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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: the 'bookshelf' (by American Scientist); cut-the-knot; the European Mathematical Society; I Love Maths (by The Institute of Mathematics and its Applications); the Notices of the American Mathematical Society, (who also do a great round-up of reviews elsewhere), the Reviews site of the Mathematical Association of America; plus magazine. They will open in a new window. Mostly, the reviews are pdf files; 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
Women in 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

Andrei, A. Bolibruch, Yury S. Osipov and Yakov G. Sinai (eds.), Mathematical Events of the Twentieth Century, Springer 2005. Review

Barry Cipra, What's Happening in the Mathematical Sciences, vol. 1, American Mathematical Society, 1993.

Barry Cipra (ed. Paul Zorn), What's Happening in the Mathematical Sciences, vol. 2, American Mathematical Society, 1994.

——— , What's Happening in the Mathematical Sciences, vol. 3, Americal Mathematical Society, 1996.

——— , What's Happening in the Mathematical Sciences, vol 4, Americal Mathematical Society, 1999.

——— , What's Happening in the Mathematical Sciences, vol. 5, American Mathematical Society, 2002.

Pierre Colmez and J.P. Serre (eds.), Grothendieck-Serre Correspondence: Bilingual Edition, American Mathematical Society, 2004. Review

S. Barry Cooper and Jan van Leeuwen, Alan Turing: His Work and Impact, Elsevier, 2013. Review, Review, Review (4.6MB)

B. Jack Copeland (ed.), The Essential Turing, Oxford University Press, 2004. [186] Review

Michelle Feynmann (ed.), Perfectly Reasonable Deviations from the Beaten Track: The Letters of Richard P. Feynman, Basic Books, 2005. Review

Timothy Gowers (ed.), June Barrow-Green & Imre Leader (assoc. eds.), The Princeton Companion to Mathematics, Princeton University Press, 2008. Review, Review, Review, Review, Review

G.H. Hardy, P. V. Seshu Aiyar and B. M. Wilson (eds.), Collected Papers of Srinivasa Ramanujan, Chelsea Publishing Co./American Mathematical Society, 2000.

Eberhard Knobloch, Hikosaburo Komatsu and Dun Liu (eds.), Seki, Founder of Modern Mathematics in Japan: A Commemoration on His Tercentenary, Springer, 2013.

Gina Kolata, The New York Times Book of Mathematics: More Than 100 Years of Writing by the Numbers, Sterling, 2013. Review

Dana Mackenzie and Barry Cipra, What's Happening in the Mathematical Sciences, vol. 6, American Mathematical Society, 2006.

Dana Mackenzie, What's Happening in the Mathematical Sciences, vol. 7, American Mathematical Society, 2009.

——— , What's Happening in the Mathematical Sciences, vol. 8, American Mathematical Society, 2011. Review

——— , 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, European Mathematical Society, 2011. Review, Review

Mircea Pitici (ed.), The Best Writing on Mathematics 2010, Princeton University Press, 2010. Review, Review, Review

——— , The Best Writing on Mathematics 2011, Princeton University Press, 2011. Review, Review

——— , The Best Writing on Mathematics 2012, Princeton University Press, 2012. Review

——— , The Best Writing on Mathematics 2013, Princeton University Press, 2013. Review

——— , The Best Writing on Mathematics 2014, Princeton University Press, 2014.

Terence Tao, Structure and Randomness: Pages from Year One of a Mathematical Blog, American Mathematical Society, 2009. Review, Review

——— , Poincare's Legacies: Pages from Year Two of a Mathematical Blog Pt. 1, American Mathematical Society, 2009.

——— , Poincare's Legacies: Pages from Year Two of a Mathematical Blog Pt. 2, American Mathematical Society, 2009.

——— , 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, American Mathematical Society, 2011. Review

——— , Compactness and Contradiction, American Mathematical Society, 2013.

Stanisław Ulam, The Scottish Book, publ. by Los Alamos, N.M. : S. Ulam, 1957. Ebook

 

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Fiction

Arthur C. Clarke and Frederik Pohl, The Last Theorem, HarperVoyager, 2008. Review, Review, Review

Gary Ernest Davis, Coffee, Love and Matrix Algebra, Republic of Mathematics, 2014. Review, Review

Apostolos Doxiadis, Uncle Petros and Goldbach's Conjecture, Faber and Faber; new edition 2001. Review, Review, Review, Review

——— , C.H. Papadimitriou, A. Papadatos, A. Di Donna, Logicomix: An Epic Search for Truth, Bloomsbury, 2009. Review, Review

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, John Wiley & Sons,1999. Review

Denis Guedj, The Parrot's Theorem, Weidenfeld & Nicolson, 2000 (originally Le Théorème du Perroquet, Editions du Seuil, Paris, 1998). Review, Review

Matt Haig, The Humans, Canongate Books Ltd, 2013. Website, Review

Fred Hoyle, The Black Cloud, Penguin Classics edition, 2010.

Alex Kasman, Reality Conditions: Short Mathematical Fiction, Mathematical Association of America, 2005. Review

David Leavitt, The Indian Clerk, Bloomsbury, 2007. Review, Review

Guillermo Martinez, The Oxford Murders, Abacus, 2006 (originally Crímenes Imperceptibles, Premio Planeta Argentina, 2003). Review, Review, Review

Annabel Monaghan, A Girl Named Digit, Graphia Books, 2013. Review, Review

——— , Double Digit, Houghton Mifflin Books for Children, 2014. Review

Dora Musielak, Sophie's Diary: A Historical Fiction, AuthorHouse, 2004.

Yoko Ogawa, The Housekeeper and the Professor, Harvill Secker, 2009 (transl. from Japanese by Stephen Snyder). Review, Review

Chris Pearson, Proof of Death, published on Kindle via Amazon Media EU S.à r.l., 2012.

Philibert Schogt, The Wild Numbers, Four Walls Eight Windows, 2000. Review

Gaurav Suri and Hartosh Singh Bal , A Certain Ambiguity: A Mathematical Novel, Princeton University Press, 2010. Review, Review

Marta Sved, Journey into Geometries, The Mathematical Association of America, 1997. Review

Hiroshi Yuki (transl. Tony Gonzalez), Math Girls, Bento Books, Inc, 2011. Review

——— (transl. ———), Math Girls2: Fermat's Last Theorem, Bento Books, Inc, 2012. Review

 

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History of mathematics (including historical reprints)

Amir D. Aczel, The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity, Washington Square Press, paperback edition, 2001.

William J. Adams, The Life and Times of the Central Limit Theorem, 2nd edition , American Mathematical Society, 2010. [8] Review

Amir Alexander, Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, Oneworld Publications, 2014. Review, Review, Review

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

David R. Bellhouse, Abraham De Moivre: Setting the Stage for Classical Probability and Its Applications, A K Peters/CRC Press, 2011. Review, 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, John Wiley and Sons, New York, 1996. Review

Norman L. Biggs, E. Keith Lloyd and Robin J. Wilson, Graph Theory, 1736-1936, Clarendon Press, 1986. [50, 189] Review

William Burnside, Theory of Groups of Finite Order, Cambridge University Press, reprint edition, 2012.

Oliver Byrne, Byrne, Six Books of Euclid: Facsimile of the famous first edition of 1847, Taschen, 2010. Review

Florian Cajori, A History of Mathematical Notations, Dover Publications Inc. edition, 1994.

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, BiblioBazaar, 2008.

Stephen Chrisomalis, Numerical Notation: A Comparative History, Cambridge University Press, 2010. Review

Brian Clegg, Brief History of Infinity: The Quest to Think the Unthinkable, Robinson Publishing, 2003. Review

Roger Cooke, The Mathematics of Sonya Kovalevskaya, Springer, reprint edition, 2011. Review

B. Jack Copeland, Carl J. Posy and Oron Shagrir (eds.) Computability: Turing, Gödel, Church, and Beyond: Turing, Gödel, Church, and Beyond, MIT Press, 2013. Review

Alex D.D. Craik, Mr Hopkins' Men: Cambridge Reform and British Mathematics in the 19th Century, Springer, London 2007. Review

Alan Cromer, Uncommon Sense: The Heretical Nature of Science, Oxford University Press, 1995.

Michael J. Crowe, A History of Vector Analysis: The Evolution of the Idea of a Vectorial System, Dover 2003.

Christopher Cullen, Astronomy and Mathematics in Ancient China: The 'Zhou Bi Suan Jing', Oxford University Press, paperback edition, 2007.

Serafina Cuomo, Ancient Mathematics (Sciences of Antiquity), Routledge, 2001. [4, 44, 63]

Charles W. Curtis, Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer, American Mathematical Society, 2000. Review

Olivier Darrigol, Worlds of Flow: A history of hydrodynamics from the Bernoullis to Prandtl, Oxford Univ. Press 2005. Review

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, W. W. Norton, 2000. Review, Review

Abraham De Moivre (Helen M. Walker, ed.), The Doctrine of Chances: A Method of Calculating the Probabilities of Events in Play, Chelsea Publishing Co./American Mathematical Society; reprint edition, 2000.

John Derbyshire, Unknown Quantity: A Real and Imaginary History of Algebra, Plume Books, 2007. Review, Review

René Descartes, The Geometry of René Descartes, 1637, translated and annotated by David Eugene Smith and Marcia Latham in 1925, this edition Cosimo Classics, 2007. [154]

Keith Devlin, The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter That Made the World Modern, Basic Books, 2010. Review

——— , The Man of Numbers: Fibonacci's Arithmetic Revolution , Bloomsbury Paperbacks, 2012. Review, Review, Review, Review

Charles L. Dodgson, An Elementary Treatise On Determinants, 1867, reprinted Rough Draft Printing, 2007. [96]

William Dunham, Euler : The Master of Us All, The Mathematical Association of America, 1999. [206]

 ——— , The Calculus Gallery: Masterpieces from Newton to Lebesgue, Princeton University Press, 2008. Review

A.W.F. Edwards, Pascal's Arithmetical Triangle: The Story of a Mathematical Idea, Johns Hopkins University Press, 2002. [39] Review

Leonhard Euler (transl. Francis Horner, ed. John Hewlett), Elements of Algebra, Cambridge University Press reprint, 2012. Review (14.6MB), Ebook

 ——— (transl. John D. Blanton), Introduction to Analysis of the Infinite: Book One: Books 1 + 2 , Springer reprint edition, 1988. Review (14.7MB)

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, Oxford University Press, 1997. Review

———, Piero della Francesca: A Mathematician's Art, Yale University Press, 2005. Review (3.1MB)

Richard Fitzpatrick, Euclid's Elements of Geometry, publ. Richard Fitzpatrick, 2007. [149]

Raymond Flood and Robin Wilson, The Great Mathematicians, Arcturus Publishing, 2011. Review

Raymond Flood, Adrian Rice and Robin Wilson (eds.), Mathematics in Victorian Britain, Oxford University Press, 2011. Review

David Fowler, The Mathematics of Plato's Academy: A New Reconstruction, Clarendon Press, 2nd edition, 1999. Review

Enrique A. González-Velasco, Journey through Mathematics: Creative Episodes in Its History, Springer, 2011. Review, Review

Judith V. Grabiner, The Origins of Cauchy's Rigorous Calculus, Dover Publications edition, 2005. Review, Review

——— , A Historian Looks Back: The Calculus as Algebra and Selected Writings, Mathematical Association of America, 2010.

Ivor Grattan-Guinness, Routes of Learning: Highways, Pathways, and Byways in the History of Mathematics, The Johns Hopkins University Press, 2009. Review

Jeremy J. Gray, The Hilbert Challenge: A Perspective on Twentieth Century Mathematics, Oxford University Press, 2000. Review, Review

 ——— , Janos Bolyai, Non-Euclidean Geometry, and the Nature of Space, MIT Press, 2004. Review, Review

 ——— , Plato's Ghost: The Modernist Transformation of Mathematics, Princeton University Press, 2008. Review, Review, Review

Niccolò Guicciardini, Isaac Newton on Mathematical Certainty and Method, The MIT Press, 2009. Review

Anders Hald, A History of Probability and Statistics and Their Applications Before 1750, Wiley-Blackwell, 1990.

Thomas Hawkins, Emergence of the Theory of Lie Groups: An Essay in the History of Mathematics 1869-1926, Springer-Verlag, New York, 2000. Review

Arie Hinkis, Proofs of the Cantor-Bernstein Theorem: A Mathematical Excursion, Birkhäuser; 2013. Review

Lancelot Hogben, Mathematics for the Million: How to Master the Magic of Numbers", The Merlin Press Ltd, 4th revised edition, 1989.

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 , Bloomsbury Press, 2011. Review

Victor J Katz (ed), A History of Mathematics, Pearson Education, 3 edition, July 2008. Review (of 2004 Brief Edition).

 ——— , 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.

Wilbur Richard Knorr, The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry, Springer, paperback edition, 1980.

A.N. Kolmogorov and A.P. Yushkevich (eds.), Mathematics of the 19th Century: Vol. I, Birkhauser, 2nd edition 2001, also Vol II and Vol. III.

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, Springer, 1998. Review

Detlef Laugwitz (transl. Abe Shenitzer), Bernhard Riemann 1826-1866: Turning Points in the Conception of Mathematics, Birkhäuser, paperback edition 2010. Review, Review

Anthony Lo Bello, Origins of Mathematical Words: A Comprehensive Dictionary of Latin, Greek, and Arabic Roots, Johns Hopkins University Press, 2013. Review

Paolo Mancosu, Philosophy of Mathematics & Mathematical Practice in the Seventeenth Century, Oxford University Press, paperback edition, 1999. [208, 220] Review

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

Joseph Mazur, Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers, Princeton University Press, 2014. Review

Sharon Bertsch McGrayne, The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy, Yale University Press, 2012. Review

Elaine McKinnon Riehm and Frances Hoffman, Turbulent Times in Mathematics: The Life of J.C. Fields and the History of the Fields Medal, American Mathematical Society, 2011. Review, Review

Calvin C. Moore, Mathematics at Berkeley: A History, A K Peters, 2007. Review (10MB), Review

Steve Nadis and Shing-tung Yau, A History in Sum: 150 Years of Mathematics at Harvard (1825-1975), Harvard University Press, 2013. Review

Paul Nahin, An Imaginary Tale: The Story of √-1, Princeton University Press, 1998. Review, Review

——— , The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age, Princeton University Press, 2012. Review, Review, 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, Cambridge University Press, 2004. Review (1.8MB)

Peter M. Neumann, The Mathematical Writings of Evariste Galois, European Mathematical Society, 2011. Review, Review

Susan Oakes, Alan Pears and Adrian Rice (eds.), The Book of Presidents 1865 - 1965, London Mathematical Society 2005. Review, Review

Paul C. Pasles, Benjamin Franklin's Numbers: An Unsung Mathematical Odyssey, Princeton University Press, 2007. Review

Miodrag Petkovic, Famous Puzzles of Great Mathematicians, American Mathematical Society, 2009. Review

Kim Plofker, Mathematics in India: 500 BCE-1800 CE, Princeton University Press, 2008. Review

David Reimer, Count Like an Egyptian: A Hands-on Introduction to Ancient Mathematics, Princeton University Press, 2014. Review

David S. Richeson, Euler's Gem: The Polyhedron Formula and the Birth of Topology, Princeton University Press, 2008. Review, Review

Tony Robbin, Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought, Yale University Press, 2006. Review (2.4MB), Review, Review

Eleanor Robson and Jacqueline Stedall, The Oxford Handbook of the History of Mathematics, Oxford University Press, reprint edition, 2011. Review

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

C. Edward Sandifer, How Euler Did It, The Mathematical Association of America, 2007.

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

Sanford L. Segal, Mathematicians under the Nazis, Princeton University Press, 2003. Review, Review, Review, Review

Charles Seife, Zero: The Biography of a Dangerous Idea, Souvenir Press Ltd, new edition, 2000. Review, Review, Review, Review

Muriel Seltman and Robert Goulding (eds.), Thomas Harriot's Artis Analyticae Praxis: An English Translation with Commentary, Springer Verlag, 2007. Review

Wilfried Sieg, Hilbert's Programs and Beyond, Oxford University Press, 2013. Review

Jacqueline A. Stedall, A Discourse Concerning Algebra: English Algebra to 1685, Oxford University Press, 2002. Review, Review

——— , The Greate Invention of Algebra: Thomas Harriot's Treatise on Equations, Oxford University Press, 2003. Review

 ——— , The Arithmetic of Infinitesimals: John Wallis 1656, Springer, 2004. [137] Review

 ——— , Mathematics Emerging: A Sourcebook 1540 - 1900, Oxford University Press, 2008. Review, Review

 ——— , 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, Review

Ian Stewart, Seventeen Equations that Changed the World , Profile Books 2013. Review, Review, Review, Review, Review (2MB)

Stephen M. Stigler, The History of Statistics: The Measurement of Uncertainty Before 1900, Harvard University Press, 1990. Review (10MB)

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, The Johns Hopkins University Press, 2012. Review

Glen Van Brummelen, The Mathematics of the Heavens and the Earth: The Early History of Trigonometry, Princeton University Press, 2009. Review, Review

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, Oxford University Press, 2012.

——— , A Wealth of Numbers: An Anthology of 500 Years of Popular Mathematics Writing, Princeton University Press, 2012. [217]

Robin J. Wilson, Stamping Through Mathematics, Springer 2001. Review, Review

——— and John J. Watkins (eds.), Combinatorics: Ancient & Modern, OUP, 2013. Review, Review, Review

 

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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, Springer-Verlag, Berlin, 2000. Review

[Albert, Abraham Adrian] Nancy E. Albert, A3 & His Algebra: How a Boy from Chicago's West Side Became a Force in American Mathematics, iUniverse, Inc., 2005. Review

[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, Little, Brown and Company, 2000. Review

[Banach, Stefan] Emilia Jakimowicz and Adam Miranowicz (eds.), Stefan Banach: Remarkable Life, Brilliant Mathematics, American Mathematical Society, 3rd edition, 2011.

[ ——— ] Roman Kaluza (transl. A. Kostant and Wojbor A. Woyczynski), Through a Reporter's Eyes: The Life of Stefan Banach, Birkhauser, 2005.

[Bourbaki, Nicholas] Amir D. Aczel, The Artist and the Mathematician: The Story of Nicolas Bourbaki, the Genius Mathematician Who Never Existed..., High Stakes Publishing, 2007. Review, Review

[ ——— ] Maurice Mashaal, Bourbaki: A Secret Society of Mathematicians, American Mathematical Society, 2006. Review (3MB)

[Brouwer, LEJ] Dirk van Dalen, Mystic, Geometer, and Intuitionist: The Life of L. E. J. Brouwer, Vol. 1 - The Dawning Revolution, Clarendon Press, 1999. Review

[ ——— ] ———, Mystic, Geometer, and Intuitionist: The Life of L.E.J. Brouwer 1881-1966: Volume 2: Hope and Disillusion: Hope and Disillusion, Clarendon Press, 2005. Review

[ ——— ] ———, L.E.J. Brouwer - Topologist, Intuitionist, Philosopher: How Mathematics Is Rooted in Life, Springer, 2012. Review

[Georg Cantor] Amir D. Aczel, The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity, Washington Square Press, paperback edition, 2001.

[Carroll, Lewis = Dodgson, Charles] Robin J. Wilson, Lewis Carroll in Numberland: His Fantastical Mathematical Logical Life, Allen Lane, 2008. Review, Review, Review, Review

[Cauchy, Augustin-Louis] Bruno Belhoste, Augustin-Louis Cauchy: A Biography, Springer-Verlag, New York, 1991. Review (17MB)

[Cayley, Arthur] Tony Crilly, Arthur Cayley: Mathematician Laureate of the Victorian Age , John Hopkins University Press, 2006. Review, Review

[Clifford, William and Lucy] M. Chisholm, Such Silver Currents: The Story of William and Lucy Clifford, 1845-1929 , Lutterworth Press, 2002. Review, Review (2MB)

[Coxeter, Donald] Siobhan Roberts, King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry, Profile Books Ltd, 2007. Review, Review

[Dee, John] Benjamin Wooley, The Queen's Conjuror: The Science and Magic of Dr. Dee, Flamingo, new edition 2002. Review

[De Moivre, Abraham] David R. Bellhouse, Abraham De Moivre: Setting the Stage for Classical Probability and Its Applications, A K Peters/CRC Press, 2011. Review

[Descartes, René] Desmond Clarke, Descartes: A Biography, Cambridge University Press, March 2006. Review (5.5MB)

[Dirac, Paul] Graham Fermelo, The Strangest Man: The Life of Paul Dirac, Faber and Faber, 2010. Review

[ ——— ] Abraham Pais, Maurice Jacob, David I. Olive and Michael F. Atiyah, Paul Dirac: The Man and his Work, Cambridge University Press, 1998. Review

[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, Review, Review

[ ——— ] Bruce Schechter, My Brain is Open: The Mathematical Journeys of Paul Erdős, Touchstone, 2000. Review

[Fermat, Pierre de] Mahoney, The Mathematical Career of Pierre de Fermat, 1601-1665, Princeton University Press, 2nd edition, 1994.

[Fibonacci = Leonardo Pisano] Keith Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution , Bloomsbury Paperbacks, 2012. Review, Review, Review, Review

[Fields, John Charles] Elaine McKinnon Riehm and Frances Hoffman, Turbulent Times in Mathematics: The Life of J.C. Fields and the History of the Fields Medal, American Mathematical Society, 2011. Review, Review

[Gardner, Martin] Martin Gardner, Undiluted Hocus-Pocus: The Autobiography of Martin Gardner, Princeton University Press, 2013. Review, Review, Review

[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, A K Peters, 1997. Review

[Green, George] D. M. Cannell, George Green: Mathematician and Physicist 1793-1841: The Background to His Life and Work, Society for Industrial and Applied Mathematics; 2nd revised edition, 1987. Review (13MB)

[Hadamard, Jacques] Vladimir Maz'ya and Tatyana Shaposhnikova (transl. P. Basarab-Horwath), Jacques Hadamard, A Universal Mathematician, American Mathematical Society, 2000. Review

[Halmos, Paul Richard] Paul R. Halmos, I Want to Be a Mathematician: An Automathography, Springer, New York, 1985. Obituary

[Hypatia of Alexandria] Michael A. B. Deakin, Hypatia of Alexandria: Mathematician and Martyr, Prometheus Books, 2007. Review

[Kac, Mark] Mark Kac, Enigmas of Chance: An Autobiography, University of California Press, reprint edition, July 1992. Review

[Kelvin, Lord = Thomsom, William] Raymond Flood, Mark McCartney and Andrew Whitaker, Kelvin: Life, Labours and Legacy, Oxford University Press, 2008. Review

[ ——— ] 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. Review

[ ——— ] Joan Spicci, Beyond the Limit: The Dream of Sofya Kovalevskaya, Forge Books, 2002. Review

[Lagrange, Joseph Louis] Irina Alexandrovna Tyulina, Joseph Louis Lagrange 1736 - 1813, Knizhnyy dom "LIBROKOM", 2010. In Russian.

Leonardo of Pisa: see Fibonacci

[Lie, Sophus] Arild Stubhaug (translated R. Daly), The Mathematician Sophus Lie: It was the Audacity of My Thinking, Springer, paperback edition 2010. Review

[Liouville, Joseph] Jesper Lützen, Joseph Liouville 1809-1882: Master of Pure and Applied Mathematics, Springer, 1990. Review (17.5MB)

[Mac Lane, Saunders] Saunders Mac Lane, Saunders Mac Lane: A Mathematical Autobiography, A K Peters, Ltd., May 25, 2005. Review

[Mandelbrot, Benoit] Benoit B. Mandelbrot, The Fractalist: Memoir of a Scientific Maverick, Pantheon Books, 2012. Review, Review, Review

[Maxwell, James Clerk] Basil Mahon, The Man Who Changed Everything: The Life of James Clerk Maxwell, John Wiley & Sons, 2004. Review

[ ——— ] Raymond Flood Mark McCartney and Andrew Whitaker (eds.), James Clerk Maxwell: Perspectives on his Life and Work, Oxford University Press, 2014. Review, Review

[Milne, Edward Arthur] Meg Weston Smith, Beating the Odds: The Life and Times of E. A. Milne, World Scientific, 2013. Review

[Mosteller, Charles Frederick] Frederick Mosteller, The Pleasures of Statistics: The Autobiography of Frederick Mosteller, Springer, 2010. Review

[Napier, John] Julian Havil, John Napier: Life, Logarithms, and Legacy, Princeton University Press, 2014.

[Newton, Isaac] James Gleick, Isaac Newton, Pantheon Books, 2003. Review

[Noether, Amelie ('Emmy')] Auguste Dick (transl. H. I. Blocher), Emmy Noether 1882-1935, Birkhäuser Boston Inc., Cambridge, Mass., 1981. Review

[ ——— ] M.B.W. Tent, Emmy Noether: The Mother of Modern Algebra, A.K. Peters 2008. Review, Review

[Norton, Simon] Alexander Masters, The Genius in my Basement, Forth Estate, 2011. Review, Review

Pisano, Leonardo: see Fibonacci

[Poincaré, Henri] Jeremy Gray, Henri Poincaré: A Scientific Biography, Princeton University Press, 2012. Review, Review

[ ——— ] Ferdinand Verhulst, Henri Poincaré: Impatient Genius, Springer, 2012. Review, Review

[Ramanujan, Srivivasa] Robert Kanigel, The Man Who Knew Infinity: a Life of the Genius Ramanujan, Abacus, new edition 1992. Review

[Riemann, Bernhard] Detlef Laugwitz (transl. Abe Shenitzer), Bernhard Riemann 1826–1866: Turning Points in the Conception of Mathematics, Birkhauser, 2nd printing, 2008.

[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, AMS, 2000. Review, Review

[Sylvester, James Joseph] Karen H. Parshall, James Joseph Sylvester: Jewish Mathematician in a Victorian World, The Johns Hopkins University Press, 2006. [142] Review, Review, Review

[Tarski, Alfred] Anita Burdman Feferman and Solomon Feferman, Alfred Tarski: Life and Logic, Cambridge University Press, 2004. Review, Review

Thomson, William: see Kelvin, Lord.

[Turing, Alan Mathison] B. Jack Copeland, Turing: Pioneer of the Information Age, Oxford University Press, 2012. Review, Review, Review

[ ——— ] Andrew Hodges, Alan Turing: The Enigma, centenary edition, Princeton University Press, 2012. Review, Review

[ ——— ] David Leavitt, The Man Who Knew Too Much: Alan Turing and the Invention of the Computer, W. W. Norton 2005. Review, Review

[ ——— ]Sara Turing, Alan M. Turing, Cambridge University Press, centenary edition, 2012. 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, Basic Books, 2005. Review

[ ——— ] 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, Springer, Berlin, 2007. Review

 

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The profession of mathematics

Amir D. Aczel, A Strange Wilderness: The Lives of the Great Mathematicians, Sterling, 2011. Review

Donald J. Albers and Gerald L. Alexanderson, Mathematical People: Profiles and Interviews, A.K. Peters, 2008. Review, Review, Review

 ——— and  ———, Fascinating Mathematical People: Interviews and Memoirs, Princeton University Press, 2011. Review, Review

Lara Alcock, How to Study for a Mathematics Degree, Oxford University Press, 2012. Review

Charles Babbage, Passages from the Life of a Philosopher, Cambridge University Press, reissue edition, 2011. Ebook

Larry Baggett, In the Dark on the Sunny Side: A Memoir of an Out-of-Sight Mathematician, The Mathematical Association of America, 2012. Review, Review, Review

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, American Mathematical Society, 2010. Review, Review, Review

Peter Borwein, Peter Liljedahl and Helen Zhai (eds.), Mathematicians on Creativity, Mathematical Association of America, 2014.

Mariana Cook, Mathematicians: An Outer View of the Inner World, Princeton University Press, 2009. Review, Review, Review

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, A K Peters, 2000. Review

——— , Reuben Hersch and Elena Anne Marchisotto, The Mathematical Experience, Study Edition, Birkhäuser, 2011.

Underwood Dudley, Mathematical Cranks, The Mathematical Association of America, 1996.

——— , The Trisectors, The Mathematical Association of America, 1996. Review

Raymond Flood and Robin Wilson, The Great Mathematicians, Arcturus Publishing, 2011. Review

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] Website, Ebook

Reuben Hersh and Vera John-Steiner, Loving and Hating Mathematics: Challenging the Myths of Mathematical Life, Princeton University Press, 2010. Review, Review

Nicolas Higham, Handbook of Writing for the Mathematical Sciences, Society for Industrial and Applied Mathematics; 2 edition, 1998.

Ioan James, Remarkable Mathematicians: From Euler to von Neumann, Cambridge University Press, 2003. Review, Review

Boris Khesin and Serge L. Tabachnikov (eds.), Arnold: Swimming Against the Tide, American Mathematical Society, 2014. Review

Donald E. Knuth, Tracy Larrabee and Paul M. Roberts, Mathematical Writing, The Mathematical Association of America, 1996. Review

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, 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, Springer, 2011. Review

Leslie Lamport, LATEX: a Document Preparation System : User's Guide and Reference Manual, LATEX 2E edition, Addison Wesley, 1994.

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, and Vol 2, Seymour (Dale) Publications, 1998. Review

Gian-Carlo Rota (Fabrizio Palombi, ed.), Indiscrete Thoughts (Modern Birkhäuser Classics), Birkhäuser, Boston, 1997. Review

David Ruelle, The Mathematician's Brain, Princeton University Press, 2007. Review, Review, Review

Leila Schneps, Alexandre Grothendieck: A Mathematical Portrait, International Press of Boston Inc, bilingual edition, 2014.

Joel Segel (editor), Recountings: Conversations with MIT Mathematicians, A K Peters/CRC Press, 2009. Review

Ian Stewart, Letters to a Young Mathematician, Basic Books, US, 2006. Review, Review, Review, Review, Review

Steven Strogatz, The Calculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Math, Princeton University Press, paperback edition, 2011. Review, Review, Review

Cédric Villani, Théorème Vivant, (in French), Librairie generale francaise, 2013. Review, Review

Charles Wells, A Handbook of Mathematical Discourse, Infinity Publishing, 2003. Review

Norbert Wiener, Ex-Prodigy. My Childhood and Youth, Simon and Schuster, New York, 1953.

Norbert Wiener, I Am a Mathematician, Victor Gollanz, London, 1956.

Robin V. Young (ed.), Notable Mathematicians from Ancient Times to the Present, Gale, 1998.

 

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Women in mathematics
Biographies of women mathematicians are listed with the other biographies. It is worth mentioning that the MAA Reviews catalogue has Women in Mathematics as a search category and appears to be very comprehensive. More links for Women in Mathematics here.

Bettye Anne Case and Anne M. Leggett (eds.), Complexities: Women in Mathematics, Princeton University Press, 2005. Review, Review

Stephen Ceci and Wendy Williams, The Mathematics of Sex: How Biology and Society Conspire to Limit Talented Women and Girls, Oxford University Press, 2009.

Roger Cooke, The Mathematics of Sonya Kovalevskaya, Springer, reprint edition, 2011. Review

Judy Green, Pioneering Women in American Mathematics: The Pre-1940 PhD's, American Mathematical Society/London Mathematical Society, 2009. Review

Louise S. Grinstein and Paul J. Campbell, Women of Mathematics: A Biobibliographic Sourcebook, Greenwood Press, 1987.

Claudia Henrion, Women in Mathematics: The Addition of Difference, Indiana University Press, 1997. Review, Review

Claire G. Jones, Femininity, Mathematics and Science 1880-1914, Palgrave Macmillan, 2009. Review

Patricia Clark Kenschaft, Change is Possible: Stories of Women and Minorities in Mathematics (amsns AMS non-series title) , American Mathematical Society, 2005. Review

Danica McKellar, Maths Doesn't Suck: How to survive year 6 through year 9 maths without losing your mind or breaking a nail, Particular Books, 2008. Review, Review

——— , Kiss My Math: Showing Pre-Algebra Who's Boss, New American Library, 2009. Review, Review

——— , Hot X: Algebra Exposed!, Plume, paperback edition, 2010. Review, Review

——— , Girls Get Curves: Geometry Takes Shape, Plume Books, 2012. Review

Annabel Monaghan, A Girl Named Digit, Graphia Books, 2013. Review, Review

Charlene Morrow and Teri Perl (eds.), Notable Women in Mathematics: A Biographical Dictionary, Greenwood Press, 1998. Review

Margaret A. M. Murray, Women Becoming Mathematicians: Creating a Professional Identity in Post-world War II America, MIT Press, 2000. Review

Deborah Nolan (ed.), Women in Mathematics: Scaling the Heights, Mathematical Association of America, 1997. Review

Laura Micheletti Puaca, Searching for Scientific Womanpower: Technocratic Feminism and the Politics of National Security, 1940-1980, The University of North Carolina Press, 2014. Review

Hiroshi Yuki (transl. Tony Gonzalez), Math Girls, Bento Books, Inc, 2011. Review

——— (transl. ———), Math Girls2: Fermat's Last Theorem, Bento Books, Inc, 2012. Review

Valerie Walkerdine, Counting Girls Out: Girls and Mathematics, Routledge, 2nd edition, 1998.

 

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Psychology, Sociology, Philosophy

Robyn Arianrhod, Einstein's Heroes: Imagining the World Through the Language of Mathematics, Icon Books, 2004. Review

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, Springer, 2012

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, Macmillian 1999. Review, Review

Gregory Chaitin, Exploring Randomness, Springer-Verlag, 2000. Review

Jean-Pierre Changeux and Alain Connes, Conversations on Mind, Matter, and Mathematics, Princeton University Press, 1998. Transl. by Malcolm DeBevoise.

Michael Suk-Young Chwe, Jane Austen, Game Theorist, Princeton University Press, 2013. Review, Review, Review (Rebuttal)

B. Jack Copeland, Carl J. Posy and Oron Shagrir (eds.) Computability: Turing, Gödel, Church, and Beyond: Turing, Gödel, Church, and Beyond, MIT Press, 2013.

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 , Oxford University Press, 2010. Review

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, Phoenix, new edition 2001. Review, Review, Review

A. K. Dewdney, A Mathematical Mystery Tour: Discovering the Truth and Beauty of the Cosmos, John Wiley & Sons, 1999. Review

Apostolos Doxiadis and Barry Mazur, Circles Disturbed: The Interplay of Mathematics and Narrative, Princeton University Press, 2012. Review, Review, Review

Michael Fitzgerald and Ioan James, The Mind of the Mathematician, The Johns Hopkins University Press, 2007. Review

Bonnie Gold and Roger A. Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy, Mathematical Association of America, 2008. Review

Jacques Hadamard, The Mathematician's Mind: The Psychology of Invention in the Mathematical Field, Princeton University Press; Reprint edition, 1996. Review

Reuben Hersh, What is Mathematics, Really?, Oxford University Press, 1999. Review, Review

——— , 18 Unconventional Essays on the Nature of Mathematics, Springer; 2005.

 ——— , Experiencing Mathematics: What Do We Do, When We Do Mathematics?, American Mathematical Society, 2014. Review, Review

John Horgan, The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age, Helix Books, 1996. Review

Imre Lakatos, Proofs and Refutations: The Logic of Mathematical Discovery, edited by Worrall and Zahar, Cambridge University Press, 1976. [26] Review

George Lakoff and Rafael E. Núñez, Where Mathematics Comes from: How the Embodied Mind Brings Mathematics into Being, Basic Books, 2000. Review, Review

Mario Livio, Is God a Mathematician?, Simon & Schuster 2009. Review, Review

Paolo Mancosu, The Philosophy of Mathematical Practice, Oxford University Press, paperback edition, 2012. Review

Roland Omnès, Converging Realities: Toward a Common Philosophy of Physics and Mathematics, Princeton University Press, 2004. Review

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

Alan Sokal and Jean Bricmont, Intellectual Impostures, Profile Books, paperback edition 2003. Review

Vladimir Tasić, Mathematics and the Roots of Postmodern Thought, Oxford University Press, 2001. Review

 

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Mathematical mountains: popular accounts of landmark problems/solutions

Amir D. Aczel, Fermat's Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem, paperback edition, Thunder's Mouth Press, 2007. Review

J. Carlson, A. Jaffe, and A. Wiles (eds.), The Millennium Prize Problems, American Mathematical Society, 2006. Ebook, 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, Basic Books, 2002. Review, Review

Underwood Dudley, The Trisectors, 2nd edition, Mathematical Association of America, 1996.

Lance Fortnow, The Golden Ticket: P, NP, and the Search for the Impossible, Princeton University Press, 2013. Review, Review, Review, Review

Mario Livio, The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry, Souvenir Press Ltd, new edition, 2007. Review, Review

Piergiorgio Odifreddi, The Mathematical Century: The 30 Greatest Problems of the Last 100 Years, transl. Arturo Sangalli, Princeton University Press, (new edition) 2006. Review

Donal O’Shea, The Poincaré Conjecture: In Search of the Shape of the Universe , Walker, 2007. Review (2.8MB), Review

Peter Pesic, Abel's Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability, MIT Press, 2003. Review

Dan Rockmore, Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers, Vintage Books USA, 2006. Review, Review, Review

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, Atlantic Books, new edition, 2003. Review

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, Harper, 2008. Review

Simon Singh, Fermat's Last Theorem, HarperPerennial, 2007 reissue. [9] Review, Review, Review

Ian Stewart, The Great Mathematical Problems, Profile Books, 2013. Review, 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 , Dutton/Signet, 2007. Review (2.8MB)

Robin Wilson, Four Colors Suffice: How the Map Problem Was Solved (Revised Color Edition), Princeton University Press, 2013. [1] Review, Review, Review

Benjamin H. Yandell, The Honors Class: Hilbert's Problems and Their Solvers, AK Peters, 2001. Review, Review

 

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Introductions to mathematical topics accessible for non-professionals

David Acheson, 1089 and All That - A Journey into Mathematics, Oxford University Press, 2002. Review, Review, Review, Review

Amir D. Aczel, Descartes' Secret Notebook: A True Tale of Mathematics, Mysticism, and the Quest to Understand the Universe, Broadway Books, paperback edition, Jan 2007.

Colin Adams, The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots, American Mathematical Society, 2004. [166] Review

———, Zombies and Calculus, Princeton University Press, 2014. Review, Review, Review

Claudi Alsina and Roger B. Nelsen, Icons of Mathematics: An Exploration of Twenty Key Images, Mathematical Association of America, 2011. Review

 ——— and  ———, Charming Proofs: A Journey into Elegant Mathematics, Mathematical Association of America, 2011. Review

Avner Ash and Robert Gross, Fearless Symmetry: Exposing the Hidden Patterns of Numbers, Princeton University Press, 2006. [34, 41, 51] Review, Review, Review

 ——— and ———, Elliptic Tales: Curves, Counting, and Number Theory, Princeton University Press, 2012. Review

Tomaso Aste and Denis Weaire, The Pursuit of Perfect Packing, Second Edition, CRC Press, 2008.

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, Review

Alex Bellos, Alex's Adventures in Numberland, Bloomsbury Publishing, paperback edition, 2011. Review, Review, Review

 ———, Alex Through the Looking-Glass: How Life Reflects Numbers and Numbers Reflect Life, Bloomsbury Publishing, 2014. Review

Ehrhard Behrends (transl. D. Kramer), Five-Minute Mathematics, American Mathematical Society, 2008.

Arthur T. Benjamin and Ezra Brown (eds.), Biscuits of Number Theory, The Mathematical Association of America , 2009. Review

Alexandre V. Borovik, Mathematics Under the Microscope: Notes on Cognitive Aspects of Mathematical Practice, American Mathematical Society, 2010. Review, Review, Review

John Bryant and Chris Sangwin, How Round Is Your Circle?: Where Engineering and Mathematics Meet, Princeton University Press, 2011. Webpage, Review, Review, Review

Edward B. Burger and Michael Starbird, The Heart of Mathematics: An Invitation to Effective Thinking, Key College Publishing; 2nd revised edition, 2004.

——— and  ———, Coincidences, Chaos and All That Math Jazz, W W Norton, 2005. Review

Chris Caldwell and G. L. Honaker, Jr., Prime Curios, BookSurge, 2009. Review

Tina Cardone and MTBoS, Nix the Tricks: A guide to avoiding shortcuts that cut out math concept development, CreateSpace Independent Publishing Platform, 2013. Ebook, Review

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

Tim Chartier, Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing, Princeton University Press, 2014. Review, Review, Review

John H. Conway, The Book of Numbers, Copernicus, 1996. [222]

——— and Derek A. Smith, On Quaternions and Octonions, A K Peters, 2003. [61] Review

 ——— , Heidi Burgiel and Chaim Goodman-Strauss, The Symmetries of Things, A.K. Peters, 2008. [160]. Review, Review

William J. Cook, In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation, Princeton University Press, 2012. Review, Review, 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

Heinrich Dörrie (transl. D. Antin), One Hundred Great Problems of Elementary Mathematics: Their History and Solution, Dover, reprint edition, 1965.

Underwood Dudley, Mathematical Cranks, The Mathematical Association of America, 1996.

——— , The Trisectors, The Mathematical Association of America, 1996. Review

——— , Is Mathematics Inevitable?, The Mathematical Association of America, 2008. Webpage, Review

William Dunham, Journey Through Genius: Great Theorems of Mathematics, John Wiley & Sons, 1990. [76]

 ——— (ed.), The Genius of Euler: Reflections on His Life and Work, The Mathematical Association of America, 2007. [134, 210] Review, Review

Rob Eastaway and Jeremy Wyndham, Why Do Buses Come in Threes?: The Hidden Maths of Everyday Life, Robson Books Ltd, paperback edition, 2005.

Rob Eastaway and John Haigh , The Hidden Mathematics of Sport, Portico, 2011. Review, Review

Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking, Penguin Press, 2014. Review, Review, Review, Review, Review

Richard Elwes, How to Build a Brain: And 34 Other Really Interesting Uses of Mathematics, Quercus Publishing Plc, 2011. Review

Hans Magnus Enzensberger (transl. Michael Henry Heim), The Number Devil: A Mathematical Adventure, Granta Books, 2008.

Martin Erikson, Beautiful Mathematics, Mathematical Association of America, 2011. Review, Review

Steven Finch, Mathematical Constants, Cambridge University Press, 2003. [144] Review, Webpage

Paulus Gerdes, Geometry from Africa. Mathematical and educational explorations, The Mathematical Association of America, 1999. Review

Rebecca Goldstein, Incompleteness: The Proof and Paradox of Kurt Gödel, W. W. Norton & Company, 2005. Review, Review, Review

David J. Hand, The Improbability Principle: Why coincidences, miracles and rare events happen all the time, Bantam Press, 2014. Website, Review, 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, Princeton University Press, 2012. Review, Review, Review

Diane L. Herrmann and Paul J. Sally Jr, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory, CRC Press, 2013. Review

Dick Hess, Golf on the Moon: Entertaining Mathematical Paradoxes and Puzzles, Dover Publications, 2014. Review

Peter M. Higgins, Number Story: From Counting to Cryptography, Springer, 2008. Review

 ———, Nets, Puzzles, and Postmen: An exploration of mathematical connections, Oxford University Press, 2009. Review

 ———, Numbers: A Very Short Introduction, Oxford University Press, 2011. Review, 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, Cambridge University Press, 2010. Review, Review

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, Dover Publications, 1970. [165]

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, Cambridge University Press, 1997. Review

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.

——— and Kenneth W. Regan, People, Problems, and Proofs: Essays from Godel's Lost Letter: 2010, Springer, 2013.

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, Princeton University Press, 2012. Review (2MB), Review, Review

Eli Maor, "e", The Story of a Number, Princeton University Press, 1998 edition. [136]

 ———, Trigonometric Delights, Princeton University Press, paperback edition, 2002. [152] Review

 ——— and Eugen Jost, Beautiful Geometry, Princeton University Press, 2014. Review

Barry Mazur, Imagining Numbers: (Particularly the Square Root of Minus Fifteen), Farrar, Straus and Giroux, 2003. Review

Danica McKellar, Maths Doesn't Suck: How to survive year 6 through year 9 maths without losing your mind or breaking a nail, Particular Books, 2008. Review, Review

——— , Kiss My Math: Showing Pre-Algebra Who's Boss, New American Library, 2009. Review, Review

——— , Hot X: Algebra Exposed!, Plume, paperback edition, 2010. Review, Review

——— , Girls Get Curves: Geometry Takes Shape, Plume Books, 2012. Review

T.S. Michael, How to Guard an Art Gallery and Other Discrete Mathematical Adventures, The Johns Hopkins University Press, 2009. Review

Melanie Mitchell, Complexity: A Guided Tour, Oxford University Press, 2009. Review

David Mumford, Caroline Series, David Wright, Indra's Pearls: The Vision of Felix Klein, Cambridge University Press, New York, 2002. Review

Paul J. Nahin, Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills, Princeton University Press, 2006. [36] Review, Review, Review

Jennifer Ouellette, The Calculus Diaries, Gerald Duckworth & Co. Ltd., 2013. Review

Sam Parc (ed.), 50 Visions of Mathematics, Oxford University Press, 2014. Review

Matt Parker, Things to Make and Do in the Fourth Dimension, Particular Books, 2014.

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, Penguin, 2004.

Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe, Vintage, 2005. [37, 121] Review

Cliff Pickover, The Mobius Strip: Dr. August Mobius's Marvelous Band in Mathematics, Games, Literature, Art, Technology, and Cosmology, Basic Books, 2007.

 ———, The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, Sterling, 2009.

 ———, The Mathematics Devotional, Sterling, 2014.

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, Prometheus, 2004.

 ———, The Fabulous Fibonacci Numbers, Prometheus, 2007.

Alfred S. Posamentier, The Pythagorean Theorem: The Story of Its Power and Beauty, Prometheus, 2010.

William Poundstone, Prisoner's Dilemma: John Von Neumann, Game Theory and the Puzzle of the Bomb, Anchor Booksn 1993. Review

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, Springer-Verlag, 1999. Review

 ———, The Little Book of Bigger Primes, 2nd edition, Springer-Verlag, 2004. [211]

David S. Richeson, Euler's Gem: The Polyhedron Formula and the Birth of Topology, Princeton University Press, 2008. Review, Review

Anne Rooney, 50 Amazing Things Kids Need to Know About Mathematics, Quercus Publishing Plc, 2011. Review

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.

Sam L. Savage, The Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty, John Wiley & Sons, paperback edition, 2012. Review

Richard E. Schwartz, You Can Count on Monsters: The First 100 Numbers and Their Characters, A K Peters/CRC Press, 2010. Review

———, Really Big Numbers, American Mathematical Society, 2014. Review, Review, Review

Simon Singh, The Simpsons and Their Mathematical Secrets, Bloomsbury Publishing, 2013. Webpage, Review, Review

Raymond Smullyan, To Mock a Mockingbird: and Other Logic Puzzles, Oxford Paperback edition, 2000. Webpage

———, What is the Name of This Book?: The Riddle of Dracula and Other Logical Puzzles, Dover Publications Inc., unabridged edition, 2011.

Adam Spencer, Adam Spencer's Book of Numbers: A Bizarre and Hilarious Journey from 1 to 100, Four Walls Eight Windows, 2004. Review

Sherman Stein, How the Other Half Thinks: Adventures in Mathematical Reasoning, McGraw-Hill, 2001. Review

Hugo Steinhaus, One Hundred Problems in Elementary Mathematics, Dover Publications, 1990.

———, 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

——— , Symmetry: A Very Short Introduction, Oxford University Press, 2013.

John Stillwell, Roads to Infinity: The Mathematics of Truth and Proof, AK Peters, 2010. Review, Review

Steven Strogatz, The Joy of X: A Guided Tour of Math, from One to Infinity, Eamon Dolan/Houghton Mifflin Harcourt, 2012. Review, Review, Review

Marta Sved, Journey into Geometries, The Mathematical Association of America, 1997. Review

Terence Tao, Solving Mathematical Problems: A Personal Perspective, Oxford University Press, 2nd edition 2006. Review, Review

Max Tegmark, Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, Allen Lane, 2014. Review, Review, Review

Rachel Thomas and Marianne Freiberger, Numericon: A Journey through the Hidden Lives of Numbers, Quercus Publishing Plc.

Glen Van Brummelen, Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry, Princeton University Press, 2012. [37, 225] Review, Review

Cédric Villani, Théorème Vivant, (in French), Librairie generale francaise, 2013. 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, A K Peters, 232 pp, 2005. Review, Review, Review, Review

Matthew Watkins, The Mystery of the Prime Numbers: Secrets of Creation v. 1, The Inamorata Press, 2010. Review

——— , The Enigma of the Spiral Waves: Secrets of Creation v. 2, The Inamorata Press, 2011.

David Wells, You Are a Mathematician, Penguin, London, 1995.

 ——— , Prime Numbers: The Most Mysterious Figures in Math, John Wiley & Sons Inc, 1995. [21]

Michael Willers, The Joy of X: How Algebra Shapes Your Daily Life, Chambers, 2009.

Robert, M. Young, Excursions in Calculus: An Interplay of the Continuous and the Discrete, Mathematical Association of America, 1996. [170]

Günter M. Ziegler, Do I Count: Stories from Mathematics, CRC Press, 2013. Review

 

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More specialised introductions to mathematical topics

Colin Adams, Joel Hass and Abigail Thompson, How to Ace Calculus: The Streetwise Guide, W.H.Freeman & Co Ltd, 1998. Review

 ———, ——— and  ———, How to Ace the Rest of Calculus: The Streetwise Guide, W.H.Freeman & Co Ltd, 2001. Review

Martin Aigner, A Course in Enumeration, Springer 2007. [171] Review

——— , Markov's Theorem and 100 Years of the Uniqueness Conjecture: A Mathematical Journey from Irrational Numbers to Perfect Matchings, Springer 2013. Review

——— and Günter M. Ziegler, Proofs from THE BOOK, Springer-Verlag Berlin, 5th Edition, 2014. [94, 163] Website, Review, Review, Review

Joan Aldous and Robin J. Wilson, Graphs and Applications: An Introductory Approach, Springer-Verlag London Ltd, 2003. [117]

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, 228]

Titu Andreescu and Dorin Andrica, Complex Numbers from A to ...Z, Birkhauser Boston, 2005. [56] Review, Review

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 Applebaum, Limits, Limits Everywhere: The Tools of Mathematical Analysis, Oxford University Press, 2012. Review, Review

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 , Springer, 2000.

Steve Awodey, Category Theory, Oxford University Press, 2nd edition, 2010. Review, Review

A.F. Beardon, Algebra and Geometry, Cambridge University Press, 2005. 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

Jörg Bewersdorff (transl. D. Kramer), Galois Theory for Beginners: A Historical Perspective, American Mathematical Society, 2006. Review, 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, Second Edition, Chapman and Hall/CRC, 2012. [143] Review

J.A. Bondy and U.S.R. Murty, Graph Theory, Springer, 2008. [150, 155, 190] Webpage, Review, Review (of 1st edition)

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, 217] Review

——— , A Radical Approach to Lebesgue's Theory of Integration, Cambridge University Press, 2008. [2] Review

Edward B. Burger, Exploring the Number Jungle: A Journey into Diophantine Analysis, American Mathematical Society, 2000. Review

——— and Robert Tubbs, Making Transcendence Transparent: An Intuitive Approach to Classical Transcendental Number Theory, Springer, 2004. [167] Review

David M. Burton, Elementary Number Theory 7th edition, McGraw-Hill, 2010. [128] Review

Peter Cameron, Combinatorics: Topics, Techniques, Algorithms, Cambridge University Press, 1994. [19, 38, 182]

———, Introduction to Algebra, 2nd edition, Oxford University Press, 2007. [49] Review

———, Sets, Logic and Categories, Springer, 1999. [196]

Gary Chartrand, Linda Lesniak and Ping Zhang, Graphs & Digraphs, Fifth Edition, Chapman and Hall/CRC, 2010. [24] Review

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, Princeton University Press, 2011. [198]

Reinhard Diestel, Graph Theory 4th edition, Springer New York, 2010. [52, 60, 70] Review

Underwood Dudley, Elementary Number Theory, Dover, 2nd edition reprint, 2008.

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, Gödel's Theorem: An Incomplete Guide to Its Use and Abuse, A.K. Peters, 2005. Review, Review, Review

Dmitry Fuchs and Serge Tabachnikov, Mathematical Omnibus: Thirty Lectures on Classic Mathematics, American Mathematical Society, 2007. [213] Review

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]

Thomas A. Garrity, All the Mathematics You Missed: But Need to Know for Graduate School, Cambridge University Press, 2001. Review

Jay Goldman, The Queen of Mathematics: A Historically Motivated Guide to Number Theory, A K Peters/CRC Press, 1997. [207] Review

Gary Gordon and Jennifer MacNulty, Matroids: A Geometric Introduction, Cambridge University Press, 2012

Ronald Graham, Donald Knuth and Oren Patashnik, Concrete Mathematics: Foundation for Computer Science, Addison Wesley, 2nd ed., 1994. Ebook

Jack E. Graver, Counting on Frameworks: Mathematics to Aid the Design of Rigid Structures, The Mathematical Association of America, 2001. [140] Review, Review

Geoffrey Grimmett and David Stirzaker, Probability and Random Processes, Oxford University Press, 3rd edition, 2001.

Liang-shin Hahn, Complex Numbers and Geometry, Mathematical Association of America, 1994.

Ernst Hairer and Gerhard Wanner, Analysis by its History, Springer, 1996. [219]

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. [48]

G.H. Hardy, Divergent Series, AMS Chelsea reprint, 2013. Review

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, OUP, 6th edition, 2008. [226]

Michael Henle, A Combinatorial Introduction to Topology, Dover Publications, 1994. [16]

I.N. Herstein, Topics In Algebra, John Wiley & Sons, 2nd edition, 1975. [215]

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, Cambridge University Press, 2009.

Stephen A. Huggett and David Jordan, A Topological Aperitif, 2nd edition, Springer-Verlag, London, 2009. [67] Review

Andrew McInerney, First Steps in Differential Geometry: Riemannian, Contact, Symplectic, Springer, 2013. Review

Harold Jeffreys and Bertha Jeffreys, Methods of Mathematical Physics, Cambridge University Press, 3rd edition, paperback edition, 1999.

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, Cambridge University Press, 1987.

Gareth A. Jones and Mary Jones, Elementary Number Theory, Springer, Berlin, 1998. [5, 7, 11, 13, 29, 32]

David Joyner, Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys, The Johns Hopkins University Press, second edition, 2008. Review

Stasys Jukna, Extremal Combinatorics: With Applications in Computer Science, Springer, 2nd edition, 2011. [195]

Dan Kalman, Uncommon Mathematical Excursions: Polynomia and Related Realms, The Mathematical Association of America, 2009. Website, Review

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]

James Lee, Axiomatic Geometry, American Mathematical Society, 2013. Review

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, Dover Publications, 2007. Review

Christopher Moore and Stephan Mertens, The Nature of Computation, Oxford University Press, 2011. [161]

Steven J. Miller and Ramin Takloo-Bighash, An Invitation to Modern Number Theory, Princeton University Press, 2006. [31, 78] Review

Frank Morgan, Geometric Measure Theory: A Beginner's Guide, Academic Press, 2000. [108]

Paul J. Nahin, Inside Interesting Integrals, Springer, 2015. [224]

Tristan Needham, Visual Complex Analysis, Clarendon Press, 1998. Review

Dwight Neuenschwander, Emmy Noether's Wonderful Theorem, The Johns Hopkins University Press, 2010. Review

Peter M. Neumann, Gabrielle A. Stoy and Edward C. Thompson, Groups and Geometry, Oxford University Press, 1994. [66, 85]

Ivan Niven, Irrational Numbers, Mathematical Association of America, reprint edition, 2005.

Christos Papadimitriou and Kenneth Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Dover Publications (New edition) 2000. [62, 168,185]

Charles Petzold, The Annotated Turing: A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine, Wiley Publishing, Inc., 2008. Review, Review, Review

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.

Sara Maad Sasane and Amol Sasane, A Friendly Approach to Complex Analysis, World Scientific, 2014. Review

 ——— 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]

David A. Singer, Geometry: Plane and Fancy, Springer, 1998. [205]

Geoff Smith, Introductory Mathematics: Algebra and Analysis, Springer, London, 1998. Review

 ——— and Olga Tabachnikova, Topics in Group Theory, Springer, London, 2000. [227]

Peter Smith, An Introduction to Formal Logic, Cambidge University Press, 2003. [73]

 ——— , An Introduction to Gödel's Theorems, Cambridge University Press, 2nd edition, 2013. [74,75]

Roel Snieder, A Guided Tour of Mathematical Methods: For the Physical Sciences, Cambridge University Press; 2 edition, 2009. Review

Alexander Soifer, How Does One Cut a Triangle?, Springer, 2nd edition, 2009.

Michael Spivak, Calculus on Manifolds, Westview Press, 1971. [177]

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]

John Stillwell, Numbers and Geometry, Springer, paperback edition 1998.

Steven H. Strogatz, Nonlinear Dynamics and Chaos, Westview Press, 2nd revised edition, 2014. Review (1st edition)

Wilson A. Sutherland, Introduction to Metric and Topological Spaces, 2nd edition, Oxford University Press, 2009. [145] Review

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.

William T. Tutte, Graph Theory As I Have Known It, Oxford University Press, 1998. [223] Review

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, Review

——— , Algorithms and Complexity, 2nd edition, A K Peters, 2003. [138,139]

Kenneth Williams, Number Theory in the Spirit of Liouville, Cambridge University Press, 2010. Review

Robin J. Wilson, Introduction to Graph Theory, 5th Edition , Prentice Hall, 2010. [12, 25, 157, 212]

J. Eldon Whitesitt, Boolean Algebra and Its Applications, Dover Publications Inc., 1995. [111]

 

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Research level

R.A. Bailey, Association Schemes: Designed Experiments, Algebra and Combinatorics, Cambridge University Press, paperback edition 2011. Review

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]

Bruce Berndt, Number Theory in the Spirit of Ramanujan, American Mathematical Society, 2006. Review, Review

——— and Fritz Gesztesy (eds.), Continued Fractions: From Analytic Number Theory to Constructive Approximation: A Volume in Honor of L. J. Lange, American Mathematical Society, 1999.

Simon R. Blackburn, Peter M. Neumann and Geetha Venkataraman, Enumeration of Finite Groups, Cambridge University Press, 2007. Review

Béla Bollobás and Andrew Thomason (eds.), Combinatorics, Geometry and Probability: A Tribute to Paul Erdős, Cambridge University Press, paperback edition, 2004. [209]

John Bray, Derek Holt and Colva Roney-Dougal, The Maximal Subgroups of the Low-Dimensional Finite Classical Groups, Cambridge University Press, 2013.

Peter Cameron, Permutation Groups, Cambridge University Press, 1999. [15, 64, 65, 135, 159,174,214]

 ——— and J. H. van Lint, Designs, Graphs, Codes and Their Links, Cambridge University Press, Cambridge, 1991. [3, 54]

James Carlson (ed.), The Poincare Conjecture, American Mathematical Society, 2014.

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

Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland and William B. Jones, Handbook of Continued Fractions for Special Functions, Springer 2008. [203]

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]

Stewart N. Ethier and Thomas G. Kurtz, By Stewart N. Ethier - Markov Processes: Characterization and Convergence, Wiley-Blackwell, 2nd revised edition, 2005.

Barbara Fantechi, Lothar Gottsche, Luc Illusie, Steven L. Kleiman, Nitin Nitsure and Angelo Vistoli, Fundamental Algebraic Geometry: Grothendieck's FGA Explained, American Mathematical Society, 2007. Review

Leopold Flatto, Poncelet's Theorem, American Mathematical Society, 2008. Review, Review

Mikio Furuta, Index Theorem 1, American Mathematical Society, 2008.

Bernd Gärtner and Jiří Matoušek, Approximation Algorithms and Semidefinite Programming, Springer 2012.

Ronald L. Graham, Bruce L. Rothschild and Joel H. Spencer, Ramsey Theory, Wiley-Blackwell, 2nd Edition, 1990. [28]

James A. Green, with Karin Erdmann and Manfred Schocker, Polynomial Representations of GL_n: with an Appendix on Schensted Correspondence and Littelmann Paths, Springer Verlag, Berlin, 2nd edition, 2007.

Dan Gusfield and Robert W. Irving, The Stable Marriage Problem: Structure and Algorithms, MIT Press, 1989. [68]

Heini Halberstam and Hans-Egon Richert, Sieve Methods, Dover reprint edition, 2011. Review

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.

G.H. Hardy, Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, Chelsea Publishing/American Mathematical Society, 2000.

Glyn Harman, Prime-Detecting Sieves, Princeton University Press, 2007. [202] Review

Brendan Hassett, Introduction to Algebraic Geometry, Cambridge University Press, 2007. Review

Stuart P. Hastings and J. Bryce McLeod, Classical Methods in Ordinary Differential Equations: With Applications to Boundary Value Problems, American Mathematical Society, 2012. 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.

Michael Jünger, Thomas M. Liebling, Denis Naddef, George L. Nemhauser, William R. Pulleyblank, Gerhard Reinelt, Giovanni Rinaldi and Laurence A. Wolsey (eds.), 50 Years of Integer Programming 1958-2008: From the Early Years to the State-of-the-Art, Springer, 2010. [187] Review

Aleksandr Khinchin, Continued Fractions, Dover Publications, 1997. [91]

Frances Kirwan and Jonathan Woolf, An Introduction to Intersection Homology Theory, Second Edition, Chapman and Hall/CRC, 2006. Review, Review

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.

Joseph P.S. Kung, Gian-Carlo Rota and Catherine H. Yan, Combinatorics: The Rota Way, Cambridge University Press, 2009. Review

Jeffrey C. Lagarias (ed.), The Ultimate Challenge: The 3x + 1 Problem, American Mathematical Society, 2010. Review

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]

Alison M. Marr and Walter D. Wallis, Magic Graphs, Birkhäuser, 2nd edition, 2012. Review, Review

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] Review

Athanase Papadopoulos, Metric Spaces, Convexity and Nonpositive Curvature, European Mathematical Society, 2004. Review

Marko Petkovsek, Herbert S Wilf, Doron Zeilberger, A=B, A K Peters/CRC Press. Ebook

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, Springer (2nd printing) 2009. [175, 178]

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]

Takeshi Saito (transl. Masato Kuwata), Fermat's Last Theorem: Basic Tools, American Mathematical Society, 2013.

Edward R. Scheinerman and Daniel H. Ullman, Fractional Graph Theory: A Rational Approach to the Theory of Graphs, Dover Publications Inc., 2012. Ebook, Review

Leila Schneps, Alexandre Grothendieck: A Mathematical Portrait, International Press of Boston Inc, bilingual edition, 2014.

Alexander Schrijver, Combinatorial Optimization: Polyhedra and Efficiency, Springer, Berlin, 2002. [57]

Jean-Paul Allouche and Jeffrey O. Shallit, Automatic Sequences: Theory, Applications, Generalizations, Cambridge University Press, 2003. Website, Review, Review, Review

Michael Stiebitz, Diego Scheide, Bjarne Toft and Lene M. Favrholdt, Graph Edge Coloring: Vizing's Theorem and Goldberg's Conjecture, Wiley-Blackwell, 2012. [80]

René Schoof, Catalan's Conjecture, Springer-Verlag London, 2008. [118] Review

Terence Tao, Hilbert's Fifth Problem and Related Topics, American Mathematical Society, 2014.

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

William T. Trotter, Combinatorics and Partially Ordered Sets: Dimension Theory, The Johns Hopkins University Press, 1992. Review

Robert Veroff (ed.), Automated Reasoning and Its Applications: Essays in Honor of Larry Wos, MIT Press, 1997 [110]

Nader Vakil, Real Analysis through Modern Infinitesimals, Cambridge University Press, 2011.

Richard S. Varga, Gersgorin and His Circles, Springer, corrected printing, 2011. Review (3.3MB)

Stan Wagon, The Banach-Tarski Paradox, Cambridge University Press, 1985.

Dominic Welsh, Matroid Theory, Dover Publications, 2009.

Neil White (ed.), Matroid Applications, Cambridge University Press, 1992.

 

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Mathematical Applications

John A. Adam, Mathematics in Nature: Modeling Patterns in the Natural World , Princeton University Press, 2003. Review, Review

Alfred Aho, John E. Hopcroft, Jeffrey Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, 1974. [95]

R.A. Bailey, Design of Comparative Experiments, Cambridge University Press, 2008.

Martin Anthony and Peter L. Bartlett, Neural Network Learning: Theoretical Foundations, Cambridge University Press, 2009. Review

John D. Barrow, 100 Essential Things You Didn't Know You Didn't Know About Sport, Bodley Head, 2012.

Dave Benson, Music: A Mathematical Offering, Cambridge University Press, 2006. [93] Ebook, Review

Michael Blastland and David Spiegelhalter, The Norm Chronicles: Stories and numbers about danger, Profile Books, 2013. Review, Review, Review (6MB)

Mark Bollman, Basic Gambling Mathematics: The Numbers Behind The Neon, CRC Press, 2014. Review

Kim Border, Fixed Point Theorems with Applications to Economics and Game Theory, Cambridge University Press, 1989.

Christoph Börgers, Mathematics of Social Choice: Voting, Compensation, and Division, Society for Industrial and Applied Mathematics, 2010. Review

Steven J. Brams, Game Theory and the Humanities: Bridging Two Worlds , MIT Press, 2011. Review

Subrahmanyan Chandrasekhar, The Mathematical Theory of Black Holes, Oxford University Press, reprint edition, 1998.

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]

Nachum Dershowitz and Edward M. Reingold, Calendrical Calculations, Cambridge University Press, 3rd edition, 2007. Review

Persi Diaconis and Ron Graham, Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks, Princeton University Press, 2011. Review, Review, Review

Rob Eastaway and John Haigh, The Hidden Mathematics of Sport, Portico, reprint edition, 2011. Review

G. Bard Ermentrout and David H. Terman, Mathematical Foundations of Neuroscience, Springer, 2010. Review

Stewart N. Ethier, The Doctrine of Chances: Probabilistic Aspects of Gambling, Springer-Verlag, 2010. [221] Review

John Fauvel, Raymond Flood and Robin Wilson (eds.), Music and Mathematics: From Pythagoras to Fractals, Oxford University Press, 2003. [106] Review, Review, Review

Norman Fenton and Martin Neil, Risk Assessment and Decision Analysis with Bayesian Networks, CRC Press 2012. Webpage

——— and James M. Bieman, Software Metrics: A Rigorous and Practical Approach, 3rd edition, CRC Press, 2014.

Richard P. Feynman, Feynman Lectures On Computation, Westview Press, paperback edition, 2000.

——— , Robert B. Leighton and Matthew Sands, The Feynman Lectures on Physics: Definitive and Extended Edition, Addison Wesley, 2005. [164]

Yoshikazu Giga and Toshiyuki Kobayashi (eds.), What Mathematics Can Do for You: Essays and Tips from Japanese Industry Leaders, Springer, 2013. Review

James Gleick, The Information: A History, a Theory, a Flood, Fourth Estate, 2011. Webpage

Anthony Hey (ed.), Feynman And Computation, Westview Press, paperback edition, 2002.

John Hopcroft and Ravi Kannan, Computer Science Theory for the Information Age. 2011. Ebook

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]

Amy Langville and Carl D. Meyer, Google's PageRank and Beyond: The Science of Search Engine Rankings, Princeton University Press, 2012. Review

S. Brent Morris, Magic Tricks, Card Shuffling and Dynamic Computer Memories, Mathematical Association of America, 1998.

Colm Mulcahy, Mathematical Card Magic: Fifty-Two New Effects, CRC Press, 2013. Review, Review, Review, Review

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

Miodrag Petković, Mathematics and Chess, Dover Publications Inc., 2003.

Orrin H. Pilkey and Linda Pilkey-Jarvis, Useless Arithmetic: Why Environmental Scientists Can't Predict the Future, Columbia University Press, 2006. Review

Burkard Polster, The Mathematics of Juggling, Springer-Verlag, New York, 2003. Review (Rebuttal), Review

William Poundstone, Gaming the Vote: Why Elections Aren't Fair (and What We Can Do about It), Hill & Wang, 2009. Review

Ian Roulstone and John Norbury, Invisible in the Storm: The Role of Mathematics in Understanding Weather, Princeton University Press, 2013. Review, Review

Liela Schneps and Coralie Colmez, Math on Trial: How Numbers Get Used and Abused in the Courtroom, Basic Books, 2013. Review, Review, Review

Tom Siegfried, A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature, Henry (Joseph) Press, 2006. Review, Review

Simon Singh, The Code Book: The Secret History of Codes and Code-breaking, Doubleday Books, 1999. Review

Ian Stewart, Mathematics Of Life: Unlocking the Secrets of Existence, Profile Books, 2011. Review, Review, Review

George G. Szpiro, Numbers Rule: The Vexing Mathematics of Democracy, from Plato to the Present, Princeton University Press, 2010. Review, Review, Review

R. Gregory Taylor, Models of Computation and Formal Languages, Oxford University Press Inc, USA, 1997. [105, 180]

Leslie Valiant, Probably Approximately Correct, Basic Books, 2013. Review, Review, Review

Peter Woit, Not Even Wrong: The Failure of String Theory and the Continuing Challenge to Unify the Laws of Physics, Jonathan Cape, 2005. Review

David Wright, Mathematics and Music, American Mathematical Society, 2009. Review

 

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Other bibliographies, bibliographic sources

Joseph Malkevitch's collection

Reviews by The Mathematical Association of America

Concerning Mathematical Reviews

AMS Notices Book List 2011


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