and Category,John C. Oxtoby

Measure and Integral,John L. KelleyT. P. Srinivasan

Metric Structures in Differential Geometry,Gerard Walschap

Model Theory,David Marker

Modern Geometry ? Methods and Applications,B. A. DubrovinA. T. FomenkoS. P. Novikov

Modern Geometry? Methods and Applications,B. A. DubrovinS. P. NovikovA. T. Fomenko

Modern Graph Theory,Bela Bollobas

Modular Functions and Dirichlet Series in Number Theory,Tom M. Apostol

Modular Functions and Dirichlet Series in Number Theory,Tom M. Apostol

Moduli of Curves,Joe HarrisIan Morrison

Multiplicative Number Theory,Harold Davenport

Noncommutative Algebra,Benson FarbR. Keith Dennis

Nonsmooth Analysis and Control Theory,F. H. ClarkeYu. S. LedyaevR. J. SternR. R. Wolenski

Number Theory in Function Fields,Michael Rosen

Numbers,Heinz-Dieter EbbinghausHans HermesFriedrich HirzebruchMax KoecherKlaus MainzerJurgen NeukirchAlexander PrestelReinhold Remmert

Numerical Analysis,Rainer Kress

One-Parameter Semigroups for Linear Evolution Equations,Klaus-Jochen EngelRainer Nagel

Optima and Equilibria,Jean-Pierre Aubin

Ordinary Differential Equations,Wolfgang Walter

?p-adic Numbers, p-adic Analysis and Zeta-Functions?

Partial Differential Equations,Jeffrey Rauch

Partial Differential Equations,Jurgen Jost

Permutation Groups,John D. DixonBrian Mortimer

Polynomials and Polynomial Inequalities,Peter BorweinTamas Erdelyi

Principles of Random Walk,Frank Spitzer

Probability Theory I,M. Loeve

Probability Theory I,M. Loeve

Probability,A. N. Shiryaev

Probability,A. N. Shiryayev

Problems in Analytic Number Theory,M. Ram Murty

Quantum Groups,Christian Kassel

Random Processes,M. Rosenblatt

Rational Homotopy Theory,Yves FelixStephen HalperinJean-Claude Thomas

Real and Functional Analysis,Serge Lang

Representation Theory,William FultonJoe Harris

Representations of Compact Lie Groups,Theodor BrockerTammo tom Dieck

Riemann Surfaces,Hershel M. FarkasIrwin Kra

Riemann Surfaces,Hershel M. FarkasIrwin Kra

Riemannian Geometry,Peter Petersen

Riemannian Manifolds,John M. Lee

Rings and Categories of Modules,Frank W. AndersonKent R. Fuller

Rings and Categories of Modules,Frank W. AndersonKent R. Fuller

Sequences and Series in Banach Spaces,Joseph Diestel

Several Complex Variables and Banach Algebras,Herbert AlexanderJohn Wermer

Several Complex Variables,H. GrauertK. Fritzsche

Sheaf Theory,Glen E. Bredon

Singular Homology Theory,William S. Massey

?SL2(R)?,Serge Lang

Smooth Manifolds and Observables,Jet Nestruev

Stable Mappings and Their Singularities,Martin GolubitskyVictor Guillemin

Tensor Geometry,Christopher Terence John DodsonTimothy Poston

The Arithmetic of Elliptic Curves,Joseph H. Silverman

The Arithmetic of Hyperbolic 3-Manifolds,Colin MaclachlanAlan W. Reid

The Geometry of Discrete Groups,Alan F. Beardon

The Geometry of Schemes,David EisenbudJoe Harris

The Symmetric Group,Bruce E. Sagan

Theory of Bergman Spaces,Haakan HedenmalmBoris KorenblumKehe Zhu

Theory of Complex Functions,Reinhold Remmert

Topological Vector Spaces,H. H. SchaeferM. P. Wolff

Topological Vector Spaces,Helmut H. Schaefer

Topology and Geometry,Glen E. Bredon

Univalent Functions and Teichmuller Spaces,Olli Lehto

Using Algebraic Geometry,David CoxJohn LittleDonal O?Shea

Weakly Differentiable Functions,William P. Ziemer

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Reference

Lists by Erik Royall, Erik Royall, Stuart Ga?e, Antonio Cangiano