In association with Amazon.com (Statement of Intent) [ Search Amazon.com Books by: Author/Title/Subject | ISBN | Publisher/Date | Boolean Expression ]

Of course, it is also recommended that you read books on other disciplines.

**How to Solve It: A New Aspect of Mathematical Method**.

G. Polya

Second Edition, Princeton University Press, 1957. [See this book at Amazon.com]

**How to Solve It: Modern Heuristics**(2nd Ed.).

Z. Michalewicz and D. B. Fogel.

Springer, 2004 (First Edition 2000). [See this book at Amazon.com]

**The Art and Craft of Problem Solving**.

Paul Zeitz.

John Wiley & Sons, 1999. [See this book at Amazon.com, Paperback]

**Problem-Solving Strategies**.

Arthur Engel.

Springer, 1998.

[See this book at Amazon.com]

**A Primer for Mathematics Competitions**.**=====NEW IN LIST=====**

Alexander Zawaira, Gavin Hitchcock. Oxford University Press, 2009.

[See this book at Amazon.com]

**Problem Solving Through Problems**.

Loren C. Larson.

Springer, 1985.

[See this book at Amazon.com]

**Solving Mathematical Problems: A Personal Perspective**(Second Edition).**=====NEW IN LIST=====**

Terence Tao.

Oxford University Press, 2006.

[See this book at Amazon.com]

Sample chapters - Errata to second edition

Summary of problems solved, and Tom's errata

**Problem-Solving Strategies For Efficient and Elegant Solutions: A Resource for the Mathematics Teacher**.

Alfred S. Posamentier, Stephen Krulik.

Corwin Press, 2003. [See this book at Amazon.com]

**First Steps for Math Olympians: Using the American Mathematics Competitions**.

J. Douglas Faires.

MAA, 2006. [See this book at Amazon.com]

**Problem Solving Through Recreational Mathematics**.

Bonnie Averbach, Orin Chein.

Dover Publications, 1999. [See this book at Amazon.com]

**Techniques of Problem Solving**.

Steven G. Krantz.

American Mathematical Society, 1997. [See this book at Amazon.com]**Solutions Manual for Techniques of Problem Solving**.

Luis Fernandez.

American Mathematical Society, 1997. [See this book at Amazon.com]

**How to Solve Mathematical Problems**.

Wayne A. Wickelgren.

Dover Publications, 1995. [See this book at Amazon.com]

This is a corrected republication of How to Solve Problems: Elements of a Theory of Problems and Problem Solving, Freeman & Co., 1974.

**The IMO Compendium: A Collection of Problems Suggested for The International Mathematical Olympiads: 1959-2004**.

Dusan Djukic, Vladimir Z. Jankovic, Ivan Matic, Nikola Petrovic.

Springer, 2005. [See this book at Amazon.com]

Companion website**The Art of Mathematics: Coffee Time in Memphis**.

Béla Bollobás.

Cambridge University Press, 2006. [See this book at Amazon.com]

Not all topics are relevant for the IMO, but it sure is a nice broad intriguing collection of some 157 problems, with hints and solutions.**102 Combinatorial Problems : From the Training of the USA IMO Team**.

Titu Andreescu, Zuming Feng.

Birkhäuser, 2003. [See this book at Amazon.com]**103 Trigonometry Problems : From the Training of the USA IMO Team**.

Titu Andreescu, Zuming Feng.

Birkhäuser, 2004. [See this book at Amazon.com]**104 Number Theory Problems : From the Training of the USA IMO Team**.

Titu Andreescu, Dorin Andrica, Zuming Feng.

Birkhäuser, 2006. [See this book at Amazon.com]- Books on
mathematical problem solving at the Australian Mathematics Trust (AMT);
here is a small selection:
**Seeking Solutions : Discussion and Solutions of the Problems from the International Mathematical Olympiads 1988-1990**.

J. C. Burns.

AMT, 2000.

[See this book at Amazon.com]**101 Problems in Algebra : From the Training of the USA IMO Team**.

Titu Andreescu, Zuming Feng.

AMT, 2001.

[See this book at Amazon.com]

- Publications on
mathematical problem solving at the UK Mathematics Trust (UKMT);
here is a small selection (I have no direct links to Amazon.com):
**Introductions to Number Theory and Inequalities**.

J. C. Burns.

UKMT, 200?.

ISBN 0-9536823-8-2**Plane Euclidean Geometry**.

A. D. Gardiner and C. J. Bradley.

UKMT, 2005.

ISBN 0-9536823-6-6

**Mathematical Puzzles: A Connoisseur's Collection**.

Peter Winkler.

A. K. Peters, 2004. [See this book at Amazon.com]-
**The Math Problems Notebook**.**=====NEW IN LIST=====**

Valentin Boju, Louis Funar.

[See this book at Amazon.com] **Ants, Bikes, and Clocks: Problem Solving for Undergraduates**.

William Briggs.

SIAM, 2004.

[See this book at Amazon.com]- Books on
problem solving published by the
*Mathematical Association of America*(MAA); here is a small selection:**International Mathematical Olympiads, 1955-1977**.

Samuel L. Greitzer (ed.).

MAA, 1979. [See this book at Amazon.com]**International Mathematical Olympiads, 1978-1985, and Forty Supplementary Problems**.

Murray S. Klamkin (ed.).

MAA, 1986. [See this book at Amazon.com]This book includes tables that list participating countries and their performance at IMOs from the beginning in 1959 to 1985.

**International Mathematical Olympiads, 1986-1999**.

Marcin E. Kuczma (ed.).

MAA, 2003.

[See this book at Amazon.com]**USA Mathematical Olympiads 1972-1986 Problems and Solutions**.

Murray S. Klamkin (ed.).

MAA, 1989. [See this book at Amazon.com]**Five Hundred Mathematical Challenges**.

Edward J. Barbeau, Murray S. Klamkin, William O. J. Moser.

MAA, 1995. [See this book at Amazon.com]Includes solutions. From the preface: ``This collection of problems is directed to students in high school, college and university. Some of the problems are easy, needing no more than common sense and clear reasoning to solve. Others may require some of the results and techniques which we have included in the Tool Chest [15 pages with results from Combinatorics, Arithmetic, Algebra, Inequalities, Geometry and Trigonomotry, and Analysis]. None of the problems require calculus... They could be described as challenging, interesting, thought-provoking, fascinating.''

**From Erdos to Kiev : Problems of Olympiad Caliber**.

Ross Honsberger.

MAA, 1996. [See this book at Amazon.com]**In Pólya's Footsteps: Miscellaneous Problems and Essays**.

Ross Honsberger.

MAA, 1997. [See this book at Amazon.com]**Mathematical Miniatures**.

Svetsoslav Savchev and Titu Andreescu.

MAA, 2003. [See this book at Amazon.com]**Problems from Murray Klamkin**.**=====NEW IN LIST=====**

Andy Liu, Bruce Shawyer (Eds.).

MAA, 2009. [See this book at Amazon.com]**Aha! Solutions**.**=====NEW IN LIST=====**

Martin Erickson.

MAA, 2009. [See this book at Amazon.com]

**Mathematical Olympiad Challenges**, Second Edition.

by Titu Andreescu and Razvan Gelca.

Birkhäuser Boston, 2000.

[See this book at Amazon.com]**Mathematical Olympiad Treasures**.

by Titu Andreescu and Bogden Eneescu.

Birkhäuser Boston, 2003.

[See this book at Amazon.com]**Winning Solutions**.

Edward Lozansky and Cecil Rousseau.

Springer-Verlag, 1996. [See this book at Amazon.com]From the preface: ``There is a significant gap between what most high school mathematics programs teach and what is expected of an IMO participant. This book is part of an effort to bridge that gap.''

Chapters on Numbers, Algebra, and Combinatorics. Explains some theory, provides examples, exercises and solutions.**Colorado Mathematical Olympiad: The First Ten Years and Further Explorations**.

Alexander Soifer.

Center of Excellence in Publ., 1994. [See this book at Amazon.com]**New Mexico Mathematics Contest Problem Book**.

Liong-shin Hahn.

University of New Mexico Press, 2005. [See this book at Amazon.com]**The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics**.

D.O. Shklarsky, N.N. Chentzov, and I.M. Yaglom (I. Sussman, ed.).

3rd ed., Freeman, 1962 (?). [See this book at Amazon.com]**The Canadian Mathematical Olympiad 1969-1993**.

Michael Doob.

Canadian Mathematical Society, 1993. [See this book at Amazon.com]**Leningrad Mathematical Olympiads 1987-1991**.

Dmitry Fomin and Alexey Kirichenko.

MathPro Press, 1994 [See this book at Amazon.com]**Math Olympiad Contest Problems for Elementary and Middle Schools**.

George Lenchner.

Glenwood, 1996. [See this book at Amazon.com]**The Mathematical Olympiad Handbook: An Introduction to Problem Solving Based on the First 32 British Mathematical Olympiads 1965-1996**.

Anthony David Gardiner.

Oxford University Press, 1997. [See this book at Amazon.com]From the preface: ``This is unashamedly a book for beginners. Unlike most Olympiad problem books, my aim has been to convince as many people as possible that Mathematical Olympiad problem are for

*them*and not just for some bunch of freaks.''**A Mathematical Mosaic: Patterns & Problem-Solving**.

Ravi Vakil.

Brendan Kelly Publishing Inc., 1996.

[See this book at Amazon.com]**Aufgaben und Lehrsätze aus der Analysis**(in German).

George Pólya and Gabor Szegö.

Band I und II, 4th ed., Springer, 1970/1971.

English translation:

**Problems and Theorems in Analysis**.

Springer:- Vol. I,
**Series, Integral Calculus, Theory of Functions**, 1978. [See this book at Amazon.com] - Vol. II,
**Theory of Functions, Zeros, Polynomials, Determinants, Number Theory, Geometry**, 1976. [See this book at Amazon.com]

- Vol. I,

**1089 and All That: A Journey into Mathematics**.

David Acheson.

Oxford University Press, 2004. [See this book at Amazon.com, Paperback, website for book ]

**Mathematics: A Very Short Introduction**.

Timothy Gowers.

Oxford University Press, 2002. [See this book at Amazon.com]

**Journey through Genius: The Great Theorems of Mathematics**.

William Dunham.

Penguin, 1990. [See this book at Amazon.com]

**The World of Mathematics: A Small Library of the Literature of Mathematics from A`h-mosé the Scribe to Albert Einstein**.

James R. Newman (editor).

4 Volumes, Tempus, reprinted 1988 (original 1956). [See this book at Amazon.com]

**Mathematics: People, Problems, Results**.

D. M. Campbell and J. C. Higgins.

3 volumes, Wadsworth, 1983. [See this book at Amazon.com]

**Mathematics: The Science of Patterns: The Search for Order in Life, Mind and the Universe**.

Keith Devlin.

Scientific American Library, Freeman, 1994, Reprinted 1997. [See this book at Amazon.com]

**The Moment of Proof : Mathematical Epiphanies**.

Donald C. Benson.

Oxford University Press, 1999.

[See this book at Amazon.com]

**What Is Mathematics?: An Elementary Approach to Ideas and Methods**.

Richard Courant and Herbert Robbins.

Oxford Univ. Press, 1941, 1969. (2nd ed. with Ian Stewart) [See this book at Amazon.com]

**Pour l'honneur de l'esprit humain**(in French).

Jean Dieudonné

..., 1987.

English translation:**Mathematics: The Music of Reason**. Springer, 1992. [See this book at Amazon.com]

**An Introduction to the Theory of Numbers**. 5th ed.

G.H. Hardy and E.M. Wright.

Clarendon Press, 1979. [See this book at Amazon.com]

**A Concise Introduction to the Thoory of Numbers**.

Alan Baker.

Cambridge University Press, 1984. [See this book at Amazon.com]

**The Encyclopedia of Integer Sequences**.

N.J.A. Sloane and Simon Plouffe.

Academic Press, 1995. [See this book at Amazon.com]

Sloane's On-Line Encyclopedia of Integer Sequences

**The Books of Numbers**.

John Horton Conway, Richard K. Guy.

Copernicus Books, 1997. [See this book at Amazon.com]

**104 Number Theory Problems : From the Training of the USA IMO Team**. Titu Andreescu, Dorin Andrica, Zuming Feng.

Birkhäuser, 2006. [See this book at Amazon.com]

**A Survey of Modern Algebra**.

Saunders MacLane and Garrett D. Birkhoff.

Hardcover: AK Peters Ltd; 5th edition, 1997. [See this book at Amazon.com]**Polynomials**.

Edward J. Barbireau.

Hardcover (hard to get): Springer, 1989. [See this book at Amazon.com]

Paperback: Springer, 2003. [See this book at Amazon.com]

**A Course in Combinatorics**.

J. H. van Lint and R. M. Wilson.

Cambridge University Press; 2nd edition, 2001. [See this book at Amazon.com]

**Generatingfunctionology**.

Herbert Wilf (author of the book A=B).

Academic Press; 2nd edition, 1993. [See this book at Amazon.com]

Also available as downloadable PDF for non-profit/non-commercial use.

**Counting and Configurations**.

Jiri Herman, Radan Kucera, and Jaromir Simsa.

Springer, 2003. [See this book at Amazon.com, Digital]

**102 Combinatorial Problems : From the Training of the USA IMO Team**.

Titu Andreescu, Zuming Feng.

Birkhäuser, 2003. [See this book at Amazon.com]

**A Course of Pure Mathematics**. 10th ed.

G.H. Hardy.

Cambridge Univ. Press, 1955. [See this book at Amazon.com]**Calculus**. 3rd ed.

Michael Spivak.

Publish or Perish, 1994. [See this book at Amazon.com]

**Anschauliche Geometrie**(in German).

D. Hilbert and S. Cohn-Vossen.

Springer, 1932.

English translation:**Geometry and the Imagination**. 2nd ed.

Chelsea Publishing Company, 1990. [See this book at Amazon.com]**Introduction to Geometry**, 2nd ed.

H.S.M. Coxeter.

John Wiley & Sons, 1969. [See this book at Amazon.com]**Geometry Revisited**.

H.S.M. Coxeter and Samuel L. Greitzer.

The Mathematical Association of America, 1996. [See this book at Amazon.com]**Challenges In Geometry: For Mathematical Olympians Past And Present**.

Christopher J. Bradley.

Oxford University Press, 2005. [See this book at Amazon.com]

Mostly concerned with number-theoretic and combinatoric problems based on geometric configurations

**Introduction to Inequalities**.

Edwin F. Beckenbach and R. Bellman. Michael Steele.

Mathematical Association of America, 1975.

[See this book at Amazon.com]

**Inequalities**.

Radmila Bulajich Manfrino, José Antonio Gómez Ortega, Rogelio Valdez Delgado.

Instituto de Matemáticas, Universidad Nacional Autónoma de México, 2005.

[See this book at IM UNAM]

**The Cauchy-Schwarz Master Class: An Introduction to the Art of Inequalities**.

J. Michael Steele.

Cambridge University Press, 2004.

[See this book at Amazon.com]

**Functional Equations and How to Solve Them**.

Christopher G. Small.

Springer, 2006.

[See this book at Amazon.com, Paperback]

**Functional Equations: A Problem Solving Approach**.

B. J. Venkatachala.

Prism Books, 2002.

ISBN 81-7286-265-2.

[Not available at Amazon.com. Can be ordered at Eswar.com, India]

**Equations and Inequalities**.

Jiri Herman, Radan Kucera, and Karl Dilcher.

Springer, 2006. [See this book at Amazon.com, Digital]

**An Introduction to Probability Theory and Its Applications**.

William Feller.

Volume 1, 3rd ed., John Wiley & Sons, 1968. [See this book at Amazon.com]

**Naive Set Theory**.

Paul R. Halmos.

Van Nostrand, 1960. [See this book at Amazon.com]**Gödel's Proof**.

Ernest Nagel and James R. Newman.

New York University Press, 1983. [See this book at Amazon.com]**The Foundations of Mathematics**.

Ian Stewart and David Tall.

Oxford University Press, 1977. [See this book at Amazon.com]**Conceptual Mathematics: A First Introduction to Categories**.

F. William Lawvere and Stephen H. Schanuel.

Cambridge University Press, 1997. [See paperback at Amazon.com; hardcover]

**Men of Mathematics**.

Eric Temple Bell.

Simon and Schuster, 1937. [See this book at Amazon.com]**Mathematical Thought from Ancient to Modern Times**.

Morris Kline.

3 volumes, Oxford University Press, 1990 (originally 1972).

[See volume 1 at Amazon.com]

[See volume 2 at Amazon.com]

[See volume 3 at Amazon.com]**A Concise History of Mathematics**.

Dirk J. Struik.

Dover, 1959. [See this book at Amazon.com]

**Mathematical Circles: Russian Experience**.

Dmitry Fomin, Sergey Genkin, Ilia Itenberg.

American Mathematical Society, 1996. [See this book at Amazon.com]**Out of the Labyrinth: Setting Mathematics Free**.

Robert Kaplan and Ellen Kaplan.

Oxford University Press, 2007. [See this book at Amazon.com]**A Decade of the Berkeley Math Circle: The American Experience, Volume 1**.**=====NEW IN LIST=====**

Zvezdelina Stankova, Tom Rike.

American Mathematical Society, 2008. [See this book at Amazon.com]**Circle in a Box**.**=====NEW IN LIST=====**

Sam Vandervelde.

American Mathematical Society, 2009. [See this book at Amazon.com]

**Library Recommendations for Undergraduate Mathematics**.

Lynn Arthur Steen.

Mathematical Association of America, 1992. [See this book at Amazon.com]**Mathematics Books Recommendations for High School and Public Libraries**.

Lynn Arthur Steen.

Mathematical Association of America, 1992. [See this book at Amazon.com]

Note that Martin Gardner, Ian Stewart (among others) are authors of many interesting mathematics books.

In alphabetic order of (first) author:

**Mathematical People: Profiles and Interviews**.

Donald J. Albers and G. L. Anderson (editors).

Birkhäuser, 1985. [See this book at Amazon.com]**Winning Ways for Your Mathematical Plays**(Second Edition).

Elwyn Berlekamp, John H. Conway, and Richard K. Guy.

A. K. Peeters, 2001, 2003, 2003, 2004.- Vol. 1:
**Foundations, Adding Games**[See this book at Amazon.com] - Vol. 2: [See this book at Amazon.com]
- Vol. 3: [See this book at Amazon.com]
- Vol. 4:
**One-Player Games**[See this book at Amazon.com]

- Vol. 1:
**Games in General** - Vol. 2:
**Games in Particular**[See this book at Amazon.com]

- Vol. 1:
**Glück, Logik und Bluff: Mathematik im Spiel - Methoden, Ergebnisse und Grenzen**.

Jörg Bewersdorff.

Vieweg, 2001 (2. Auflage). [See this book at Amazon.com]

English translation:**Luck, Logic, and White Lies: The Mathematics of Games**.

A. K. Peters, 2004. [See this book at Amazon.com]**The Mathematical Experience**.

Philip J. Davis and Reuben Hersh.

Birkhäuser, 1981. [See this book at Amazon.com]**Number Sense: How the Mind Creates Mathematics**.

Stanislas Dehaene.

Oxford University Press, 1997. [See this book at Amazon.com]**Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics**.

John Derbyshire.

Joseph Henry Press, 2003. [See this book at Amazon.com]**A Mathematician's Apology**.

G.H. Hardy.

Cambridge Univ. Press, 1967. [See this book at Amazon.com]**How to Lie with Statistics**.

Darrell Huff.

Penguin, 1979. [See this book at Amazon.com]**Surreal Numbers: How Two Ex-Students Turn on to Pure Mathematics and Found Total Happiness / A Mathematical Novelette**.

Donald E. Knuth.

Addison-Wesley, 1974. [See this book at Amazon.com]

Related:**On Numbers and Games**.

John Horton Conway.

AK Peters, 2000.

[See this book at Amazon.com]

**The Pleasures of Counting**.

T. W. Körner.

Cambridge Univ. Press, 1996. [See this book at Amazon.com]This book also deals with Physics, Biology, and Computing Science (although the author treats these topics as mathematics). It contains an appendix on further reading with extensively documented recommendations.

**E: The Story of a Number**.

Eli Maor.

Princeton University Press, 1998. [See this book at Amazon.com]**An Imaginary Tale: The Story of the Square Root of Minus One**.

Paul J. Nahin.

Princeton University Press, 1998. [See this book at Amazon.com]**Count Down: Six Kids Vie for Glory at the World's Toughest Math Competition**. (About IMO 2001 in Washington DC)

Steve Olson.

Houghton Mifflin, 2004. [See this book at Amazon.com]**Innumeracy: Mathematical Illiteracy and Its Consequences**.

John Allen Paulos.

Penguin Books, 1988. [See this book at Amazon.com]**Mathematical Recreations and Essays**, 13th ed.

W.W. Rouse Ball and H.S.M. Coxeter.

Macmillan, 1939. [See this book at Amazon.com]**Symmetry**.

Hermann Weyl.

Princeton Univ. Press, 1989. [See this book at Amazon.com]

**How to Teach Your Baby Math: More Gentle Revolution**.

Janet Doman and Glenn Doman.

Avery Publishing Group, 1993. [See this book at Amazon.com]

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