Free Books on Mathematics XII

  1. Semiriemannian Geometry- Shlomo Sternberg
  2. Essential Mathematics - Franco Vivaldi
  3. Analytic Combinatorics - Philippe Flajolet,and Robert Sedgewick
  4. Calculus, Applications and Theory - Kenneth Kuttler
  5. One Variable Advanced Calculus -Kenneth Kuttler
  6. Many Variable Advanced Calculus -Kenneth Kuttler
  7. Elementary linear algebra book -Kenneth Kuttler
  8. Derivations of Applied Mathematics - Thaddeus H. Black
  9. Algorithmic Mathematics - Leonard Soicher, Franco Vivaldi
  10. Elementary Mathematics - William Chen and Xian Duong
  11. Logic For Computer Science - Foundations of Automatic Theorem Proving - Jean H. Gallier
  12. Combinatorial Algorithms for Computers and Calculators- Albert Nijenhuis and Herbert S. Wilf
  13. Logic and Computation - Jean Gallier
  14. Geometry, Topology, Geometric Modeling -Jean Gallier
  15. Notes on Differential Geometry and Lie Groups - Jean Gallier
  16. Convex Sets, Polytopes, Combinatorial Topology, Voronoi Diagrams and Delaunay Triangulations- Jean Gallier
  17. Algebra- Jean Gallier
  18. Algebraic Geometry- Jean Gallier
  19. Discrete Mathematics for Computer Scienc- Jean Gallier
  20. Basic Algebra and Analysis - Jean Gallier
  21. Languages, Automata, Theory of Computation- Jean Gallier
  22. Computational Geometry: Methods and Applications - Jianer Chen
  23. Computational Optimization - Jianer Chen
  24. Algorithms for Modular Elliptic Curves- John E. Cremona
  25. An Introduction to the Theory of Numbers - Leo Moser
  26. Basic Concepts of Mathematics -Elias Zakon
  27. Mathematical Analysis I-Elias Zakon
  28. A Cook-Book Of Mathematics - Viatcheslav Vinogradov
  29. Linear Programming: Foundations and Extensions- Robert Vanderbei

Free Book on Algebra, Algebraic Geometry X

Algebra, Abstract

  1. Workbook in Higher Algebra by David Surowski
  2. Differential Algebra by Joseph Fels Ritt
  3. Structure and Representations of Jordan Algebras by Nathan Jacobson
  4. A Course in Universal Algebra by Stanley N. Burris, and H.P. Sankappanavar
  5. An Invitation to General Algebra and Universal Constructions by George M. Bergman
  6. Varieties of Lattices by Peter Jipsen, and Henry Rose
  7. Lectures on Matrices by Joseph Henry Maclagen Wedderburn
  8. Elementary Abstract Algebra by Edwin Clark
  9. Intro to Abstract Algebra by Paul Garrett
  10. Elements of Abstract and Linear Algebra by Edwin H. Connell
  11. Abstract Algebra:The Basic Graduate Year by Robert Ash
  12. A Course In Commutative Algebra by Robert Ash
  13. Notes for geometric group theory course by John R. Stallings
  14. Advanced Linear Algebra lecture notes (with real algorithm for the real Jordan form) by Keith Matthews
  15. Commutative algebra by Ivan Fesenko
  16. Abstract Algebra - Number Theory, Group Theory, Galois Theory by Daviidd Wilkins
  17. Abstract group theory by Chuck Miller
  18. The Classification of the Finite Simple Groups by Daniel Gorenstein, Richard Lyons, and Ronald Solomon
  19. Group Characters, Symmetric Functions, and the Hecke Algebra by David M. Goldschmidt
  20. Finite Groups and their Representations by Andrew Baker
  21. Classical Groups by Peter Cameron
  22. Galois theory by Miles Reid
  23. Toeplitz and Circulant Matrices by Robert M. Gray
  24. Homogeneous spaces and equivariant embeddings by Dmitri A. Timashev
  25. Algebra: Abstract and Concrete by Frederick M. Goodman
  26. Commutative Algebra, Algebraic Geometry, Number theory, Field Theory, Galois Theory by Sudhir R. Ghorpade
  27. Fundamental Problems in Algorithmic Algebra by Chee Yap
  28. Braid groups and Galois theory by Frazer Jarvis
  29. A. N. Whitehead's Geometric Algebra by Stephen Blake
  30. Commutator Theory for Congruence Modular Varieties by Ralph Freese, and Ralph McKenzie
  31. Constructive Aspects of the Inverse Galois Problem by A. Ledet, and N. Yui, and C. Jensen
  32. Publications and prepublications about braids
  33. Basics of Algebra and Analysis for Computer Science by Jean Gallier
  34. Abstract Algebra with GAP, Authored by By J. G. Rainbolt and J. A. Gallian
  35. Mathematical Methods of Engineering Analysis, by Erhan Çinlar and Robert J. Vanderbei

Algebraic Geometry

Elliptic Curves

Category Theory

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

Lie Algebras

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

Free Books on Mathematical Analysis IX

Analysis

  1. Homeomorphisms in Analysis by Casper Goffman, Togo Nishiura, and Daniel Waterman
  2. Why the Boundary of a Round Drop Becomes a Curve of Order Four by A. N. Varchenko, and P. I. Etingof
  3. Lectures on Entire Functions by B. Ya. Levin
  4. Constructive Real Numbers and Constructive Function Spaces by N. A. Sanin
  5. Complex Variables by W.P. Novinger, and Robert B. Ash
  6. Foundations of Nonstandard Analysis by Erland Gadde
  7. Analytic functions by Stanislaw Saks, and Antoni Zygmund
  8. Theory of Functions of real variable by Shlomo Sternberg

Functional Analysis

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

Differential Equations

  1. Nonlinear Analysis and Ordinary Differential Equations by Klaus Schmitt
  2. Ordinary Differential Equations and Dynamical Systems by Gerald Teschl
  3. Ordinary Differential Equations by Sheldon Newhouse
  4. Partial Differential Equations of Mathematical Physics by William W. Symes
  5. Analytic differential equations by Yulij Ilyashenko, and Sergei Yakovenko
  6. Exterior Differential Systems and Euler-Lagrange Partial Differential Equations by Robert L. Bryant, Phillip A. Griffiths, and Daniel A. Grossman
  7. Monograph on quasilinear partial differential equations by Marco Squassina
  8. Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations by Lloyd N. Trefethen

Free Book On Mathemathics VIII (Topology)

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

Algebraic Topology

K-Theory

Knots

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

Free Books on Mathematical Physics VII

Dynamics

Entropy

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

Quantum Mechanics

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

Quantum Field Theory

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

Condensed Matter

Special and General Relativity

Physics

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

Free Books on Mathematics VII

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

Fractals

  1. Fractals in the Plane - the Ergodic Theory Methods by F. Przytycki, and M. Urbanski
  2. Conformal Dynamics by Curt McMullen
  3. Fractals by P. G. Dixon

Graph Theory

  1. Graph Theory with Applications by J.A. Bondy, and U.S.R. Murty
  2. Graph Theory by Reinhard Diestel
  3. Interactive Graph theory tutorials by Chris K. Caldwell

Coxeter groups

Nielsen Fixed Point Theory

Permutation Puzzles

  1. Mathematics of Rubik's cube by David Joyner

Free Book on Mathemathics V (Number Theory)

Introductory Number Theory

p-adic numbers

Arithmetic Geometry

Fermat's Last Theorem

Algebraic Number Theory

Analytic Number Theory

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

Free Books on Mathematics IV (Applied Mathematics)

Applied Mathematics

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

Numerical Analysis

  1. Numerical Analysis by Lucio Tavernini
  2. Finite Element Method/Boundry Element Method by Peter Hunter
  3. 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
  4. Numerical Analysis at the University of Cambridge
  5. Numerical Mathematics and Scientific Computation by Germund Dahlquist, and Åke Björck
  6. The Boundary Element Method in Acoustics by Stephen Kirkup
  7. Computational geometry, mesh generation, numerical methods by Jonathan Shewchuk
  8. Numerical Analysis by Steven Elliot Pav
  9. Convex Optimization by Stephen Boyd, and Lieven Vandenberghe
  10. Optimization by Pravin Varaiya

Information Theory

Financial mathematics

Game Theory

Cryptography

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

Free Books on Mathematics III (Geometry )

Differential Geometry

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

Free Books on Mathematics II

Probability and Statistics

  1. Introduction to Probability, Charles M. Grinstead, J. Laurie Snell
  2. Probability Theory, S.R.Srinivasa Varadhan
  3. Probability, Random Processes, and Ergodic Properties, R.M. Gray
  4. An Introduction to Probability and Random Processes, Gian-Carlo Rota and Kenneth Baclawski
  5. Probability Theory: The Logic of Science, Edwin Thompson Jaynes
  6. Probability on Trees and Networks, Russell Lyons with Yuval Peres
  7. Probability, Douglas Kennedy
  8. Probability and Stochastic Processes with Applications , Oliver Knill
  9. Markov Chains and Stochastic Stability, S.P. Meyn and R.L. Tweedie
  10. Reversible Markov Chains and Random Walks on Graphs, David Aldous
  11. Lectures on Statistics-Robert B. Ash
  12. A Programmed Introduction To Statistics - Elzey
  13. Lecture Notes in Statistics- G. Larry Bretthorst
  14. Charting Statistics - Spear, Mary Eleanor
  15. Concepts and Applications of Inferential Statistics - Richard Lowry
  16. Convergence of Stochastic Processes - David Pollard
  17. Discriminant Analysis and Clustering - NAP
  18. Electronic Statistics Textbook -
  19. An Anthology of Chance Operations- La Monte Young, editor
  20. Advanced probability theory- Prof. Boris Tsirelson
  21. An Exploration of Random Processes for Engineers - B. Hajek
  22. Elementary Statistical Analysis - Wilks, S.S
  23. Probability Tutorials by Noel Vaillant
  24. Random Walks and Diffusion by Martin Z. Bazant
  25. Reversible Markov Chains and Random Walks on Graphs by David Aldous, and Jim Fill
  26. Notes on probability theory by Hendrik W. Lenstra, Jr.
  27. An introduction to stochastic differential equations by Lawrence Craig Evans
  28. Stochastic Calculus by Alan Bain
  29. Statistics by S.R.S.Varadhan
  30. Stochastic Processes by S.R.S.Varadhan
  31. Stochastic Differential Equations by Thomas G. Kurtz
  32. Stochastic Integration and Stochastic Differential Equations by Klaus Bichteler

Free Books on Mathematics I

Algebra and Calculus

  1. Elementary Linear Algebra, Keith Matthews
  2. New Calculus without Limits - Karl Heinz Dovermann
  3. A Summary of Calculus-Karl Heinz Dovermann
  4. A First Course in Linear Algebra, Robert A. Beezer
  5. Abstract Algebra: The Basic Graduate Year-Robert B. Ash
  6. A Course In Algebraic Number Theory-Robert B. Ash
  7. The Calculus of Functions of Several Variables - Dan Sloughter
  8. Difference Equations to Differential Equations: An Introduction to Calculus- Dan Sloughter
  9. Graphics for the Calculus-Douglas N. Arnold
  10. Multivariable Calculus - George Cain & James Herod
  11. Steven Shreve: Stochastic Calculus and Finance - Prasad Chalasani and Somesh Jha
  12. Algebra and Analysis for Computer Science -Jean Gallier
  13. Visual Calculus - Lawrence S. Husch
  14. Complex Variables- Robert B. Ash and W.P. Novinger
  15. Advanced Calculus, Lynn Loomis and Shlomo Sternberg
  16. Discrete Oscillation Theory, Ravi P. Agarwal, Martin Bohner, Said R. Grace, and Donal O'Regan
  17. Abstract Algebra with GAP- J. G. Rainbolt and J. A. Gallian
  18. A Course In Algebraic Number Theory - Robert B. Ash
  19. Mathematical Methods of Engineering Analysis - Erhan Çinlar and Robert J. Vanderbei.
  20. Impulsive Differential Equations and Inclusions, M. Benchohra, J. Henderson, and S. Ntouyas
  21. Introduction to the Theory of Functional Differential Equations: Methods and Applications, N. V. Azbelev, V. P. Maksimov, and L. F. Rakhmatullina
  22. Qualitative Analysis of Delay Partial Difference Equations, Binggen Zhang, and Yong Zhou
  23. Solvability of Nonlinear Singular Problems for Ordinary Differential Equations, Irena Rachunkova, Svatoslav Stanek, and Milan Tvrdy
  24. Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations, Vicenţiu D. Rădulescu
  25. Calculus, Benjamin Crowell
  26. A Course In Commutative Algebra-Robert B. Ash
  27. A Pari/GP Tutorial- Robert B. Ash
  28. Real Variables with Basic Metric Space Topology - Robert B. Ash
  29. A Survey of Venn Diagrams-Frank Ruskey and Mark Weston
  30. A Course in Universal Algebra- Stanley Burris and H.P. Sankappanavar
  31. Algebra: Abstract And Concrete-Frederick M. Goodman
  32. Applied Abstract Algebra - D. Joyner, R. Kreminski, J. Turisco
  33. Galois Connections and Fixed Point Calculus-Roland Backhouse
  34. The Structure of Finite Algebras - David Hobby and Ralph McKenzie
  35. Introduction to Matrix Algebra - Autar K Kaw
  36. Elements of Abstract and Linear Algebra - Edwin H. Connell
  37. Elementary Linear Algebra - Keith Matthews
  38. Solutions to Elementary Linear Algebra prepared - Keith Matthews
  39. Linear Algebra and Applications Textbook - Thomas S. Shores
  40. Visual Linear Algebra for Maple and Mathematica -
  41. Differential Equations With Boundary Value Problems - Selwyn Hollis
  42. Elementary PDEs and Applications - Björn Birnir,