Recommended Books in Mathematics

General Mathematics Number Theory Algebra, Algebraic Geometry Topology Analysis

Geometry Mathematical Physics Probability Theory Applied Mathematics Miscellanea

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Derivations of Applied Mathematics  (Related From Amazon.com...) by Thaddeus H. Black (GNU Free Documentation License)
General Mathematics

elementary mathematics, Analysis, Lebesgue Integrals ..

Basic Concepts of Mathematics  (Related From Amazon.com...) by Elias Zakon
Mathematical Analysis I  (Related From Amazon.com...) by Elias Zakon
Calculus  (Related From Amazon.com...) by Gilbert Strang, also Student Study Guide to Calculus  (Related From Amazon.com...) and Instructor's Manual  (Related From Amazon.com...)
Basic algebra and trigonometry.  (Related From Amazon.com...) by Thomas Ward

  (Related From Amazon.com...), (notes by William Chen)
Multivariable Calculus  (Related From Amazon.com...) by George Cain & James Herod

Complex Analysis  (Related From Amazon.com...) by George Cain

Linear Algebra  (Related From Amazon.com...) byJim Hefferon

Elementary Linear Algebra  (Related From Amazon.com...) by Keith Matthews

A First Course in Linear Algebra  (Related From Amazon.com...) by Robert A. Beezer (GNU Free Documentation License)
Measure Theory and Integration by V. Liskevich

MEASURE THEORY  (Related From Amazon.com...) by D.H.Fremlin plain tex sources
Complex Analysis  (Related From Amazon.com...) by Douglas N. Arnold

Real Analysis for Engineers by Erhan Cinlar and Robert J. Vanderbei

Set Theoretic Real Analysis  (Related From Amazon.com...) by Krzysztof Ciesielski

Expository notes  (Related From Amazon.com...) by Daniel Allcock in The finite reflection groups
Classical Geometry  (Related From Amazon.com...) by Danny Calegari
Classical Geometry and Low-Dimensional Topology  (Related From Amazon.com...) by Danny Calegari
Difference Equations to Differential Equations  (Related From Amazon.com...) by Dan Sloughter
Course of linear algebra and multidimensional geometry  (Related From Amazon.com...) by Ruslan Sharipov
Examples, Lecture Notes and Specimen Exam Questions and Natural Sciences Tripos  (Related From Amazon.com...)
Calculus project  (Related From Amazon.com...) of Michael Livshits
The Matrix Cookbook by Kaare Brandt Petersen
The Octonions  (Related From Amazon.com...) by John C. Baez
Advanced Calculus   (Related From Amazon.com...) by Shlomo Sternberg

Mathematical Logic and Set theory

Mathematical Logic - an Introduction  (Related From Amazon.com...) by Michal Walicki
Set theory  (Related From Amazon.com...) by Dr. P. G. Dixon
Mathematical Logic  (Related From Amazon.com...) by Stephen G. Simpson
Foundations of Mathematics  (Related From Amazon.com...) by Stephen G. Simpson
Model Theory  (Related From Amazon.com...) by Stephen G. Simpson
The theory of the foundations of mathematics - 1870 to 1940
A Problem Course in Mathematical Logic  (Related From Amazon.com...) by Stefan Bilaniuk
Computability and Incompleteness   (Related From Amazon.com...)by Jeremy Avigad
Complete proofs of Gödel's Incompleteness Theorems   (Related From Amazon.com...)
Fundamentals of Model Theory  (Related From Amazon.com...) by William Weiss and Cherie D'Mello

Logic for Everyone  (Related From Amazon.com...) by Robert A. Herrmann
For more logic lecture notes go to: ASSOCIATION FOR SYMBOLIC LOGIC  (Related From Amazon.com...) members.
For more set theory materials go to: Set Theory Preprint Sites  (Related From Amazon.com...)

Discrete Math

Lecture Notes on Discrete Mathematics  (Related From Amazon.com...) by Lálóvá

Number Theory

Introductory Number Theory

An Introduction to the Theory of Numbers  (Related From Amazon.com...) by Leo Moser
Elementary Number Theory  (Related From Amazon.com...) by W. Edwin Clark
Lecture notes on elementary number theory  (Related From Amazon.com...) (Bruce Ikenaga)
exercizes with solutions on elementary number theory  (Related From Amazon.com...) (Nigel Byott)
Naoki Sato's Number Theory Notes  (Related From Amazon.com...)
Math 780: Elementary Number Theory  (Related From Amazon.com...), Notes by Michael Filaseta, 1997

p-adic numbers

Lecture notes on p-adic numbers  (Related From Amazon.com...) (Andrew Baker)

Arithmetic Geometry

Draft of PCMI Lecture Notes on Open Questions in Arithmetic Algebraic Geometry (Alice Silverberg)

Fermat's Last Theorem

William Hammond's Fermat Archive  (Related From Amazon.com...)
Notes on Fermat's Last Theorem  (Related From Amazon.com...), A.J. van der Poorten, Canadian Mathematical Society Series of Monographs and Advanced Texts, Wiley-Interscience, January, 1996, ISBN 0-471-06261-8

Review of Alf van der Poorten's Notes on Fermat's Last Theorem by Andrew Granville

Algebraic Number Theory

A Computational Introduction to Number Theory and Algebra   (Related From Amazon.com...) by Victor Shoup
A Course In Algebraic Number Theory  (Related From Amazon.com...) by Robert B. Ash
Course Notes for elementary and algebraic number theory  (Related From Amazon.com...) by Ivan Fesenko
Course Notes by Jim Milne: Algebraic Number Theory  (Related From Amazon.com...)

Algebraic Number Theory  (Related From Amazon.com...), Course notes by Robin Chapman
Invitation to higher local fields  (Related From Amazon.com...), by Ivan Fesenko and Masato Kurihara (editors)
Survey of Euclidean Number Fields (ps file 371K) (Franz Lemmermeyer)
Algebra and Number Theory  (Related From Amazon.com...) by Andrew Baker
Elementary Number Theory  (Related From Amazon.com...) by William A. Stein
Notes for Dick Gross' Algebraic Number Theory Course  (Related From Amazon.com...) by S. Sather-Wagstaff
Algebraic Number Theory & Introduction to Automorphic L-functions  (Related From Amazon.com...) by Ching-Li Chai
Lecture notes on Algebraic Number Theory  (Related From Amazon.com...) by Jerome Hoffmann
Introduction to Number Theory   (Related From Amazon.com...)by Franz Lemmermeyer

Analytic Number Theory

Distribution of Prime Numbers  (Related From Amazon.com...), Lecture notes by William Chen
Course notes for analytic number theory (Graham Everest) (ps 442K)
Introduction to Analytic Number Theory  (Related From Amazon.com...) by Noam Elkies

Algebra, Algebraic Geometry

Algebra, Abstract

Lectures on Matrices  (Related From Amazon.com...) by J. H. M. Wedderburn
Elementary Abstract Algebra  (Related From Amazon.com...) by Edwin Clark

Intro to Abstract Algebra  (Related From Amazon.com...) by Paul Garrett

Elements of Abstract and Linear Algebra  (Related From Amazon.com...) by Edwin H. Connell

Abstract Algebra:The Basic Graduate Year  (Related From Amazon.com...) by Robert Ash

A Course In Commutative Algebra  (Related From Amazon.com...) by Robert Ash

Notes for geometric group theory course  (Related From Amazon.com...), by John R. Stallings

Advanced Linear Algebra lecture notes  (Related From Amazon.com...) by Keith Matthews (with real algorithm for the real Jordan form)

Commutative algebra  (Related From Amazon.com...) by Ivan Fesenko

Abstract Algebra - Number Theory, Group Theory, Galois Theory  (Related From Amazon.com...) by Daviiddd Wilkins

Workbook in Higher Algebra by David Surowski with index, many exercises

Abstract group theory   (Related From Amazon.com...)Papers and Notes by Chuck Miller
The Classification of the Finite Simple Groups  (Related From Amazon.com...) by Daniel Gorenstein, Richard Lyons, and Ronald Solomon
Group Characters, Symmetric Functions, and the Hecke Algebra  (Related From Amazon.com...) by David M. Goldschmidt
Finite Groups and their Representations  (Related From Amazon.com...) by Andrew Baker
Classical Groups  (Related From Amazon.com...) by Peter Cameron
Galois theory  (Related From Amazon.com...) by Miles Reid
Toeplitz and Circulant Matrices  (Related From Amazon.com...) by R. M. Gray
Homogeneous spaces and equivariant embeddings  (Related From Amazon.com...) by Dmitri A. Timashev

Differential Algebra  (Related From Amazon.com...) by Joseph Fels Ritt
Structure and Representations of Jordan Algebras  (Related From Amazon.com...) by Nathan Jacobson
An Invitation to General Algebra and Universal Constructions  (Related From Amazon.com...), by George M. Bergman

A Course in Universal Algebra  (Related From Amazon.com...) by Stanley N. Burris and H.P. Sankappanavar

Fundamental Problems in Algorithmic Algebra  (Related From Amazon.com...) by Chee Yap

Braid groups and Galois theory   (Related From Amazon.com...) by Frazer Jarvis
A. N. Whitehead's Universal Algebra  (Related From Amazon.com...) by Stephen Blake
Varieties of Lattices  (Related From Amazon.com...) by Peter Jipsen and Henry Rose
Commutator Theory for Congruence Modular Varieties  (Related From Amazon.com...) by Ralph Freese and Ralph McKenzie
Constructive Aspects of the Inverse Galois Problem  (Related From Amazon.com...) by C. Jensen, A. Ledet, and N. Yui
Publications and prepublications about braids  (Related From Amazon.com...)

Algebraic Geometry

Algebraic geometry and projective differential geometry  (Related From Amazon.com...) by Joseph M. Landsberg
Introduction to Algebraic Geometry, Igor V. Dolgachev

Notes on Algebraic Geometry  (Related From Amazon.com...), J.S. Milne.

Introduction to Algebraic Geometry  (Related From Amazon.com...) by Yuriy Drozd
Undergraduate tutorial on modular forms  (Related From Amazon.com...) by Marty Weissman
Modular forms  (Related From Amazon.com...) (Igor Dolgachev)
Complex analytic and algebraic geometry  (Related From Amazon.com...) - Jean-Pierre Demailly

Moduli Spaces in Algebraic Geometry  (Related From Amazon.com...) edited by L. Goettsche

Algebraic Curves  (Related From Amazon.com...) by Hendrik L. Lenstra

Lectures by David A. Cox  (Related From Amazon.com...) - Introduction to Algebraic Geometry, Minicourse on Toric Varieties, etc.
Quasi-projective Moduli for Polarized Manifolds  (Related From Amazon.com...) by Eckart Viehweg
Lectures on Vanishing Theorems  (Related From Amazon.com...) by Héne Esnault, Eckart Viehweg
Introduction to Algebraic Geometry  (Related From Amazon.com...) by Ravi Vakil
Determinantal rings  (Related From Amazon.com...) by Winfried Bruns and Udo Vetter
Simplification of Hironaka's resolution of singularities  (Related From Amazon.com...) by János Kollár
Eleven books on geometry, topology, and algebra  (Related From Amazon.com...) by Andrew Ranicki

Elliptic Curves

Elliptic curves  (Related From Amazon.com...) by Miles Reid
Elliptic curves, student project, Annegret Weng (ps 726K)
Arithmetic on hyperelliptic curves, Annegret Weng (ps 148K)
Course Notes by Jim Milne: Elliptic Curves, Modular functions and forms, Abelian varieties, Etale Cohomology  (Related From Amazon.com...)
The Modular curves  (Related From Amazon.com...) X₀(N), Lecture notes by Bas Edixhoven
Expository articles - Computing rational points on curves, Elliptic curves  (Related From Amazon.com...) by Bjorn Poonen

Category Theory

A Gentle Introduction to Category Theory  (Related From Amazon.com...), by Maarten M.Fokkinga

Mixed Motives  (Related From Amazon.com...) by Marc Levine

Chris Hillman's Eprints  (Related From Amazon.com...) has a concise introduction to category theory.

David Madore's Math Page  (Related From Amazon.com...) has a 50 page treatise on categories, in DVI and PS.

Lecture notes on Categories, Derived Categories, Homological Algebra  (Related From Amazon.com...) by Pierre Schapira

Toposes, Triples and Theories  (Related From Amazon.com...) by Michael Barr and Charles Wells

Higher-Dimensional Categories: an illustrated guide book  (Related From Amazon.com...) by Eugenia Cheng and Aaron Lauda
Abstract and Concrete Categories by J. Adamek, H. Herrlich, G. Strecker
Higher Operads, Higher Categories  (Related From Amazon.com...) by Tom Leinster

Lie Algebras

Algebraic Groups and Discontinuous Subgroups  (Related From Amazon.com...) by Armand Borel and George D. Mostow
Theory of representations etc.  (Related From Amazon.com...) by Claudio Procesi
Semisimple Lie Algebras and their Representations  (Related From Amazon.com...), by Robert N. Cahn,

Linear Algebraic Groups - minor thesis by David Dumas
Lie Algebras  (Related From Amazon.com...) by Shlomo Sternberg

Topology

Textbook in Problems on Elementary Topology  (Related From Amazon.com...) by O.Ya.Viro, O.A.Ivanov, V.M.Kharlamov and N.Y.Netsvetaev unfinished

Topology Course Lecture Notes  (Related From Amazon.com...) by Aisling McCluskey and Brian McMaster

Topology lecture notes(3rd year)  (Related From Amazon.com...) by Thomas Ward

Foliations and the topology of 3-manifolds  (Related From Amazon.com...) by Danny Calegari

Algebraic Topology

Allen Hatcher's homepage  (Related From Amazon.com...) has a (nearly complete) textbook.

Introduction to Sheaf Theory and Algebraic Topology  (Related From Amazon.com...), by Pierre Schapira

Cohomology, Connections, Curvature and Characteristic Classes   (Related From Amazon.com...) by David Mond
Introduction to Characteritic Classes and Index Theory  (Related From Amazon.com...) by Jean-Pierre Schneiders

Algebraic Topology  (Related From Amazon.com...) by Solomon Lefschetz, AMS 1942, 389 pp.

Abstract group theory and topology articles  (Related From Amazon.com...) by Walter Neumann

K-Theory

An introduction to algebraic K-theory  (Related From Amazon.com...), by Charles Weibel.

Knots

Knots Knotes.  (Related From Amazon.com...) by J. D. Roberts
Vassiliev invariants and combinatorial structures  (Related From Amazon.com...) by S.V.Duzhin
Introduction to Vassiliev knot invariants  (Related From Amazon.com...) by S.Chmutov, S.Duzhin
Collection: "History of Knot Theory"  (Related From Amazon.com...) by Andrew Ranicki
Lecture Notes On Knot Theory  (Related From Amazon.com...) by Swatee Naik
Knot theory from Vandermonde to Jones by Jozef H. Przytycki

Analysis

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

Functional Analysis

Functional Analysis  (Related From Amazon.com...) by Douglas N. Arnold

Paul Garrett's lecture notes  (Related From Amazon.com...)

Functional Analysis (3rd year) lecture notes  (Related From Amazon.com...) by Thomas Ward

Functional Analysis and Semi-Groups  (Related From Amazon.com...) by Einar Hille and R. S. Phillips, AMS 1957, 808 pp

The Convenient Setting of Global Analysis  (Related From Amazon.com...) by Andreas Kriegl and Peter W. Michor, AMS 1997, 618pp

Hilbert Space Methods for Partial Differential Equations  (Related From Amazon.com...), by R.E. Showalter

Monotone Operators in Banach Space and Nonlinear Partial Differential Equations  (Related From Amazon.com...), by R. E. Showalter

Harmonic Analysis and Partial Differential Equations  (Related From Amazon.com...) - BjöE.J. Dahlberg and Carlos E. Kenig

Functional Analysis  (Related From Amazon.com...) by Thomas Ward

Harmonic Function Theory  (Related From Amazon.com...) by Sheldon Axler, Paul Bourdon, and Wade Ramey printing disabled

An Introduction to C-Algebras  (Related From Amazon.com...)* by Pierre de la Harpe and Vaughan Jones
Functional Analysis  (Related From Amazon.com...) by Dr. P. G. Dixon
Introduction to Microlocal Analysis  (Related From Amazon.com...) by Richard Melrose

Bernoulli Periodic distributions   (Related From Amazon.com...) Notes by Miguel Lerma
Holomorphic Methods in Analysis and Mathematical Physics by Brian C. Hall

Differential Equations

Nonlinear Analysis and Ordinary Differential Equations  (Related From Amazon.com...) by Klaus Schmitt
Ordinary Differential Equations and Dynamical Systems  (Related From Amazon.com...) by Gerald Teschl
Ordinary Differential Equations Notes  (Related From Amazon.com...) by Sheldon Newhouse
Partial Differential Equations  (Related From Amazon.com...) by William W. Symes
Lectures on analytic differential equations  (Related From Amazon.com...) by Yulij Ilyashenko and Sergei Yakovenko
Exterior Differential Systems and Euler-Lagrange Partial Differential Equations  (Related From Amazon.com...) by Robert L. Bryant, Phillip A. Griffiths, Daniel A. Grossman
Monograph on quasilinear partial differential equations  (Related From Amazon.com...) by Marco Squassina

Geometry

Differential Geometry

Introduction to Tensor Calculus and Continuum Mechanics  (Related From Amazon.com...), by John H. Heinbockel

Topics in Differential Geometry  (Related From Amazon.com...), Peter W. Michor.

Natural operations in differential geometry  (Related From Amazon.com...) by Ivan Kolar, Jan Slovak and Peter W. Michor

Intrinsic Geometry of Surfaces  (Related From Amazon.com...) by A. D. Aleksandrov and V. A. Zalgaller
An Introduction to Riemannian Geometry  (Related From Amazon.com...) - Sigmundur Gudmundsson, Lund University

Riemann Surfaces, Dynamics and Geometry  (Related From Amazon.com...) Curtis McMullen

Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem  (Related From Amazon.com...) by Peter B. Gilkey

Differentiable Manifolds lecture notes  (Related From Amazon.com...) (growing) by Mariusz Wodzicki
Lecture notes for the course in Differential Geometry  (Related From Amazon.com...) by Sergei Yakovenko
Lectures On Symplectic Geometry with and Eye Toward Combinatorics  (Related From Amazon.com...) by Sue Tolman
Differential Geometry lecture notes  (Related From Amazon.com...) by Gabriel Lugo
Differential geometry reconstructed  (Related From Amazon.com...) by Alan U. Kennington
Course of Differential Geometry  (Related From Amazon.com...) by Ruslan Sharipov
A Modern Course on Curves and Surfaces  (Related From Amazon.com...) by Richard S. Palais
Undergraduate notes on Projective Geometry, Manifolds etc.  (Related From Amazon.com...) by Nigel Hitchin
Vector Bundles and an Introduction to Gauge Theory  (Related From Amazon.com...) by Steven Bradlow, (Hung-Jen Hsu and Chris Willett)
Twistor Geometry and Gauge Theory  (Related From Amazon.com...) by Martin Wolf
Complex Geometry of Nature and General Relativity  (Related From Amazon.com...) by Giampiero Esposito

Geometric Asymptotics  (Related From Amazon.com...) by Victor Guillemin and Shlomo Sternberg
Projective Geometry  (Related From Amazon.com...) by Balá Csikó
Differential Geometry  (Related From Amazon.com...) by Balá Csikóli> Projective and Polar Spaceas  (Related From Amazon.com...) by Peter Cameron
Transformation groups for begginers  (Related From Amazon.com...) by S. V. Duzhin and B. D. Tcherbotarevsky
Cartan's Corner  (Related From Amazon.com...) Differential geometry & Topology

Mathematical Physics

Dynamics

Mechanism of the Heavens (1831), by Mary Somerville  (Related From Amazon.com...). This second edition was prepared by Russell McNeil

Dynamical Systems  (Related From Amazon.com...) George D. Birkhoff, AMS 1927, 305 pp.

Dynamics in One Complex Variable: Introductory Lectures  (Related From Amazon.com...), John Milnor

Geometrical theory of dynamical systems  (Related From Amazon.com...) by Nils Berglun
Lectures on Mechanics, Dynamics, and Symmetry  (Related From Amazon.com...) by Jerrold E. Marsden

Introduction to Statics and Dynamics  (Related From Amazon.com...) by Andy Ruina and Rudra Pratap

Entropy

Entropy on the World Wide Web  (Related From Amazon.com...) has links to expository articles, journals, software, and conferences pertaining to entropy.

Dynamical Systems and Ergodic Theory  (Related From Amazon.com...), by Mark Pollicott and Michiko Yuri
see also
Ergodic Theory & Dyn. Sys.  (Related From Amazon.com...) for errata and additions.

Entropy of Compact Group Automorphisms  (Related From Amazon.com...) by Thomas Ward

Valuations and Hyperbolicity in Dynamics  (Related From Amazon.com...) by Thomas Ward

Lecture Notes on Mechanics, Probability and Irreversibility by Alexandre J. Chorin
Effective Hamiltonians and averaging for Hamiltonian dynamics  (Related From Amazon.com...) - Lawrence Craig Evans

Entropy and partial differential equations - Lawrence Craig Evans  (Related From Amazon.com...)

CLASSICAL AND QUANTUM CHAOS  (Related From Amazon.com...) by Predrag Cvitanovic'
Dynamical systems  (Related From Amazon.com...) by Shlomo Sternberg

Quantum Mechanics

Schrödinger Operators  (Related From Amazon.com...) by Gerald Teschl
Quantum Mechanics  (Related From Amazon.com...) by Klaus Schulten
lecture notes in Quantum Mechanics  (Related From Amazon.com...) by Scott Pratt
ADVANCED QUANTUM MECHANICS  (Related From Amazon.com...) by Jouko Mickelsson
Foundations of Quantum Mechanics & Quantum Information  (Related From Amazon.com...) by M.B. Plenio
Quantum Geometry and more  (Related From Amazon.com...) by Micho Durdevich
Quantum Probability Theory  (Related From Amazon.com...) by Miklos Redei, Stephen J. Summers

Quantum Field Theory

Comprehensive textbook on quantum (and classical) field theory  (Related From Amazon.com...) by Warren Siegel
Quantum Field Theory  (Related From Amazon.com...) by Ben Simons
Mathematical ideas and notions of quantum field theory  (Related From Amazon.com...) by Pavel Etingof
Introduction to Algebraic and Constructive Quantum Field Theory  (Related From Amazon.com...) by John C. Baez, Irving E. Segal and Zhengfang Zhou scanned pdf. extermely big 200 megabytes
Lecture Notes from the Quantum Field Theory program at IAS, 1996-1997  (Related From Amazon.com...)

Books by Warren Siegel  (Related From Amazon.com...)
Introduction to String Theory  (Related From Amazon.com...) by Igor V. Dolgachev

What is String Theory   (Related From Amazon.com...)by Joseph Polchinski
Fluctuating Geometries in Statistical Mechanics and Field Theory  (Related From Amazon.com...) Les Houches Session LXII
Operator Algebras and Quantum Statistical Mechanics, Volumes I & II  (Related From Amazon.com...) by Ola Bratteli
D-Brane Primer  (Related From Amazon.com...)