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Bibliography
The main purpose of this bibliography is to collect all the books given as "Further Reading" on individual theorem pages. Numbers in square brackets against an entry link to the theorems which cite it.
Clicking on the book names will take you to amazon.co.uk where you will find more detailed bibliographic information, customer reviews and, increasingly, their excellent 'Search Inside' facility.
If you buy the book during your visit to amazon.co.uk I receive a referral fee, for which I am grateful. However, inclusion of a book in this bibliography does not mean the book is recommended. Wherever possible an expert review is cited, denoted by the word Review, and these are by no means always entirely complimentary!
Reviews are mostly from plus magazine, the London Mathematical Society's newsletter, the Notices of the American Mathematical Society, the Reviews site of the Mathematical Association of America, and the 'bookshelf' section of American Scientist. They are generally pdf files and will open in a new window. Some of the AMS reviews are extended essays, including images, and can be relatively large files (a size indication is given where appropriate).
If you know of an additional online review of any of the books here (or would like to contribute one) I would be very glad to include a link to it.
Occasionally there is a legitimate free electronic version of a book. I link to this with the word Ebook. Again, I'd be very pleased to know of more. Increasingly books have webpages supporting them (sometimes even Wikipedia entries) and these are linked with the word Webpage.
I have grouped the entries below into, necessarily somewhat arbitrary, categories as follows:
Collections, Dictionaries, Encyclopedias
Fiction
History of mathematics (including historical reprints)
Biography
The profession of mathematics
Psychology, Sociology, Philosophy
Mathematical mountains: popular accounts of landmark problems/solutions
Introductions to mathematical topics accessible
for non-professionals
More specialised introductions to mathematical
topics
Research level
Mathematical applications
Other bibliographies, bibliographic sources
(You may actually be one of the books in the 'Research level' category: David Savitt lets you find out here.)
Collections, Dictionaries, Encyclopedias
Barry Cipra, What's Happening in the Mathematical Sciences, vol. 1
Barry Cipra (ed. Paul Zorn), What's Happening in the Mathematical Sciences, vol. 2
——— , What's Happening in the Mathematical Sciences, vol. 3
——— , What's Happening in the Mathematical Sciences, vol 4
——— , What's Happening in the Mathematical Sciences, vol. 5
Pierre Colmez and J.P. Serre (eds.), Grothendieck-Serre Correspondence: Bilingual Edition, American Mathematical Society, 2004. Review
B. Jack Copeland (ed.), The Essential Turing
Timothy Gowers (ed.), June Barrow-Green & Imre Leader (assoc. eds.), The Princeton Companion to Mathematics
Dana Mackenzie and Barry Cipra, What's Happening in the Mathematical Sciences, vol. 6
Dana Mackenzie, What's Happening in the Mathematical Sciences, vol. 7, American Mathematical Society, 2009.
——— , What's Happening in the Mathematical Sciences, vol. 8
——— , What's Happening in the Mathematical Sciences, vol. 9, American Mathematical Society, 2013.
Yuri I. Manin, Mathematics as Metaphor: Selected Essays of Yuri I. Manin, American Mathematical Society, 2008.
Charles A. Micchelli (ed.), Selected Papers of Alan J.Hoffman, World Scientific Publishing, 2003. Review
Peter M. Neumann, The Mathematical Writings of Evariste Galois (Heritage of European Mathematics)
Terence Tao, Structure and Randomness: Pages from Year One of a Mathematical Blog
——— , Poincare's Legacies: Pages from Year Two of a Mathematical Blog Pt. 1
——— , Poincare's Legacies: Pages from Year Two of a Mathematical Blog Pt. 2
——— , An Epsilon of Room, I: Real Analysis: Papers from Year Three of a Mathematical Blog, American Mathematical Society, 2011.
——— , An Epsilon of Room, II: 2: Papers from Year Three of a Mathematical Blog
——— , Compactness and Contradiction
Stanisław Ulam, The Scottish Book, publ. by Los Alamos, N.M. : S. Ulam, 1957. Ebook
Fiction
Arthur C. Clark and Frederik Pohl, The Last Theorem
Apostolos Doxiadis, Uncle Petros and Goldbach's Conjecture, Faber and Faber; new edition 2001. Review, Review, Review
——— , C.H. Papadimitriou, A. Papadatos, A. Di Donna, Logicomix: An Epic Search for Truth
Hans Magnus Enzensberger, The Number Devil: A Mathematical Adventure, Metropolitan Books, 1998. Review
Clifton Fadiman, Fantasia Mathematica, Springer-Verlag New York Inc., new ed. 1997. Review
——— , The Mathematical Magpie, Springer-Verlag New York Inc., new ed. 1997. Review
William Frucht (ed.), Imaginary Numbers: An Anthology of Marvellous Mathematical Stories, Diversions, Poems and Musings
Denis Guedj, The Parrot's Theorem
Alex Kasman, Reality Conditions: Short Mathematical Fiction
David Leavitt, The Indian Clerk
Guillermo Martinez, The Oxford Murders, Abacus, 2006 (originally Crímenes Imperceptibles, Premio Planeta Argentina, 2003). Review, Review, Review
Dora Musielak, Sophie's Diary: A Historical Fiction, AuthorHouse, 2004.
Yoko Ogawa, The Housekeeper and the Professor
Chris Pearson, Proof of Death, published on Kindle via Amazon Media EU S.à r.l., 2012.
Philibert Schogt, The Wild Numbers
History of mathematics (including historical reprints)
William J. Adams, The Life and Times of the Central Limit Theorem, 2nd edition
Marlow Anderson, Victor Katz and Robin Wilson (eds.), Sherlock Holmes in Babylon and Other Tales of Mathematical History, The Mathematical Association of America, 2004. Review, Review
——— , ——— and ——— (eds.), Who Gave you the Epsilon? & Other Tales of Mathematical History, The Mathematical Association of America, 2004. Review
Petr Beckmann, A History of Pi, 3rd ed., Saint Martin's Press Inc., 1976.
Janet Beery and Jacqueline Stedall (eds.), Thomas Harriot's Doctrine of Triangular Numbers: The Magisteria Magna, European Mathematics Society, 2008. Review
J. Lennart Berggren, Jonathan M. Borwein and Peter B. Borwein, PI: A Source Book, 3rd edition, Springer-Verlag, New York, 2004. [40, 102]
William Berlinghoff and Fernando Gouvêa, Math through the Ages: A Gentle History for Teachers and Others, Oxton House Publishers, 2002. Review
Peter L. Bernstein, Against the Gods: The Remarkable Story of Risk
Norman L. Biggs, E. Keith Lloyd and Robin J. Wilson, Graph Theory, 1736-1936, Clarendon Press, 1986. [50, 189] Review
Oliver Byrne, Byrne, Six Books of Euclid: Facsimile of the famous first edition of 1847
Bruce Chandler and Wilhelm Magnus, The History of Combinatorial Group Theory: A Case Study in the History of Ideas, Springer, 1982
William Chauvanet, Binomial Theorem and Logarithms
Brian Clegg, Brief History of Infinity: The Quest to Think the Unthinkable, Robinson Publishing, 2003. Review
Alex D.D. Craik, Mr Hopkins' Men: Cambridge Reform and British Mathematics in the 19th Century
Alan Cromer, Uncommon Sense: The Heretical Nature of Science
Michael J. Crowe, A History of Vector Analysis: The Evolution of the Idea of a Vectorial System, Dover 2003.
Serafina Cuomo, Ancient Mathematics (Sciences of Antiquity), Routledge, 2001. [4, 44, 63]
Olivier Darrigol, Worlds of Flow: A history of hydrodynamics from the Bernoullis to Prandtl
Joseph W. Dauben and Christoph J. Scriba (eds.), Writing the History of Mathematics - Its Historical Development, Birkhauser, 2002. Review
Martin Davis, The Universal Computer: The Road from Leibniz to Turing
John Derbyshire, Unknown Quantity: A Real and Imaginary History of Algebra
René Descartes, The Geometry of René Descartes
Keith Devlin, The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter That Made the World Modern, Basic Books, 2010. Review
Charles L. Dodgson, An Elementary Treatise On Determinants, 1867, reprinted Rough Draft Printing, 2007. [96]
A.W.F. Edwards, Pascal's Arithmetical Triangle: The Story of a Mathematical Idea, Johns Hopkins University Press, 2002. [39] Review
John Fauvel, Raymond Flood and Robin Wilson, (eds.), Oxford Figures: 800 Years of the Mathematical Sciences, Oxford University Press, 2000. [20] Review
José Ferreirós and Jeremy Gray, The Architecture of Modern Mathematics: Essays in History and Philosophy, Oxford University Press, 2006. [34]
J.V. Field and Jeremy Gray, The Geometrical Work of Girard Desargues, Springer-Verlag, New York, 1987.
——— , The Invention of Infinity: Mathematics and Art in the Renaissance
———, Piero della Francesca: A Mathematician's Art
Richard Fitzpatrick, Euclid's Elements of Geometry
Raymond Flood and Robin Wilson, The Great Mathematicians
Raymond Flood, Adrian Rice and Robin Wilson (eds.), Mathematics in Victorian Britain
Jeremy J. Gray, The Hilbert Challenge: A Perspective on Twentieth Century Mathematics
——— , Janos Bolyai, Non-Euclidean Geometry, and the Nature of Space
——— , Plato's Ghost: The Modernist Transformation of Mathematics
Thomas Hawkins, Emergence of the Theory of Lie Groups: An Essay in the History of Mathematics 1869-1926, Springer-Verlag, New York, 2000. Review
Ioan James, Driven to Innovate: A Century of Jewish Mathematicians and Physicists: A Century of Mathematicians and Physicists, Peter Lang 2009. Review
Ellen Kaplan and Robert Kaplan, Hidden Harmonies: The Lives and Times of the Pythagorean Theorem
Victor J Katz (ed), A History of Mathematics
——— , Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton University Press, 2007. [92] Review
Morris Kline, Mathematics: The Loss of Certainty, Oxford University Press, USA, 1983 re-edition. [17, 22, 23]
——— , Mathematical Thought from Ancient to Modern Times: Vol 1, Oxford University Press, 1990 re-edition, also Vol 2 and Vol 3.
A.N. Kolmogorov and A.P. Yushkevich (eds.), Mathematics of the 19th Century: Vol. I, Birkhauser, 2nd edition 2001, also Vol II
Edna Ernestine Kramer, The Nature and Growth of Modern Mathematics, Princeton University Press, 1983.
Richard Laubenbacher and D. Pengelley, Mathematical Expeditions: Chronicles by the Explorers, Springer New York, 2000. [59] Review
Olli Lehto, Mathematics Without Borders: A History of the International Mathematical Union
Eli Maor, The Pythagorean Theorem: A 4,000-year History, Princeton University Press, 2007. [27] Review
Richard Mankiewicz, The Story Of Mathematics, Princeton University Press, 2001. Review
Calvin C. Moore, Mathematics at Berkeley: A History
Paul Nahin, An Imaginary Tale: The Story of √-1, Princeton University Press, 1998. Review, Review
Reviel Netz (editor and translator), The Works of Archimedes: Volume 1, The Two Books On the Sphere and the Cylinder: Translation and Commentary
Susan Oakes, Alan Pears and Adrian Rice (eds.), The Book of Presidents 1865 - 1965, London Mathematical Society 2005. Review
Kim Plofker, Mathematics in India: 500 BCE-1800 CE
Anne Rooney, The Story of Mathematics, Arcturus Publishing 2009. Review
Peter Roquette, The Brauer-Hasse-Noether Theorem in Historical Perspective, Springer, 2004. [158] Review
Walter William Rouse Ball, A History of the Study of Mathematics at Cambridge , Cambridge University Press, 2009 facsimile reprint. Review
Winfried Scherlau and Hans Opolka (transl. W.K. Bühler and G. Cornell) From Fermat to Minkowski: Lectures on the Theory of Numbers and Its Historical Development, Springer-Verlag, New York, 2010. [199] Review
Charles Seife, Zero: The Biography of a Dangerous Idea
Muriel Seltman and Robert Goulding (eds.), Thomas Harriot's Artis Analyticae Praxis: An English Translation with Commentary, Springer Verlag, 2007. Review
Jacqueline A. Stedall, The Arithmetic of Infinitesimals: John Wallis 1656, Springer, 2004. [137] Review
——— , Mathematics Emerging: A Sourcebook 1540 - 1900
——— , From Cardano's Great Art to Lagrange's Reflections: Filling a Gap in the History of Algebra, European Mathematical Society, 2011.
——— , The History of Mathematics: A Very Short Introduction, Oxford University Press, 2012. Review
John Stillwell, Mathematics and Its History, 3rd edition, Springer, 2010.
Dirk J. Struik, A Concise History of Mathematics, Fourth Revised Edition], Dover Publications, 1987. Review
Frank J. Swetz, Mathematical Expeditions: Exploring Word Problems across the Ages
Benjamin Wardhaugh, How to Read Historical Mathematics, Princeton University Press, 2010. Review
——— , Poor Robin's Prophecies: A curious Almanac, and the everyday mathematics of Georgian Britain
Robin J. Wilson, Stamping Through Mathematics
——— and John J. Watkins (eds.), Combinatorics: Ancient & Modern
Biography
Exceptionally, entries in this section are listed alphabetically by name of subject — Archimedes by Stein appearing before Zermelo by Ebbinghaus. Subject names are specified in square brackets and cross-link to Index of Mathematicians where applicable, and otherwise to The MacTutor History of Mathematics Archive.
Links to Review or to Obituary often provide a first rate summary of the subject's life and achievements.
Collections of biographies appear separately under The Profession of Mathematics.
[Abel, Niels Henrik] Arild Stubhaug (translated R. Daly), Niels Henrik Abel and his Times: Called Too Soon by Flames Afar
[Albert, Abraham Adrian] Nancy E. Albert, A3 & His Algebra: How a Boy from Chicago's West Side Became a Force in American Mathematics
[Archimedes of Syracuse] Sherman Stein, Archimedes: What Did He Do Beside Cry Eureka?, The Mathematical Association of America, 1999. Review
[Babbage, Charles] Doron Swade, The Cogwheel Brain: Charles Babbage and the quest to build the first computer
[Banach, Stefan] Emilia Jakimowicz and Adam Miranowicz (eds.), Stefan Banach: Remarkable Life, Brilliant Mathematics
[Banach, Stefan] Roman Kaluza (transl. A. Kostant and Wojbor A. Woyczynski), Through a Reporter's Eyes: The Life of Stefan Banach
[Bourbaki, Nicholas] Maurice Mashaal, Bourbaki: A Secret Society of Mathematicians, American Mathematical Society, 2006. Review (3MB)
[Carroll, Lewis = Dodgson, Charles] Robin J. Wilson, Lewis Carroll in Numberland: His Fantastical Mathematical Logical Life
[Cayley, Arthur] Tony Crilly, Arthur Cayley: Mathematician Laureate of the Victorian Age
[Clifford, William and Lucy] M. Chisholm, Such Silver Currents: The Story of William and Lucy Clifford, 1845-1929
[Coxeter, Donald] Siobhan Roberts, King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry
[Dee, John] Benjamin Wooley, The Queen's Conjuror: The Science and Magic of Dr. Dee, Flamingo, new edition 2002. Review
[Descartes, René] Desmond Clarke, Descartes: A Biography
[Dirac, Paul] Graham Fermelo, The Strangest Man: The Life of Paul Dirac
[Dirac, Paul] Abraham Pais, Maurice Jacob, David I. Olive and Michael F. Atiyah, Paul Dirac: The Man and his Work
[Erdős, Paul] Paul Hoffman, The Man Who Loved Only Numbers: the Story of Paul Erdős and the Search for Mathematical Truth, Fourth Estate, new edition 1999. Review
[Erdős, Paul] Bruce Schechter, My Brain is Open: The Mathematical Journeys of Paul Erdős
[Gauss, Carl Friedrich] Hans Wußing, Carl Friedrich Gauß: Biographie und Documente, EAGLE, Leipzig, 2011. Review
[Gödel, Kurt] John W. Dawson Jr, Logical Dilemmas: The Life and Work of Kurt Gödel
[Halmos, Paul Richard] Paul R. Halmos, I Want to Be a Mathematician: An Automathography, Springer, New York, 1985. Obituary
[Kac, Mark] Mark Kac, Enigmas of Chance: An Autobiography
[Kelvin, Lord = Thomsom, William] Raymond Flood, Mark McCartney and Andrew Whitaker, Kelvin: Life, Labours and Legacy
[Kelvin, Lord = Thomsom, William] Silvanus P. Thompson, The Life of Lord Kelvin: vol. 2, Oxford University Press, 2006 edition. [134]
[Kovalevskaia, Sofia] Ann Hibner Köblitz, A Convergence of Lives: Sofia Kovalevskaia: Scientist, Writer, Revolutionary, Rutgers University Press, reprint edition 1993.
[Kovalevskaia, Sofia] Joan Spicci, Beyond the Limit: The Dream of Sofya Kovalevskaya
[Lagrange, Joseph Louis] Irina Alexandrovna Tyulina, Joseph Louis Lagrange 1736 - 1813, Knizhnyy dom "LIBROKOM", 2010. In Russian.
[Lie, Sophus] Arild Stubhaug (translated R. Daly), The Mathematician Sophus Lie: It was the Audacity of My Thinking
[Mac Lane, Saunders] Saunders Mac Lane, Saunders Mac Lane: A Mathematical Autobiography
[Mosteller, Charles Frederick] Frederick Mosteller, The Pleasures of Statistics: The Autobiography of Frederick Mosteller
[Newton, Isaac] James Gleick, Isaac Newton
[Noether, Amelie ('Emmy')] M.B.W. Tent, Emmy Noether: The Mother of Modern Algebra
[Norton, Simon] Alexander Masters, The Genius in my Basement
[Poincaré, Henri] Jeremy Gray, Henri Poincaré: A Scientific Biography, Princeton University Press, 2012
[Ramanujan, Srivivasa] Robert Kanigel, The Man Who Knew Infinity: a Life of the Genius Ramanujan, Abacus, new edition 1992.
[Robinson, Julia] Constance Reid, Julia: A Life in Mathematics, The Mathematical Association of America, 1997.
[Smale, Stephen] Steve Batterson, Stephen Smale: The Mathematician Who Broke the Dimension Barrier
[Sylvester, James Joseph] Karen H. Parshall, James Joseph Sylvester: Jewish Mathematician in a Victorian World, The Johns Hopkins University Press, 2006. [142] Review
[Tarski, Alfred] Anita Burdman Feferman and Solomon Feferman, Alfred Tarski: Life and Logic
[Turing, Alan Mathison] Andrew Hodges, The Alan Turing: The Enigma
[Turing, Alan Mathison] David Leavitt, The Man Who Knew Too Much: Alan Turing and the Invention of the Computer, W. W. Norton 2005. Review, Review
[Ulam, Stanisław] Stanisław Ulam, The Adventures of a Mathematician, University of California Press; reprinted edition 1992.
[Volterra, Vito] Judith R. Goodstein, The Volterra Chronicles: The Life and Times of an Extraordinary Mathematician 1860-1940, American Mathematical Society, 2007. Review (2.8MB)
[Weil, André] André Weil (Souvenirs d’apprentissage, translated by Jennifer Gage), The Apprenticeship of a Mathematician, Birkhaüser, 1991. Review
[Wiener, Norbert] Flo Conway and Jim Siegelman, Dark Hero of the Information Age: In Search of Norbert Wiener - Father of Cybernetics
[Wiener, Norbert] Norbert Wiener, I Am a Mathematician, Victor Gollanz, London, 1956.
[Zariski, Oscar] Carol Parikh, The Unreal Life of Oscar Zariski, Springer, 2009, Review
[Zermelo, Ernst] Heinz-Dieter Ebbinghaus with Volker Peckhaus, Ernst Zermelo: An Approach to His Life and Work
The profession of mathematics
Donald J. Albers and Gerald L. Alexanderson, Mathematical People: Profiles and Interviews
Charles Babbage, Passages from the Life of a Philosopher, Cambridge University Press, reissue edition, 2011. Ebook
E. Bell, Men of Mathematics, Simon & Schuster Inc, 1986.
William Byers, How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics, Princeton University Press, 2007. Review
Alexandre V. Borovik, Mathematics Under the Microscope: Notes on Cognitive Aspects of Mathematical Practice
Mariana Cook, Mathematicians: An Outer View of the Inner World
Richard Courant and Herbert Robbins, revised by Ian Stewart, What is Mathematics?: An Elementary Approach to Ideas and Methods, Oxford University Press Inc, 2nd Revised, 1996. Review
Philip J. Davis, The Education of a Mathematician
Raymond Flood and Robin Wilson, The Great Mathematicians
Timothy Gowers, Mathematics: A Very Short Introduction, Oxford Paperbacks, 2002. Review, Review, Review
Paul R. Halmos, I Want to Be a Mathematician: An Automathography, Springer, New York, 1985.
——— , I Have a Photographic Memory, American Mathematical Society, 1987. [127]
G.H. Hardy, A Mathematician's Apology, with a Forward by C.P. Snow, Cambridge University Press, 1992 edition. [98]
Reuben Hersh and Vera John-Steiner, Loving and Hating Mathematics: Challenging the Myths of Mathematical Life
Nicolas Higham, Handbook of Writing for the Mathematical Sciences
Ioan James, Remarkable Mathematicians: From Euler to von Neumann, Cambridge University Press, 2003. Review, Review
Donald E. Knuth, Tracy Larrabee and Paul M. Roberts, Mathematical Writing, The Mathematical Association of America, 1996.
Stephen Krantz, A Primer of Mathematical Writing, The Mathematical Association of America, 1997. Review
——— , Mathematical Apocrypha: Stories and Anecdotes of Mathematicians and the Mathematical, The Mathematical Association of America, 2002. Review, Review
——— ,A Mathematician's Survival Guide: Graduate School and Early Career Development, American Mathematical Society, 2003. Review
——— , Mathematical Apocrypha Redux: More Stories and Anecdotes of Mathematicians and the Mathematical, The Mathematical Association of America, 2006. Review
——— , The Proof is in the Pudding: The Changing Nature of Mathematical Proof
Charlene Morrow and Teri Perl (eds.), Notable Women in Mathematics: A Biographical Dictionary, Greenwood Press, 1998. Review
Luetta Reimer and Wilbert Reimer, Mathematicians are People Too: Stories from the Lives of Great Mathematicians, vol. 1
Gian-Carlo Rota (Fabrizio Palombi, ed.), Indiscrete Thoughts (Modern Birkhäuser Classics)
David Ruelle, The
Mathematician's Brain
Ian Stewart, Letters to a Young Mathematician, Basic Books, US, 2006. Review, Review, Review, Review, Review
Charles Wells, A Handbook of Mathematical Discourse
Norbert Wiener, I Am a Mathematician, Victor Gollanz, London, 1956.
Robin V. Young (ed.), Notable
Mathematicians from Ancient Times to the Present
Psychology, Sociology, Philosophy
Robyn Arianrhod, Einstein's Heroes: Imagining the World Through the Language of Mathematics
Marcia Ascher, Mathematics Elsewhere: An Exploration of Ideas Across Cultures, Princeton University Press, 2002. Review
Ehrhard Behrends, Nuno Crato and José Francisco Rodrigues (Editors), Raising Public Awareness of Mathematics
James Robert Brown, Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures, Routledge, 2nd edition, 2008. Review
Brian Butterworth, The Mathematical Brain
Bettye Anne Case and Anne M. Leggett (eds.), Complexities: Women in Mathematics
Stephen Ceci and Wendy Williams, The Mathematics of Sex: How Biology and Society Conspire to Limit Talented Women and Girls
Gregory Chaitin, Exploring Randomness, Springer-Verlag, 2000. Review
Jean-Pierre Changeux and Alain Connes, Conversations on Mind, Matter, and Mathematics
David Corfield, Towards a Philosophy of Real Mathematics, Cambridge University Press, 2003. Review, Review
E. Brian Davis, Why Beliefs Matter: Reflections on the Nature of Science
Stanislas Dehaene, The Number Sense: How the Mind Creates Mathematics, revised edition, Oxford University Press, USA, 2011. Review
Keith Devlin, The Maths Gene: Why Everyone Has It, But Most People Don't Use It
A. K. Dewdney, A Mathematical Mystery Tour: Discovering the Truth and Beauty of the Cosmos
Apostolos Doxiadis and Barry Mazur, Circles Disturbed: The Interplay of Mathematics and Narrative, Princeton University Press, 2012. Review
Bonnie Gold and Roger A. Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy
Claudia Henrion, Women in Mathematics: The Addition of Difference, Indiana University Press, 1997. Review
Reuben Hersh, What is Mathematics, Really?
John Horgan, The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age
Claire G. Jones, Femininity, Mathematics and Science 1880-1914
Imre Lakatos, Proofs and Refutations: The Logic of Mathematical Discovery, edited by Worrall and Zahar, Cambridge University Press, 1976. [26]
George Lakoff and Rafael E. Núñez, Where Mathematics Comes from: How the Embodied Mind Brings Mathematics into Being
Mario Livio, Is God a Mathematician?
Margaret A. M. Murray, Women Becoming Mathematicians: Creating a Professional Identity in Post-world War II America
Roland Omnès, Converging Realities: Toward a Common Philosophy of Physics and Mathematics
John Allen Paulos, Mathematics and Humour, University of Chigago Press, 1990.
Roger Penrose, The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics, Oxford Paperbacks; New Ed, 1999. Review
——— , Shadows of the Mind: A Search for the Missing Science of Consciousness, Vintage, 1995. Review, Review, Review, Rebuttals
Vladimir Tasić, Mathematics and the Roots of Postmodern Thought
Valerie Walkerdine, Counting Girls Out: Girls and Mathematics, Routledge, 2nd edition, 1998.
Mathematical mountains: popular accounts of landmark problems/solutions
J. Carlson, A. Jaffe, and A. Wiles (eds.), The Millennium Prize Problems, American Mathematical Society, 2006. Review
John Derbyshire, Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, Plume Books, 2004. Review
Keith Devlin, The Millennium Problems: The Seven Greatest
Unsolved Mathematical Puzzles of Our Time
Underwood Dudley, The Trisectors, 2nd edition, Mathematical Association of America, 1996.
Lance Fortnow, The Golden Ticket: P, NP, and the Search for the Impossible
Mario Livio, The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry
Piergiorgio Odifreddi, The Mathematical Century: The 30 Greatest Problems of the Last 100 Years
Donal O’Shea, The Poincaré Conjecture: In Search of the Shape of the Universe
Peter Pesic, Abel's Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability
Mark Ronan, Symmetry and the Monster: One of the Greatest Quests of Mathematics, Oxford University Press, 2006. [35] Review, Review, Review
Paul Sabbagh, Dr.Riemann's Zeros
Marcus du Sautoy, The Music of the Primes: Why an Unsolved Problem in Mathematics Matters, HarperPerennial, 2004 edition. Review, Review, Review, Review, Review
——— , Symmetry: A Journey Into the Patterns of Nature
Simon Singh, Fermat's Last Theorem, HarperPerennial, 2007 reissue. [9] Review
George Szpiro, Kepler's Conjecture: How Some of the Greatest Minds in History Helped Solve One of the Oldest Math Problems in the World, John Wiley & Sons, 2003. [101] Review, Review
——— , Poincare's
Prize: The Hundred-year Quest to Solve One of Math's Greatest Puzzles
Robin Wilson, Four Colors Suffice: How the Map Problem Was Solved (Revised Color Edition)
Benjamin H. Yandell, The Honors Class: Hilbert's Problems and Their Solvers, AK Peters, 2001. Review, Review
Introductions to mathematical topics accessible for non-professionals
David Acheson, 1089 and All That - A Journey into Mathematics
Colin Adams, The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots, American Mathematical Society, 2004. [166] Review
Titu Andreescu and Dorin Andrica, Complex Numbers from A to ...Z, Birkhauser Boston, 2005. [56] Review
Avner Ash and Robert Gross, Fearless Symmetry: Exposing the Hidden Patterns of Numbers, Princeton University Press, 2006. [34, 41, 51] Review, Review
———, Elliptic Tales: Curves, Counting, and Number Theory, Princeton University Press, 2012.
Tomaso Aste and Denis Weaire, The Pursuit of Perfect Packing, Second Edition
V.K. Balakrishnan, Graph Theory: Including Hundreds of Solved Problems (Schaum), McGraw-Hill Publishing Co., 1997.
Robert B. Banks, Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics, Princeton University Press, new edition 2013. Review
Alex Bellos, Alex's Adventures in Numberland
Ehrhard Behrends (transl. D. Kramer), Five-Minute Mathematics
Arthur T. Benjamin and Ezra Brown (eds.), Biscuits of Number Theory, The Mathematical Association of America , 2009. Review
John Bryant and Chris Sangwin, How Round Is Your Circle?: Where Engineering and Mathematics Meet
Edward B. Burger and Michael Starbird, Coincidences, Chaos and All That Math Jazz, W W Norton, 2005. Review
Chris Caldwell and G. L. Honaker, Jr., Prime Curios
John L Casti, Five Golden Rules: Great Theories of 20th Century Mathematics and Why They Matter, John Wiley, 1997. [18]
Gengzhe Chang and Thomas W. Sederberg, Over and Over Again, Mathematical Association of America, 1998. [71,124] Review
John H. Conway, The Book of Numbers
——— and Derek A. Smith, On Quaternions and Octonions, A K Peters, 2003. [61] Review
——— , Heidi Burgiel and Chaim Goodman-Strauss, The Symmetries of Things
William J. Cook, In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation, Princeton University Press, 2012. Review, Review
Tony Crilly, 50 Mathematical Ideas You Really Need to Know, Quercus Publishing, London 2007. Review
——— , The Big Questions: Mathematics, Quercus Publishing, 2011. Review
Keith Devlin, The Language of Mathematics: Making the Invisible Visible, W.H.Freeman & Co Ltd, 2000. Review
Underwood Dudley, Mathematical Cranks, The Mathematical Association of America, 1996.
——— , Is Mathematics Inevitable?, The Mathematical Association of America, 2008. Review
William Dunham, Journey Through Genius: Great Theorems of Mathematics, John Wiley & Sons, 1990. [76]
——— , The
Genius of Euler: Reflections on His Life and Work
Rob Eastaway and John Haigh
, The Hidden Mathematics of Sport
Richard Elwes, How to Build a Brain: And 34 Other Really Interesting Uses of Mathematics
Steven Finch, Mathematical Constants, Cambridge University Press, 2003. [144] Review
Paulus Gerdes, Geometry from Africa. Mathematical and educational explorations
Rebecca Goldstein, Incompleteness: The Proof and Paradox of Kurt Godel, W. W. Norton & Company, 2005. Review, Review
Julian Havil, Gamma: Exploring Euler's Constant, Princeton University Press, 2003. Review, Review, Review
———, Nonplussed: Mathematical Proof of Implausible Ideas, Princeton University Press, 2007. Review, Review
———, The Irrationals: A Story of the Numbers You Can't Count On
Peter M. Higgins, Number Story: From Counting to Cryptography
———, Nets, Puzzles, and Postmen: An exploration of mathematical connections
———, Numbers: A Very Short Introduction, Oxford University Press, 2011. Review
Peter Hilton, Derek Holton, and Jean Pedersen, Mathematical Vistas: From a Room with Many Windows, Springer-Verlag, New York, 2002. Review
——— and Jean Pedersen, with illustrations by Sylvie Donmoyer, A Mathematical Tapestry: Demonstrating the Beautiful Unity of Mathematics
Ross Honsberger, Episodes in Nineteenth and Twentieth Century Euclidean Geometry, Mathematical Association of America, 1996. [55, 84]
H.E. Huntley, The Divine Proportion: A Study in Mathematical Beauty
Vincent Icke, The Force of Symmetry, Cambridege University Press, 1995. [86]
Dan Kalman, Uncommon Mathematical Excursions: Polynomia and Related Realms, The Mathematical Association of America, 2009.
T. W. Körner, The Pleasures of Counting
D.V. Lindley, Making Decisions, 2nd edition, John Wiley and Sons Ltd, 1985. [10]
Richard J. Lipton, The P=NP Question and Gödel's Lost Letter, Springer, New York, 2010.
Mario Livio, The Golden Ratio: The Story of Phi, the Extraordinary Number of Nature, Art and Beauty, Headline Review, new edition 2003. Review, Review
Dana Mackenzie, The Universe in Zero Words: The Story of Mathematics as Told through Equations
Eli Maor, "e", The Story of a Number, Princeton University Press, 1998 edition. [136]
———, Trigonometric Delights
Barry Mazur, Imagining Numbers: (Particularly the Square Root of Minus Fifteen)
T.S. Michael, How to Guard an Art Gallery and Other Discrete Mathematical Adventures
Melanie Mitchell, Complexity: A Guided Tour
David Mumford, Caroline Series, David Wright, Indra's Pearls: The Vision of Felix Klein
Paul J. Nahin, Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills, Princeton University Press, 2006. [36] Review, Review
John Allen Paulos, A Mathematician Reads the Newspaper: Making Sense of the Numbers in the Headlines, Basic Books, 1999. Review
———, A Mathematician Plays the Market
Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe, Vintage, 2005. [121] Review
Cliff Pickover, The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics
Burkard Polster, Q.E.D.: Beauty in Mathematical Proof, Wooden Books Ltd, 2006. Review
Alfred S. Posamentier and Ingmar Lehmann, Pi: A Biography of the World's Most Mysterious Number
———, The Fabulous Fibonacci Numbers
Alfred S. Posamentier, The Pythagorean Theorem: The Story of Its Power and Beauty
William Poundstone, Prisoner's Dilemma: John Von Neumann, Game Theory and the Puzzle of the Bomb
George Pólya, How to Solve it: A New Aspect of Mathematical Method, Penguin, new edition 1990. Review
Constance Reid, From Zero to Infinity: What Makes Numbers Interesting, A K Peters/CRC Press; 5th revised edition, 2006. Review, Review
Paulo Ribenboim, Fermat's Last Theorem for Amateurs
David S. Richeson, Euler's Gem: The Polyhedron Formula and the Birth of Topology, Princeton University Press, 2008. Review
Anne Rooney, 50 Amazing Things Kids Need to Know About Mathematics
Lionel Salem, Frederic Testard and Coralie Salem, The Most Beautiful Mathematical Formulas: An Entertaining Look at the Most Insightful, Useful and Quirky Theorems of All Time, John Wiley & Sons, 1997.
Sherman Stein, How the Other Half Thinks: Adventures in Mathematical Reasoning
Hugo Steinhaus, One Hundred Problems in Elementary Mathematics
———, Mathematical Snapshots, Dover Publications, 2000. [77]
Ian Stewart, Does God Play Dice?: The New Mathematics of Chaos, 2nd edition, Penguin, 1997.
——— , Why Beauty is Truth: The History of Symmetry, Basic Books, 2008. [90] Review, Review
John Stillwell, Roads to Infinity: The Mathematics of Truth and Proof
Steven Strogatz, The Joy of X: A Guided Tour of Math, from One to Infinity
Terence Tao, Solving Mathematical Problems: A Personal Perspective, Oxford University Press, 2nd edition 2006. Review, Review
Hans Walser (translated Peter Hilton), The Golden Section, Mathematical Association of America 2001. Review
Leonard M. Wapner, The Pea and the Sun: A Mathematical Paradox
Matthew Watkins, The Mystery of the Prime Numbers: Secrets of Creation v. 1
——— , The Enigma of the Spiral Waves: Secrets of Creation v. 2
David Wells, You Are a Mathematician, Penguin, London, 1995.
——— , Prime Numbers: The Most Mysterious Figures in Math, John Wiley & Sons Inc, 1995. [21]
Robert, M. Young, Excursions in Calculus: An Interplay of the Continuous and the Discrete, Mathematical Association of America, 1996. [170]
More specialised introductions to mathematical topics
Martin Aigner, A Course in Enumeration, Springer 2007. [171] Review
——— and Günter M. Ziegler, Proofs from The Book
Joan Aldous and Robin J. Wilson, Graphs
and Applications: An Introductory Approach
Noga Alon and Joel H. Spencer, The Probabilistic Method, 3rd ed., WileyBlackwell, 2008. [112, 120, 193] Review
Ian Anderson, Combinatorial Designs and Tournaments, Oxford University Press, 1997. [100, 131]
George E. Andrews and Kimmo Eriksson, Integer Partitions, 2nd revised ed., Cambridge University Press, 2004. [115, 153, 156] Review
M. Ya. Antimirov, A. A. Kolyshkin and Rémi Vaillancourt, Complex Variables, Academic Press, San Diego, 1998.
David L. Applegate, Robert E. Bixby, Vašek Chvátal and William J. Cook, The Traveling Salesman Problem: A Computational Study, Princeton University Press, 2006. [109] Review
M.A. Armstrong, Basic Topology, Springer-Verlag New York Inc., 1997. [122]
Jörg Arndt and Christoph Haenel (translated, C. Lischka and D. Lischka), Pi - Unleashed
A.F. Beardon, Algebra and Geometry, Cambridge University Press, 2005. [37] Review
Arthur T. Benjamin and Jennifer J. Quinn, Proofs that Really Count: The Art of Combinatorial Proof, The Mathematical Association of America, 2003. [194] Review
Norman Biggs, Algebraic Graph Theory, 2nd edition, Cambridge University Press, 1994. [46, 169]
K.G. Binmore, The Foundations of Analysis: A Straightforward Introduction: Book 1 Logic, Sets and Numbers, Cambridge University Press, 1981.
——— , The Foundations of Analysis: A Striaghtforward Introduction: Book 2 Topological Ideas, Cambridge University Press, 1981. [162]
Miklós Bóna, A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory, 2nd edition, World Scientific Publishing, 2006. Review
——— , Combinatorics of Permutations, Chapman and Hall, 2004. [143] Review
J.A. Bondy and U.S.R. Murty, Graph Theory, Springer, 2008. [150, 155, 190] Review, Webpage
Jonathan M. Borwein, David H. Bailey and Roland Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery, A K Peters, 2008. [147] Review, Review, Review
David M. Bressoud, Proofs and Confirmations: The Story of the Alternating-Sign Matrix Conjecture, Cambridge University Press, 1999. Review
——— , A Radical Approach to Real Analysis, 2nd edition, The Mathematical Association of America, 2007. [191] Review
——— , A Radical Approach to Lebesgue's Theory of Integration, Cambridge University Press, 2008. [2] Review
Edward B. Burger and Robert Tubbs, Making Transcendence Transparent: An Intuitive Approach to Classical Transcendental Number Theory
David M. Burton, Elementary Number Theory 7th edition
Peter Cameron, Combinatorics: Topics, Techniques, Algorithms, Cambridge University Press, 1994. [19, 38, 182]
———, Introduction to Algebra, 2nd edition
———, Sets, Logic and Categories, Springer, 1999. [196]
G. Chartrand and L. Lesniak, Graphs and Digraphs, 4th Edition, Chapman and Hall/CRC, 2004. [80]
Fan Chung and Ronald Graham, Erdős on Graphs: His Legacy of Unsolved Problems, AK Peters, 1998. [146]
John Horton Conway (with Francis Y.C.Fung), The Sensual (Quadratic) Form, The Mathematical Association of America, 1998. [79]
H.S.M. Coxeter, Regular Polytopes, Dover Publications, 1974. [132]
B.A. Davey and H.A. Priestly, Introduction to Lattices and Order, Cambridge University Press, 1990.
Satyan L. Devadoss and Joseph O'Rourke, Discrete and Computational Geometry
Reinhard Diestel, Graph Theory 4th edition
R.A. Dunlap, The Golden Ratio and Fibonacci Numbers, World Scientific, 1998. [42, 45]
Paul Erdős and János Surányi, Topics in the Theory of Numbers, Springer 2003. [151] Review
William Feller, An Introduction to Probability Theory and Its Applications: vol. 2 (Probability & Mathematical Statistics), John Wiley, Canada, 1971.
Benjamin Fine and Gerhard Rosenberger, The Fundamental Theorem of Algebra, Springer New York, 1997. [6]
Torkel Franzén, Godel's Theorem: An Incomplete Guide to Its Use and Abuse
M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness, W.H.Freeman & Co Ltd, 1979. [14, 187]
Gary Gordon and Jennifer MacNulty, Matroids: A Geometric Introduction
Ronald Graham, Donald Knuth and Oren Patashnik, Concrete Mathematics: Foundation for Computer Science
Jack E. Graver, Counting on Frameworks: Mathematics to Aid the Design of Rigid Structures, The Mathematical Association of America, 2001. [140] Review, Review
Ernst Hairer and Gerhard Wanner, Analysis by its History, Springer, 1996.
Marshall Hall, The Theory of Groups, MacMillan, 1959 (this ed. Chelsea Publishing Co./American Mathematical Society,1999). [114]
Frank Harary, Graph Theory, Perseus Books, 1999. [24, 48]
G.H. Hardy and E.W. Wright (with additional material by D.R. Heath-Brown, J.H. Silverman and A. Wiles), An Introduction to the Theory of Numbers
Michael Henle, A Combinatorial Introduction to Topology, Dover Publications, 1994. [16]
Ann Hirst and David Singerman, Basic Algebra and Geometry, Prentice Hall, 2000.
Kevin Houston, How to Think Like a Mathematician: A Companion to Undergraduate Mathematics
Stephen A. Huggett and David Jordan, A Topological Aperitif
Arthur Jones, Sidney A. Morris and Kenneth R. Pearson, Abstract Algebra and Famous Impossibilities, Springer-Verlag, New York, 1991.
Gareth A. Jones and David Singerman, Complex Functions: An Algebraic and Geometric Viewpoint
Gareth A. Jones and Mary Jones, Elementary Number Theory, Springer, Berlin, 1998. [5, 7, 11, 13, 29, 32]
Stasys Jukna, Extremal Combinatorics: With Applications in Computer Science, Springer, 2nd edition, 2011. [195]
Alexander Kheyfits, A Primer in Combinatorics, De GruyterGmbH & Co. KG, Berlin, 2010. Review
Anthony W. Knapp, Basic Algebra, Birkhauser Boston, 2006, and Advanced Algebra, Birkhauser Boston, 2007. [125] Review, Review
——— , Basic Real Analysis, Birkhauser Verlag, 2004, and Advanced Real Analysis, Birkhäuser Boston, 2005. [88]
Steven G. Krantz and Harold R. Parks, A Primer of Real Analytic Functions, 2nd edition, Birkhäuser Verlag AG, 2002. [47]
Barbara D. MacCluer, Elementary Functional Analysis, Springer Science + Business Media, 2009. Review, Review
Yuri Matiyasevich, Hilbert's 10th Problem, MIT Press, 1993. [43]
Jiří Matoušek, Lectures on Discrete Geometry, Springer-Verlag, New York, 2002. [107, 200]
——— , Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra, American Mathematical Society, 2010. Review
Melzak, Z.A., Companion to Concrete Mathematics: Two Volumes Bound as One: Volume I: Mathematical Techniques and Various Applications, Volume II: Mathematical Ideas, Modeling and Applications
Christopher Moore and Stephan Mertens, The Nature of Computation
Steven J. Miller and Ramin Takloo-Bighash, An
Invitation to Modern Number Theory
Frank Morgan, Geometric
Measure Theory: A Beginner's Guide
Tristan Needham, Visual Complex Analysis, Clarendon Press, 1998. Review
Dwight Neuenschwander, Emmy Noether's Wonderful Theorem, The Johns Hopkins University Press, 2010.
Peter M. Neumann, Gabrielle A. Stoy and Edward C. Thompson, Groups and Geometry, Oxford University Press, 1994. [66, 85]
Christos Papadimitriou and Kenneth Steiglitz, Combinatorial
Optimization: Algorithms and Complexity
Charles Petzold, The Annotated Turing: A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine
Jim Pitman, Probability, Springer, New York, 1999. [89]
Harriet Pollatsek, Lie Groups: A Problem-Oriented Introduction via Matrix Groups, Mathematical Association of America, 2009. Review
H.E. Priestly, Introduction to Complex Analysis, 2nd edition, Oxford University Press, 2003.
Andrew N. Pressley, Elementary Differential Geometry, Springer, London, 2nd edition, 2010. [181,183] Review
Miles Reid, Undergraduate Algebraic Geometry, Cambridge University Press, 1988.
——— and Balázs Szendrői, Geometry and Topology, Cambridge University Press, 2005.
Joseph H. Silverman, A Friendly Introduction to Number Theory, Pearson Education, 2005. Review
——— and John Tate, Rational Points on Elliptic Curves, Springer-Verlag, New York, 1994. [81]
Geoff Smith, Introductory Mathematics: Algebra and Analysis, Springer, London, 1998. Review
——— and Olga Tabachnikova, Topics in Group Theory, Springer, London, 2000.
Peter Smith, An Introduction to Formal Logic, Cambidge University Press, 2003. [73]
——— , An Introduction to Godel's Theorems, Cambridge University Press, 2007. [74,75] Review
Michael Spivak, Calculus on Manifolds
R. P. Stanley, Enumerative Combinatorics: Volume 1 (new ed. 2000) and Volume 2, (new ed. 2001) Cambridge University Press. [103, 126] Review, Review
Kenneth Stephenson, Introduction to Circle Packing: The Theory of Discrete Analytic Functions, Cambridge University Press, 2005. [130, 179] Review, Review
J. Michael Steele, The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities, Mathematical Association of America, 2004. [201] Review
Ian Stewart, Galois Theory, Chapman and Hall/CRC, 3rd Revised Edition, 2003. [58]
Wilson A. Sutherland, Introduction to Metric and Topological Spaces, 2nd edition, Oxford University Press, 2009. [145]
Thomas M. Thompson, From Error-Correcting Codes through Sphere Packings to Simple Groups, Mathematical Association of America, 2004. [83] Review
Silvanus P. Thomson and Martin Gardner, Calculus Made Easy, Palgrave Macmillan, revised edition, 1999.
Dennis Wackerly, William Mendenhall III and Richard Scheaffer, Mathematical Statistics with Applications, Duxbury, 2001. [8, 30, 133]
Robert A. Wilson, Graphs, Colourings and the Four-colour Theorem, Oxford University Press, 2002.
Herbert S. Wilf, generatingfunctionology, 3rd rev. ed., A K Peters, 2006. [116] Review
——— , Algorithms and Complexity, 2nd edition, A K Peters, 2003. [138,139]
Robin J. Wilson, Introduction to Graph Theory, 5th Edition
J. Eldon Whitesitt, Boolean Algebra and Its Applications, Dover Publications Inc., 1995. [111]
Research level
Alan Baker, Transcendental Number Theory, Cambridge University Press, New Edition, 1990.
R. B. Bapat and T. E. S. Raghavan, Nonnegative Matrices and Applications, Cambridge University Press, 1997. [113]
Simon R. Blackburn, Peter M. Neumann and Geetha Venkataraman, Enumeration of Finite Groups, Cambridge University Press, 2007. Review
Peter Cameron, Permutation Groups, Cambridge University Press, 1999. [15, 64, 65, 135, 159,174]
——— and J. H. van Lint, Designs, Graphs, Codes and Their Links, Cambridge University Press, Cambridge, 1991. [3, 54]
Cho-Ho Chu, Jordan Structures in Geometry and Analysis, Cambridge University Press, 2011.
Richard Crandall and Carl Pomerance, Prime Numbers: A Computational Perspective, 2nd revised edition, Springer-Verlag, New York, 2005. [127] Review
J. Dénes and A.D. Keedwell, Latin Squares: New Developments in the Theory and Applications, North-Holland, 1991. [53, 176]
John D. Dixon and Brian Mortimer, Permutation Groups, Springer, 1996.
Yurij A. Drozd and Vladimir V. Kirichenko, Finite-Dimensional Algebras, Springer-Verlag Berlin, 1994. [123]
Leopold Flatto, Poncelet's Theorem
Mikio Furuta, Index Theorem 1, American Mathematical Society, 2008.
Bernd Gärtner and Jiří Matoušek, Approximation Algorithms and Semidefinite Programming
Ronald L. Graham, Bruce L. Rothschild and Joel H. Spencer, Ramsey Theory, Wiley-Blackwell, 2nd Edition, 1990. [28]
Dan Gusfield and Robert W. Irving, The Stable Marriage Problem: Structure and Algorithms, MIT Press, 1989. [68]
Thomas C. Hales and Samuel P. Ferguson, The Kepler Conjecture: The Hales-Ferguson Proof, Springer, 2011.
Thomas C. Hales, Dense Sphere Packings: A Blueprint for Formal Proofs, Cambridge University Press, 2012.
Glyn Harman, Prime-Detecting Sieves, Princeton University Press, 2007. [202]
Brendan Hassett, Introduction to Algebraic Geometry, Cambridge University Press, 2007. Review
W.K. Hayman, Multivalent Functions, 2nd edition, Cambridge University Press, 2008. [98]
Youssef Jabri, The Mountain Pass Theorem: Variants, Generalizations and Some Applications, Cambridge University Press, 2003.
G.J.O. Jameson, The Prime Number Theorem, Cambridge University Press, 2003. [33, 197] Review
Ole G. Jorsboe and Leif Mejlbro, The Carleson-Hunt Theorem on Fourier Series, Springer, 1982.
Aleksandr Khinchin, Continued Fractions, Dover Publications, 1997. [91]
Anthony W. Knapp, Elliptic Curves, Princeton University Press, 1993.
Neal Koblitz, Introduction to Elliptic Curves and Modular Forms, 2nd edition, Springer-Verlag New York, 1993. [104]
Yvette Kosmann-Schwarzbach (transl. Bertram E. Schwarzbach), The Noether Theorems: Invariance and Conservation Laws in the Twentieth Century: Invariance and Conservation Laws in the 20th Century, Springer New York, 2011. Review
Steven G. Krantz and Harold R. Parks, The Implicit Function Theorem: History, Theory and Applications, Birkhäuser Boston, 2002.
Jeffrey C. Lagarias (ed.), The Ultimate Challenge: The 3x + 1 Problem
Tsit-Yuen Lam, A First Course in Noncommutative Rings, 2nd ed., Springer, 2001.
I.G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford University Press, 2nd edition, 1998. [182]
F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, North-Holland, 1983. [72]
Jiří Matoušek, Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry, Springer Berlin, 2003. [119] Review
Richard B. Melrose, The Atiyah-Patodi-Singer Index Theorem, AK Peters, 1993.
David Witte Morris, Ratner's Theorems on Unipotent Flows, University of Chicago Press, 2005.
Olavi Nevanlinna, Meromorphic Functions and Linear Algebra, American Mathematical Society, 2003.
Kathleen Ollerenshaw and David Brée, Most Perfect Pandiagonal Magic Squares: Their Construction and Enumeration, The Institute of Mathematics and its Applications, Southend-on-Sea, 1988. [129]
Frank W. J. Olver, Daniel W. Lozier, Ronald F. Boisvert, Charles W. Clark (eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, 2010. Review
Joseph O'Rourke, Art Gallery Theorems and Algorithms,Oxford University Press, 1987 . Ebook
Jean-Pierre Otal, The Hyperbolization Theorem for Fibered 3-manifolds, American Mathematical Society, 2002.
James G. Oxley, Matroid Theory 2nd Edition, Oxford University Press, 2011. [141]
Athanase Papadopoulos, Metric Spaces, Convexity and Nonpositive Curvature, European Mathematical Society, 2004. Review
Marko Petkovsek, Herbert S Wilf, Doron Zeilberger, A=B
George Pólya and Gabor Szegő, (transl. Dorothee Aeppli) Problems and Theorems in Analysis, vol. 1: Series. Integral Calculus. Theory of Functions, Springer 1997.
——— , (transl. C.E. Billigheimer) Problems and Theorems in Analysis, vol. 2: Theory of Functions, Zeros, Polynomials, Determinants, Number Theory, Geometry, Springer 1997. [148]
Victor Prasolov, Polynomials
D.J.S. Robinson, A Course in the Theory of Groups, 2nd edition, Springer-Verlag, 1998. [82]
Lee A. Rubel and James E. Colliander, Entire and Meromorphic Functions, Springer-Verlag New York, 1996. [97]
Alexander Schrijver, Combinatorial Optimization: Polyhedra and Efficiency, Springer, Berlin, 2002. [57]
René Schoof, Catalan's Conjecture, Springer-Verlag London, 2008. [118] Review
Audrey Terras, Zeta Functions of Graphs: A Stroll through the Garden, Cambridge University Press, 2011.
William P. Thurston (ed. by Silvio Levy), Three-Dimensional Geometry and Topology: Volume 1, Princeton University Press, 1997. Review
Robert Veroff (ed.), Automated
Reasoning and Its Applications: Essays in Honor of Larry Wos
Nader Vakil, Real Analysis through Modern Infinitesimals, Cambridge University Press, 2011.
Stan Wagon, The Banach-Tarski Paradox
Dominic Welsh, Matroid Theory, Dover Publications, 2009.
Neil White (ed.), Matroid Applications, Cambridge University Press, 1992.
Mathematical Applications
John A. Adam, Mathematics in Nature: Modeling Patterns in the Natural World
Alfred Aho, John E. Hopcroft, Jeffrey Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, 1974. [95]
John D. Barrow, 100 Essential Things You Didn't Know You Didn't Know About Sport
Dave Benson, Music: A Mathematical Offering, Cambridge University Press, 2006. [93] Review, Ebook
Kim Border, Fixed Point Theorems with Applications to Economics and Game Theory
Steven J. Brams, Game Theory and the Humanities: Bridging Two Worlds
Andrew M. Colman, Game Theory and Its Applications in the Social and Biological Sciences, Routledge Falmer, 1995. [69]
T. Cormen, C. Leiserson, R. Rivest and C. Stein, Introduction to Algorithms, MIT Press, 3rd edition, 2009. [192]
John Fauvel, Raymond Flood and Robin Wilson (eds.), Music
and Mathematics: From Pythagoras to Fractals
Norman Fenton and Martin Neil, Risk Assessment and Decision Analysis with Bayesian Networks, CRC Press 2012. Webpage
Richard P. Feynman, Robert B. Leighton and Matthew Sands, The Feynman Lectures on Physics: Definitive and Extended Edition
James Gleick, The Information: A History, a Theory, a Flood, Fourth Estate, 2011. Webpage
A.J. Jones, Game Theory: Mathematical Models of Conflict, Woodhead Publishing (new edition), 2000. [184]
Donald E. Knuth, The Art of Computer Programming: Vol 1-3, Addison-Wesley, 1999 (this edition). [87]
S. Brent Morris, Magic Tricks, Card Shuffling and Dynamic Computer Memories, Mathematical Association of America, 1998.
Martin A Nowak, Evolutionary Dynamics: Exploring the Equations of Life, Harvard University, 2006. Review
Roland Omnès, The Interpretation of Quantum Mechanics, Princeton University Press, 1994. Review
J.K. Percus, Mathematics of Genome Analysis, Cambridge University Press, 2002. Review
Orrin H. Pilkey and Linda Pilkey-Jarvis, Useless Arithmetic: Why Environmental Scientists Can't Predict the Future
Burkard Polster, The Mathematics of Juggling
William Poundstone, Gaming the Vote: Why Elections Aren't Fair (and What We Can Do about It)
Tom Siegfried, A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature
Simon Singh, The Code Book: The Secret History of Codes and Code-breaking
Ian Stewart, Mathematics Of Life: Unlocking the Secrets of Existence
George G. Szpiro, Numbers Rule: The Vexing Mathematics of Democracy, from Plato to the Present
R. Gregory Taylor, Models of Computation and Formal Languages, Oxford University Press Inc, USA, 1997. [105, 180]
Peter Woit, Not Even Wrong: The Failure of String Theory and the Continuing Challenge to Unify the Laws of Physics
David Wright, Mathematics and Music, American Mathematical Society, 2009. Review
Other bibliographies, bibliographic sources
Joseph Malkevitch's collection
Reviews by The Mathematical Association of America
