A list of links to useful mathematical textbooks available for free on the Internet. They are all legal and maintained by their authors or by the legitimate publisher.
All the documents are in English. They are in a printable format - Postscript or Adobe Portable Document Format. You are free to download, read and print them. Here are some links to other sites offering lists of free mathematical textbooks.
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- A<B notes for the Math Olympiad Program by Kiran S. Kedlaya
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Basic Concepts of Mathematics by Elias Zakon
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Mathematical Analysis I by Elias Zakon
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Calculus by Gilbert Strang
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MEASURE THEORY Vol1 by David H. Fremlin
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MEASURE THEORY Vol2 by David H. Fremlin
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MEASURE THEORY Vol3 by David H. Fremlin
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MEASURE THEORY Vol4 by David H. Fremlin
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Real Analysis for Engineers by Erhan Cinlar, and Robert J. Vanderbei
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Measure Theory and Integration by Vitali Liskevich
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The Matrix Cookbook by Kaare Brandt Petersen
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Classical Geometry and Low-Dimensional Topology by Danny Calegari
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Basic algebra and trigonometry by Thomas Ward
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First Year Mathematics by William Chen
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Multivariable Calculus by George Cain, and James Herod
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Complex Analysis by George Cain
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Linear Algebra by Jim Hefferon
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Elementary Linear Algebra by Keith Matthews
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A First Course in Linear Algebra by Robert A. Beezer
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Complex Analysis by Douglas N. Arnold
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Set Theoretic Real Analysis by Krzysztof Ciesielski
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Expository notes in The finite reflection groups by Daniel Allcock
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Classical Geometry by Danny Calegari
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Difference Equations to Differential Equations by Dan Sloughter
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Course of linear algebra and multidimensional geometry by Ruslan Sharipov
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Examples, Lecture Notes and Specimen Exam Questions and Natural Sciences Tripos
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Calculus project by Michael Livshits
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The Octonions by John C. Baez
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Advanced Calculus by Shlomo Sternberg
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Whitman Calculus by David Guichard
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Olympiad Inequalities by Thomas J. Mildorf
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Elementary Real Analysis by Andrew M. Bruckner, Brian S. Thomson, and Judith B. Bruckner
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Precalculus (Electronic version annually updated.) by David H. Collingwood, and K. David Prince
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Understanding Calculus by Faraz Hussain [new]
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A ProblemText in Advanced Calculus by John M. Erdman [new]
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Mathematical Logic - an Introduction by Michal Walicki
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Set theory by Peter G. Dixon
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Mathematical Logic by Stephen G. Simpson
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Foundations of Mathematics by Stephen G. Simpson
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Model Theory by Stephen G. Simpson
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A Problem Course in Mathematical Logic by Stefan Bilaniuk
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Computability and Incompleteness by Jeremy Avigad
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Complete proofs of Gödel's Incompleteness Theorems by Byunghan Kim
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Fundamentals of Model Theory by William Weiss, and Cherie D'Mello
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Logic for Everyone by Robert A. Herrmann
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Proofs and Concepts by Dave Witte Morris, and Joy Morris [new]
- Lecture Notes on Discrete Mathematics by László Lovász
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An Introduction to the Theory of Numbers by Leo Moser
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Number Theory Notes for students at IMO level by Naoki Sato
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Elementary Number Theory by William Edwin Clark
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Lecture notes on elementary number theory by Bruce Ikenaga
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Exercises with solutions on elementary number theory by Nigel Byott
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Elementary Number Theory by Michael Filaseta
- Lecture notes on p-adic numbers by Andrew Baker
- Open Questions in Arithmetic Algebraic Geometry by Alice Silverberg
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Review of Alf van der Poorten's Notes on Fermat's Last Theorem by Andrew Granville
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Survey of Euclidean Number Fields by Franz Lemmermeyer
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A Computational Introduction to Number Theory and Algebra by Victor Shoup
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A Course In Algebraic Number Theory by Robert B. Ash
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Elementary and algebraic number theory by Ivan Fesenko
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Algebraic Number Theory by Jim Milne
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Algebraic Number Theory by Robin Chapman
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Invitation to higher local fields by Ivan Fesenko, and Masato Kurihara
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Euclidean Number Fields by Franz Lemmermeyer
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Algebra and Number Theory by Andrew Baker
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Elementary Number Theory by William A. Stein
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Notes for Dick Gross' Algebraic Number Theory Course by S. Sather-Wagstaff
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Algebraic Number Theory & Introduction to Automorphic L-functions by Ching-Li Chai
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Algebraic Number Theory by Jerome William Hoffmann
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Introduction to Number Theory by Franz Lemmermeyer
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Course notes for analytic number theory by Graham Everest
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Distribution of Prime Numbers by William Chen
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Introduction to Analytic Number Theory by Noam Elkies
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Workbook in Higher Algebra by David Surowski
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Differential Algebra by Joseph Fels Ritt
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Structure and Representations of Jordan Algebras by Nathan Jacobson
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A Course in Universal Algebra by Stanley N. Burris, and H.P. Sankappanavar
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An Invitation to General Algebra and Universal Constructions by George M. Bergman
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Varieties of Lattices by Peter Jipsen, and Henry Rose
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Lectures on Matrices by Joseph Henry Maclagen Wedderburn
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Elementary Abstract Algebra by Edwin Clark
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Intro to Abstract Algebra by Paul Garrett
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Elements of Abstract and Linear Algebra by Edwin H. Connell
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Abstract Algebra:The Basic Graduate Year by Robert Ash
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A Course In Commutative Algebra by Robert Ash
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Notes for geometric group theory course by John R. Stallings
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Advanced Linear Algebra lecture notes (with real algorithm for the real Jordan form) by Keith Matthews
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Commutative algebra by Ivan Fesenko
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Abstract Algebra - Number Theory, Group Theory, Galois Theory by Daviidd Wilkins
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Abstract group theory by Chuck Miller
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The Classification of the Finite Simple Groups by Daniel Gorenstein, Richard Lyons, and Ronald Solomon
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Group Characters, Symmetric Functions, and the Hecke Algebra by David M. Goldschmidt
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Finite Groups and their Representations by Andrew Baker
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Classical Groups by Peter Cameron
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Galois theory by Miles Reid
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Toeplitz and Circulant Matrices by Robert M. Gray
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Homogeneous spaces and equivariant embeddings by Dmitri A. Timashev
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Algebra: Abstract and Concrete by Frederick M. Goodman
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Commutative Algebra, Algebraic Geometry, Number theory, Field Theory, Galois Theory by Sudhir R. Ghorpade
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Fundamental Problems in Algorithmic Algebra by Chee Yap
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Braid groups and Galois theory by Frazer Jarvis
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A. N. Whitehead's Geometric Algebra by Stephen Blake
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Commutator Theory for Congruence Modular Varieties by Ralph Freese, and Ralph McKenzie
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Constructive Aspects of the Inverse Galois Problem by A. Ledet, and N. Yui, and C. Jensen
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Determinantal rings by Winfried Bruns, and Udo Vetter
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Algebraic geometry and projective differential geometry by Joseph M. Landsberg
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Introduction to Algebraic Geometry by Igor V. Dolgachev
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Algebraic Geometry by J.S. Milne
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Modular forms by Igor Dolgachev
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Complex analytic and algebraic geometry by Jean-Pierre Demailly
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Introduction to Algebraic Geometry by Yuriy Drozd
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Algebraic Curves by Hendrik L. Lenstra
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Algebraic Geometry, Toric Varieties, Galois Theory by David A. Cox
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Quasi-projective Moduli for Polarized Manifolds by Eckart Viehweg
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Lectures on Vanishing Theorems by Eckart Viehweg, and Hélène Esnault
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Introduction to Algebraic Geometry by Ravi Vakil
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Resolution of Singularities by János Kollár
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Eleven books on geometry, topology, and algebra by Andrew Ranicki
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Elliptic curves by Miles Reid
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Elliptic Curves by Jim Milne
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Modular curves by Bas Edixhoven
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Expository articles - Computing rational points on curves, Elliptic curves by Bjorn Poonen
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Mixed Motives by Marc Levine
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Toposes, Triples and Theories by Michael Barr, and Charles Wells
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Abstract and Concrete Categories by J. Adamek, H. Herrlich, and G. Strecker
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A Gentle Introduction to Category Theory by Maarten M.Fokkinga
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Introduction to The Theory of Categories by David Madore
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Higher-Dimensional Categories: an illustrated guide book by Eugenia Cheng, and Aaron Lauda
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Higher Operads, Higher Categories by Tom Leinster
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Algebraic Groups and Discontinuous Subgroups by Armand Borel, and George D. Mostow
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Theory of representations etc by Claudio Procesi
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Semisimple Lie Algebras and their Representations by Robert N. Cahn
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Lie Algebras by Shlomo Sternberg
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Textbook in Problems on Elementary Topology by O.Ya.Viro, O.A.Ivanov, V.M.Kharlamov, and N.Y.Netsvetaev
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Topology Course by Aisling McCluskey, and Brian McMaster
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Topology by Thomas Ward
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Foliations and the topology of 3-manifolds by Danny Calegari
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Algebraic Topology by Allen Hatcher
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Cohomology, Connections, Curvature and Characteristic Classes by David Mond
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Introduction to Characteritic Classes and Index Theory by Jean-Pierre Schneiders
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Algebraic Topology by Solomon Lefschetz
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Abstract group theory and topology articles by Walter Neumann
- An introduction to algebraic K-theory by Charles Weibel
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Knots Knotes by J. D. Roberts
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Vassiliev invariants and combinatorial structures by Sergei V. Duzhin
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Introduction to Vassiliev knot invariants by Sergei V. Duzhin, and Sergei Chmutov
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History of Knot Theory by Andrew Ranicki
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Knot Theory by Swatee Naik
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Knot theory from Vandermonde to Jones by Jozef H. Przytycki
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Homeomorphisms in Analysis by Casper Goffman, Togo Nishiura, and Daniel Waterman
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Why the Boundary of a Round Drop Becomes a Curve of Order Four by A. N. Varchenko, and P. I. Etingof
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Lectures on Entire Functions by B. Ya. Levin
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Constructive Real Numbers and Constructive Function Spaces by N. A. Sanin
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Complex Variables by W.P. Novinger, and Robert B. Ash
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Foundations of Nonstandard Analysis by Erland Gadde
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Analytic functions by Stanislaw Saks, and Antoni Zygmund
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Theory of Functions of real variable by Shlomo Sternberg
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Real Analysis by Andrew M. Bruckner, Brian S. Thomson, and Judith B. Bruckner
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Introduction to Real Analysis by William F. Trench [new]
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Vector Calculus by Michael Corral [new]
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Functional Analysis by Douglas N. Arnold
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Functional Analysis by Paul Garrett
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Functional Analysis by Thomas Ward
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Functional Analysis and Semi-Groups by Einar Hille, and Ralph S. Phillips
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The Convenient Setting of Global Analysis by Andreas Kriegl, and Peter W. Michor
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Hilbert Space Methods for Partial Differential Equations by Ralph E. Showalter
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Monotone Operators in Banach Space and Nonlinear Partial Differential Equations by Ralph E. Showalter
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Harmonic Analysis and Partial Differential Equations by Björn E.J. Dahlberg, and Carlos E. Kenig
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Functional Analysis by Thomas Ward
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Harmonic Function Theory by Sheldon Axler, Paul Bourdon, and Wade Ramey
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An Introduction to C*-Algebras by Pierre de la Harpe, and Vaughan Jones
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Functional Analysis by Peter G. Dixon
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Introduction to Microlocal Analysis by Richard Melrose
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Bernoulli Periodic Functions by Miguel Lerma
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Holomorphic Methods in Analysis and Mathematical Physics by Brian C. Hall
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Nonlinear Analysis and Ordinary Differential Equations by Klaus Schmitt
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Ordinary Differential Equations and Dynamical Systems by Gerald Teschl
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Ordinary Differential Equations by Sheldon Newhouse
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Partial Differential Equations of Mathematical Physics by William W. Symes
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Analytic differential equations by Yulij Ilyashenko, and Sergei Yakovenko
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Exterior Differential Systems and Euler-Lagrange Partial Differential Equations by Robert L. Bryant, Phillip A. Griffiths, and Daniel A. Grossman
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Monograph on quasilinear partial differential equations by Marco Squassina
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Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations by Lloyd N. Trefethen
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Notes on Diffy Qs: Differential Equations for Engineers by Jiří Lebl [new]
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Introduction to Tensor Calculus and Continuum Mechanics by John H. Heinbockel
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Topics in Differential Geometry by Peter W. Michor
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Natural operations in differential geometry by Peter W. Michor, Ivan Kolar, and Jan Slovak
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Intrinsic Geometry of Surfaces by A. D. Aleksandrov, and V. A. Zalgaller
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An Introduction to Riemannian Geometry by Sigmundur Gudmundsson, and Lund University
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Riemann Surfaces, Dynamics and Geometry by Curtis McMullen
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Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem by Peter B. Gilkey
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Differentiable Manifolds by Mariusz Wodzicki
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Differential Geometry by Sergei Yakovenko
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Symplectic Geometry with and Eye Toward Combinatorics by Sue Tolman
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Differential Geometry and Physics by Gabriel Lugo
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Differential geometry reconstructed by Alan U. Kennington
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Course of Differential Geometry by Ruslan Sharipov
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The Geometrization of Physics by Richard S. Palais
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Projective Geometry, Geometry of Surfaces, Differentiable Manifolds by Nigel Hitchin
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Vector Bundles and an Introduction to Gauge Theory by Steven Bradlow, Hung-Jen Hsu, and Chris Willett
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Twistor Geometry and Gauge Theory by Martin Wolf
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Complex Geometry of Nature and General Relativity by Giampiero Esposito
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Geometric Asymptotics by Victor Guillemin, and Shlomo Sternberg
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Projective Geometry by Balázs Csikós
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Differential Geometry by Balázs Csikós
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Projective and Polar Spaceas by Peter Cameron
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Transformation groups for begginers by S. V. Duzhin, and B. D. Tcherbotarevsky
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An Introduction to Differentiable Manifolds and Riemannian Geometry by William M. Boothby
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Mechanism of the Heavens (1831), by Mary Somerville by Russell McNeil
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Dynamical Systems by George D. Birkhoff
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Dynamics in One Complex Variable: Introductory Lectures by John Milnor
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Geometrical theory of dynamical systems by Nils Berglun
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Introduction to Statics and Dynamics by Andy Ruina, and Rudra Prata
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Entropy of Compact Group Automorphisms by Thomas Ward
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Valuations and Hyperbolicity in Dynamics by Thomas Ward
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Effective Hamiltonians and averaging for Hamiltonian dynamics by Lawrence Craig Evans
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Entropy and Partial Differential Equations by Lawrence Craig Evans
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CLASSICAL AND QUANTUM CHAOS by Predrag Cvitanovic', Roberto Artuso, Ronnie Mainieri, Gregor Tanner, Gábor Vattay, Niall Whelan, and Andreas Wirzba
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Dynamical systems by Shlomo Sternberg
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Mathematical Methods in Quantum Mechanics by Gerald Teschl
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Quantum Mechanics by Klaus Schulten
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Foundations of Quantum Mechanics & Quantum Information by M.B. Plenio
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Quantum Geometry and more by Micho Durdevich
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Quantum Probability Theory by Miklos Redei, and Stephen J. Summers
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Comprehensive textbook on quantum (and classical) field theory by Warren Siegel
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Quantum Field Theory by Ben Simons
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Mathematical ideas and notions of quantum field theory by Pavel Etingof
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Introduction to Algebraic and Constructive Quantum Field Theory by Irving E. Segal, Zhengfang Zhou, and John C. Baez
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Quantum Field Theory program at IAS by Irving E. Segal, Zhengfang Zhou, and John C. Baez
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Graduate textbooks: Field Theory, Relativity, Superspace, Strings by Warren Siegel
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What is String Theory by Joseph Polchinski
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Fluctuating Geometries in Statistical Mechanics and Field Theory
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Operator Algebras and Quantum Statistical Mechanics, Vol I by Ola Bratteli
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Operator Algebras and Quantum Statistical Mechanics, Vol II by Ola Bratteli
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D-Brane Primer by Clifford V. Johnson
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Introduction to Superstring Theory by Elias Kiritsis
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Algebraic Quantum Field Theory by Hans Halvorson, and Michael Mueger
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Worked examples in the Geometry of Crystals by HKDH Bhadeshia
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Introduction to Solid-State Physics; Many-Body Theory by Chetan Nayak
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Many-Body Physics by Piers Coleman
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Theory of Superconductivity by Helmut Eschrig
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High-Temperature Superconductivity by Peter Hirschfeld
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Solid State Physics by Peter Hirschfeld
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Photonic Crystals: Molding the Flow of Light by John D. Joannopoulos, Steven G. Johnson, Joshua N. Winn, and Robert D. Meade
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General Relativity, Nonlinear PDEs, etc by Sergiu Klainerman
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Special Relativity and Geometry by C. E. Harle, and R. Bianconi
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Differential Geometry (and Relativity) by Bob Gardner
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General Relativity and Quantum Cosmology by Sean M. Carroll
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Essential Physics 1 by Frank Firk
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Introduction to Groups, Invariants & Particles by Frank W.K. Firk
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Classical Electrodynamics by Bo Thidé
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Classical electrodynamics and theory of relativity by Ruslan Sharipov
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Electromagnetic Theory and Computation: A Topological Approach by Paul W. Gross, and P. Robert Kotiuga
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MOTION MOUNTAIN TEXTBOOK Hiking beyond space and time along the concepts of modern physics by Christoph Schiller
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Fundamentals of Thermodynamics by J. Karl Johnson
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Non-Equilibrium Statistical Mechanics by Klaus Schulten
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Course in Electrodynamics by Franz Wegner
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Light and Matter by Ben Crowell
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Order-of-magnitude-physics by Sanjoy Mahajan
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Physical Applications of Geometric Algebra by Anthony Lasenby, and Chris Doran
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Group Theory: Lie's, Tracks, And Exceptional Groups by Predrag Cvitanovic'
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An Elementary Introduction to Groups and Representations by Brian C. Hall
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Geometric Models for Noncommutative Algebras by A. Cannas da Silva, and A. Weinstein
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Differential Forms in Electromagnetic Theory by Richard H. Selfridge, David V. Arnold, and Karl F. Warnick
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Lectures on integration of several variables by Michael Adler
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Methods of Mathematical Physics by Mark Trodden
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Further Mathematical Methods by Niels Walet
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Computational Physics by Angus MacKinnon
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Zeno meets modern science by Zurab K. Silagadze
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Feynman's derivation of Maxwell equations and extra dimensions by Zurab K. Silagadze
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TeV scale gravity, mirror universe, and ... dinosaurs by Zurab K. Silagadze
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Quick introduction to tensor analysis by Ruslan Sharipov
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Traveling Wave Solutions of Parabolic Systems by Aizik I. Volpert, Vitaly A. Volpert, and Vladimir A. Volpert
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Introduction to Probability by Charles Grinstead, and J. Laurie Snell
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Probability Tutorials by Noel Vaillant
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Probability Theory: The Logic of Science by Edwin Thompson Jaynes
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Probability Theory As Extended Logic by Larry Bretthorst
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Introduction to Probability by Oliver Knill
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Random Walks and Diffusion by Martin Z. Bazant
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Reversible Markov Chains and Random Walks on Graphs by David Aldous, and Jim Fill
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An Invitation to Sample Paths of Brownian Motion by Yuval Peres
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Notes on probability theory by Hendrik W. Lenstra, Jr.
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An introduction to stochastic differential equations by Lawrence Craig Evans
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Stochastic Calculus by Alan Bain
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Probability Theory by S.R.S.Varadhan
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Statistics by S.R.S.Varadhan
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Stochastic Processes by S.R.S.Varadhan
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Stochastic Differential Equations by Thomas G. Kurtz
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Stochastic Integration and Stochastic Differential Equations by Klaus Bichteler
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Probability, Random Processes, and Ergodic Properties by Robert M. Gray
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Derivations of Applied Mathematics by Thaddeus H. Black
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Linear Methods of Applied Mathematics by Evans Harrell, and James Herod
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Linear Algebra, Infinite Dimensions, and Maple by James Herod
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generatingfunctionology by Herbert Wilf
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Algorithms and Complexity by Herbert S. Wilf
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A=B by Herbert Wilf, Marko Petkovsek, and Doron Zeilberger
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Applied Math Textbook by Sean Mauch
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Mathematical Tools for Physics by James Nearing
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Applied Mathematics by Peter J. Olver, and Chehrzad Shakiban
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Computational Complexity: A Conceptual Perspective by Oded Goldreich
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Papers on Combinatorial Enumeration and Asymptotics by Andrew Odlyzko
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Hyperplane Arrangements by Richard Stanley
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Introduction to Statistical Signal Processing by R.M. Gray, and L.D. Davisson
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Applied Abstract Algebra by David Joyner, Richard Kreminski, and Joann Turisco
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Numerical Analysis by Lucio Tavernini
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Finite Element Method/Boundry Element Method by Peter Hunter
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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
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Numerical Mathematics and Scientific Computation by Germund Dahlquist, and Åke Björck
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The Boundary Element Method in Acoustics by Stephen Kirkup
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Computational geometry, mesh generation, numerical methods by Jonathan Shewchuk
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Numerical Analysis by Steven Elliot Pav
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Convex Optimization by Stephen Boyd, and Lieven Vandenberghe
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Optimization by Pravin Varaiya
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Information Theory, Inference and Learning Algorithms by David J. C. MacKay
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A Short Course in Information Theory by David J. C. MacKay
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Primer on Information Theory by Thomas Schneider
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Several books (not only Information Theory) by Gregory J. Chaitin
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Applied Quantitative Finance by W. Härdle, T. Kleinow, and G. Stahl
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Measure theory, Probability, Stochastic calculus, General theory of processes, Financial mathematics by Rich Bass
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Structural Analysis of Discrete Data and Econometric Applications by Charles F. Manski, and Daniel L. McFadden
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Essential Principles of Economics by Roger McCain
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Game theory examples by Roger McCain
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Discrete Time Finance by Christian Ewald
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Mathematical Finance: Introduction to Continuous Time Financial Market Models by Christian Ewald
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Games, Fixed Points and Mathematical Economics by Christian Ewald
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Determinacy in infinite games by Jindrich Zapletal
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Handbook of Applied Cryptography by Alfred J. Menezes, Paul C. van Oorschot, and Scott A. Vanstone
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Foundations of Cryptography, Vol 1 by Oded Goldreich
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Foundations of Cryptography, Vol 2 by Oded Goldreich
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Cryptography by S. Goldwasser, and M. Bellare
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Introduction to Modern Cryptography by Mihir Bellare, and Phillip Rogaway
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Cryptography and Cryptanalysis by Anna Lysyanskaya
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Modern Cryptography by Mihir Bellare and Phillip Rogaway
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Cryptography and Cryptanalysis by Glenn Durfee
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Coding Theory and Cryptography: From Enigma and Geheimschreiber to Quantum Theory by David Joyner
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Mathematics under the Microscope by Alexandre Borovik
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What is and what will be: Integrating spirituality and science by Paul Budnik
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Fractals in the Plane - the Ergodic Theory Methods by F. Przytycki, and M. Urbanski
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Conformal Dynamics by Curt McMullen
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Fractals by P. G. Dixon
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Graph Theory with Applications by J.A. Bondy, and U.S.R. Murty
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Graph Theory by Reinhard Diestel
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Interactive Graph theory tutorials by Chris K. Caldwell
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Miscellaneous facts about Coxeter groups by Robert B. Howlett
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Buildings, BN-pairs, Hecke algebras, classical groups by Paul Garrett
- Nielsen fixed point theory, Geometric group theory by Ross Geoghegan
- Mathematics of Rubik's cube by David Joyner
Last edited: July 12, 2015 03:55:00 (GMT).