Theorem of the Day

Bibliography

This is more or less just a compilation of all the further reading references from the various theorems of the day. I have been completely inconsistent in chosing these: some are popular acccounts, some are historical works, some are text books (school, undergraduate, even postgraduate). Clicking on the links will take you to amazon.co.uk where you will find more detailed bibliographic information, reviews and, increasingly, their excellent 'Search Inside' facility.

Mathematicians on their profession and its professionals

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.

Timothy Gowers, Mathematics: A Very Short Introduction, Oxford Paperbacks, 2002.

Paul Halmos, I Want to Be a Mathematician, Springer, New York, 1985.

G.H. Hardy, A Mathematician's Apology, with a Forward by C.P. Snow, Cambridge University Press, 1992 edition.

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

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

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

History and philosophy of Mathematics

Marlow Anderson, Victor Katz and Robin Wilson, Sherlock Holmes in Babylon and Other Tales of Mathematical History, The Mathematical Association of America, 2004.

J. Lennart Berggren, Jonathan M. Borwein and Peter B. Borwein, PI: A Source Book, 3rd edition, Springer-Verlag, New York, 2004.

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

Serafina Cuomo, Ancient Mathematics (Sciences of Antiquity), Routledge, 2001.

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

John Fauvel, Raymond Flood and Robin Wilson, (eds.), Oxford Figures: 800 Years of the Mathematical Sciences, Oxford University Press, 2000.

Victor Katz (ed.), Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton University Press, 2007.

Morris Kline, Mathematics: The Loss of Certainty, Oxford University Press, USA, 1983 re-edition.

Morris Kline, Mathematical Thought from Ancient to Modern Times: Vol 1, Oxford University Press, 1990 re-edition, also Vol 2 and Vol 3.

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

Richard Laubenbacher and D. Pengelley, Mathematical Expeditions: Chronicles by the Explorers, Springer New York, 2000.

Eli Maor, The Pythagorean Theorem: A 4,000-year History, Princeton University Press, 2007.

John Allen Paulos, Mathematics and Humour, University of Chigago Press, 1990.

Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness, Vintage, 1995.

Popular accounts of mathematical genius at work

Paul Hoffman, The Man Who Loved Only Numbers: Story of Paul Erdos and the Search for Mathematical Truth, Fourth Estate, London, 1999 edition.

Marcus du Sautoy, The Music of the Primes: Why an Unsolved Problem in Mathematics Matters, HarperPerennial, 2004 edition.

Simon Singh, Fermat's Last Theorem, HarperPerennial, 2007 reissue.

George G. Szpiro, Poincare's Prize: The Hundred-year Quest to Solve One of Math's Greatest Puzzles , Dutton/Signet, 2007.

Bruce Schechter, My Brain is Open: The Mathematical Journeys of Paul Erdos, Prentice Hall, 2000.

Robin Wilson, Four Colours Suffice: How the Map Problem Was Solved, Penguin Books, 2003 edition.

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

Introductions to mathematical topics accessible for non-professionals

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

Avner Ash and Robert Gross, Fearless Symmetry: Exposing the Hidden Patterns of Numbers, Princeton University Press, 2006.

V.K. Balakrishnan, Graph Theory: Including Hundreds of Solved Problems (Schaum), McGraw-Hill Publishing Co., 1997.

Edward B. Burger and Michael Starbird, Coincidences, Chaos and All That Math Jazz, W W Norton, 2005.

John L Casti, Five Golden Rules: Great Theories of 20th Century Mathematics and Why They Matter, John Wiley, 1997.

John H. Conway and Derek A. Smith, On Quaternions and Octonions, A K Peters, 2003.

Tony Crilly, 50 Mathematical Ideas You Really Need to Know, Quercus Publishing, London 2007.

John Derbyshire, Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, Plume Books, 2004.

Keith Devlin, The Language of Mathematics: Making the Invisible Visible, W.H.Freeman & Co Ltd, 2000.

Charles L. Dodgson, An Elementary Treatise On Determinants, Rough Draft Printing, 2007.

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

Steven Finch, Mathematical Constants, Cambridge University Press, 2003.

Julian Havil, Nonplussed: Mathematical Proof of Implausible Ideas, Princeton University Press, 2007.

Ross Honsberger, Episodes in Nineteenth and Twentieth Century Euclidean Geometry, Mathematical Association of America, 1996.

Vincent Icke, The Force of Symmetry, Cambridege University Press, 1995.

D.V. Lindley, Making Decisions, 2nd edition, John Wiley and Sons Ltd, 1985.

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

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

Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe, Vintage, 2005.

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

Mark Ronan, Symmetry and the Monster: One of the Greatest Quests of Mathematics, Oxford University Press, 2006.

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.

H. Steinhaus, Mathematical Snapshots, Dover Publications, 2000.

Ian Stewart, Does God Play Dice?: The New Mathematics of Chaos, 2nd edition, Penguin, 1997.

Ian Stewart, Why Beauty is Truth: The History of Symmetry, Basic Books, 2008.

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.

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

David Wells, Prime Numbers: The Most Mysterious Figures in Math, John Wiley & Sons Inc, 1995.

More specialised introductions to mathematical topics

Martin Aigner and Gunter M. Ziegler, Proofs from the Book , Springer-Verlag Berlin, 3rd Revised Edition, 2003.

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

Noga Alon and Joel H. Spencer, The Probabilistic Method, 3rd ed., WileyBlackwell, 2008.

George E. Andrews and Kimmo Eriksson, Integer Partitions, 2nd revised ed., Cambridge University Press, 2004.

M. Ya. Antimirov, A. A. Kolyshkin and Rémi Vaillancourt, Complex Variables, Academic Press, San Diego, 1998.

David L. Applegate, Robert E. Bixby, Vašek Chvátal and William J. Cook, The Traveling Salesman Problem: A Computational Study, Princeton University Press, 2006.

M.A. Armstrong, Basic Topology, Springer-Verlag New York Inc., 1997

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

Arthur T. Benjamin and Jennifer J. Quinn, Proofs that Really Count: The Art of Combinatorial Proof, The Mathematical Association of America, 2003

Norman Biggs, Algebraic Graph Theory, 2nd edition, Cambridge University Press, 1994.

Miklós Bóna, A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory, 2nd edition, World Scientific Publishing, 2006.

G. Chartrand and L. Lesniak, Graphs and Digraphs, 4th Edition, Chapman and Hall/CRC, 2004.

John Horton Conway (with Francis Y.C.Fung), The Sensual (Quadratic) Form, The Mathematical Association of America, 1998.

B.A. Davey and H.A. Priestly, Introduction to Lattices and Order, Cambridge University Press, 1990.

Reinhard Diestel, Graph Theory, 2nd edition, Springer New York, 2000.

R.A. Dunlap, The Golden Ratio and Fibonacci Numbers, World Scientific, 1998.

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.

M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness, W.H.Freeman & Co Ltd, 1979.

Frank Harary, Graph Theory, Perseus Books, 1999.

G.H. Hardy and E.W. Wright, An Introduction to the Theory of Numbers, 5th edition, OUP, 1980.

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

Stephen A. Huggett and David Jordan, A Topological Aperitif, Springer-Verlag, London, 2001.

Arthur Jones, Sidney A. Morris and Kenneth R. Pearson, Abstract Algebra and Famous Impossibilities, Springer-Verlag, New York, 1991.

Gareth Jones and Mary Jones, Elementary Number Theory, Springer, Berlin, 1998.

Anthony W. Knapp, Basic Real Analysis, Birkhauser Verlag, 2004, and Advanced Real Analysis, Birkhäuser Boston, 2005.

Steven G. Krantz and Harold R. Parks, A Primer of Real Analytic Functions, 2nd edition, Birkhäuser Verlag AG, 2002.

Yuri Matiyasevich, Hilbert's 10th Problem, MIT Press, 1993.

Jiří Matoušek, Lectures on Discrete Geometry, Springer-Verlag, New York, 2002.

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

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

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

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

Jim Pitman, Probability, Springer, New York, 1999.

H.E. Preistly, Introduction to Complex Analysis, 2nd edition, Oxford University Press, 2003.

Miles Reid, Undergraduate Algebraic Geometry, Cambridge University Press, 1988.

Miles Reid and Balázs Szendrői, Geometry and Topology, Cambridge University Press, 2005.

Joseph H. Silverman and John Tate, Rational Points on Elliptic Curves, Springer-Verlag, New York, 1994.

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

Peter Smith, An Introduction to Godel's Theorems, Cambridge University Press, 2007.

R. P. Stanley, Enumerative Combinatorics: Volume 1 (new ed. 2000) and Volume 2, (new ed. 2001) Cambridge University Press.

Ian Stewart, Galois Theory, Chapman and Hall/CRC, 3rd Revised Edition, 2003

Thomas M. Thompson, From Error-Correcting Codes through Sphere Packings to Simple Groups, Mathematical Association of America, 2004.

Silvanus P. Thomson and Martin Gardner, Calculus Made Easy, Palgrave Macmillan, revised edition, 1999.

Dennis Wackerly, William Mendenhall III and Richard Scheaffer, Mathematical Statistics with Applications, Duxbury, 2001.

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.

Robin J. Wilson, Introduction to Graph Theory, 4th edition, Longman, 1996.

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

Research level

R. B. Bapat and T. E. S. Raghavan, Nonnegative Matrices and Applications, Cambridge University Press, 1997.

Peter Cameron, Permutation Groups, Cambridge University Press, 1999.

P. J. Cameron and J. H. van Lint, Designs, Graphs, Codes and Their Links, Cambridge University Press, Cambridge, 1991.

J. Dénes and A.D. Keedwell, Latin Squares: New Developments in the Theory and Applications, North-Holland, 1991.

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

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

W.K. Hayman, Multivalent Functions, 2nd edition, Cambridge University Press, 2008.

G.J.O. Jameson, The Prime Number Theorem, Cambridge University Press, 2003.

Anthony W. Knapp, Elliptic Curves, Princeton University Press, 1993.

Aleksandr Khinchin, Continued Fractions, Dover Publications, 1997.

Steven G. Krantz and Harold R. Parks, The Implicit Function Theorem: History, Theory and Applications, Birkhäuser Boston, 2002.

F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, North-Holland, 1983.

Jiří Matoušek, Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry, Springer Berlin, 2003.

Olavi Nevanlinna, Meromorphic Functions and Linear Algebra, American Mathematical Society, 2003.

Christos Papadimitriou and Kenneth Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Dover Publications (New edition) 2000.

D.J.S. Robinson, A Course in the Theory of Groups, 2nd edition, Springer-Verlag, 1998.

Lee A. Rubel and James E. Colliander, Entire and Meromorphic Functions, Springer-Verlag New York, 1996.

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

René Schoof, Catalan's Conjecture, Springer-Verlag London, 2008.

Robert Veroff (ed.), Automated Reasoning and Its Applications: Essays in Honor of Larry Wos

Mathematical Applications

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

Dave Benson, Music: A Mathematical Offering, Cambridge University Press, 2006.

Andrew M. Colman, Game Theory and Its Applications in the Social and Biological Sciences, Routledge Falmer, 1995.

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

Donald E. Knuth, The Art of Computer Programming: Vol 1-3, Addison-Wesley, 1999 (this edition).

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