Recommended Mathematics Literature

Enter keywords:

Problem Solving

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

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]

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]

. Steven G. Krantz. 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.

Collections of Mathematical (Competition) Problems

Anthologies and Surveys

Very Short Introduction

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]

Number Theory

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 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]

Algebra

Combinatorics

A Course in Combinatorics .

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

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

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]

Analysis

A Course of Pure Mathematics . 10th ed.

G.H. Hardy.

Cambridge Univ. Press, 1955. [See this book at Amazon.com]

. 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]

Geometry

Equations and Inequalities

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]

Probability

An Introduction to Probability Theory and Its Applications .

William Feller.

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

Foundations

History of Mathematics

Mathematical Circles

Other Recommendations

`Bedside' Mathematics Literature

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

In alphabetic order of (first) author:

For the Very Young