Welcome to MathOverflow

Question

11

22

Hello, I would want all book tips you could think of regarding Problem solving and books in general, in elementary mathematics, with a certain flavour for "advanced problem solving". An example would be the books from The art of problem solving, Engels book and Paul Zeits book. Books on certain topics, say geometry is also appreciated!

edited Dec 30 2009 at 16:01

Charles Siegel

community wiki

5

This should be community wiki, because it's looking for a sorted list. – Charles Siegel Dec 30 2009 at 16:01

I've wikified it. Please make such questions CW in the future. – Anton Geraschenko♦ Dec 30 2009 at 19:07

Charles Siegel · Accepted Answer · 2009-12-30 16:00:33Z UTC

7

Polya's "How to Solve It" is a good one. When prepping for the Putnam, I used "Problem Solving Through Problems" by Larson, also.

answered Dec 30 2009 at 16:00

Charles Siegel

community wiki

Grétar Amazeen · Answer 2 · 2009-12-30 17:05:34Z UTC

10

I enjoyed The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics by Shklarsky, Chentzov and Yaglom.

answered Dec 30 2009 at 17:05

Grétar Amazeen

community wiki

A truly great book! – Péter Komjáth Jun 28 2010 at 15:33

Richard Stanley · Answer 3 · 2013-02-21 02:09:22Z UTC

8

For a slightly annotated list of some books on problem-solving, see http://math.mit.edu/~rstan/refs.pdf.

edited Feb 21 at 2:09

Richard Stanley

community wiki

3 revisions

The link seems to be broken. – José Figueroa-O'Farrill Dec 31 2009 at 6:07

@Richard Stanley: The link doesn't seem to work. Could you please rectify your link. – Chandrasekhar Aug 5 2011 at 17:52

1

Broken link has been fixed. – Richard Stanley Jun 24 at 12:22

Scott Carter · Answer 4 · 2009-12-30 17:03:29Z UTC

5

Gelca and Andreescu have at least one book on the subject. See also the links to Math Circles and our own (University of South Alabama) list of suggested books.

answered Dec 30 2009 at 17:03

Scott Carter

community wiki

John Mangual · Answer 5 · 2009-12-30 17:32:46Z UTC

Have you looked at the problems section in the Mathematical Reflections? It's a free online journal edited by Titu Andreescu. They publish six times a year and their problems tend to reflect current olympiad trends.

Also, The Art of Problem Solving and Mathlinks.ro are message boards where olympiad contestants publish solutions from almost every contest in the world. Art of Problem Solving also publishes special textbooks geared towards olympiad students such as this one on Precalculus.

mathphysicist · Answer 6 · 2009-12-30 18:23:51Z UTC

5

See also Solving mathematical problems: a personal perspective by Terence Tao.

answered Dec 30 2009 at 18:23

mathphysicist

community wiki

Qiaochu Yuan · Answer 7 · 2009-12-30 20:42:36Z UTC

5

Titu Andreescu and Gabriel Dospinescu's Problems from the Book is new but quite nice. There are lots of beautiful examples in it proving a great deal of nontrivial results by what are essentially elementary methods.

answered Dec 30 2009 at 20:42

Qiaochu Yuan

community wiki

Zach Conn · Answer 8 · 2009-12-30 20:30:35Z UTC

I've read and enjoyed Putnam and Beyond. It covers more topics from algebra and analysis than I think are typically included in these books. Problems are selected from all sorts of competitions throughout the world including the IMO, various national selection tests for the IMO, and of course the Putnam itself.

Sudip Paul · Answer 9 · 2011-01-14 05:08:11Z UTC

4

Knuth's Concrete Mathematics is not only a fun place to learn great combinatorics; it also contains lots of amazing problems.

answered Jan 14 2011 at 5:08

Sudip Paul

community wiki

José Figueroa-O'Farrill · Answer 10 · 2009-12-30 16:26:08Z UTC

3

"Number Theory: structures, examples and problems", by Titu Andreescu and Dorin Andrica, contains many problems taken from the IMOs.

answered Dec 30 2009 at 16:26

José Figueroa-O'Farrill

community wiki

GH · Answer 11 · 2011-01-14 06:34:26Z UTC

3

High school level: Hungarian Problem Book I, II, III, IV

University level: Contests in Higher Mathematics: Miklos Schweitzer Competitions, 1962-1991

answered Jan 14 2011 at 6:34

GH

community wiki

Tomaž Pisanski · Answer 12 · 2010-03-05 16:14:42Z UTC

There is a book called 50 National Mathematical Olympiads in Slovenia published in English in 2006 by the Society of Mathematicians, Physicists and Astronomers of Slovenia at the occasion of the 47th IMO that took place in Slovenia. It contains all problems and solutions.

Chandrasekhar · Answer 13 · 2012-06-24 08:17:32Z UTC

These are some of the books / links which I would recommend:

Functional Equations and How to solve them by Christopher G. Small. This book especially discusses techniques for solving functional equations which appear in the Olympiads.
Geometry Unbound by Kiran Kedlaya.
The Math problems notebook by Louis Funar and Valentin Boju.
Komal, I think is a Hungarian Magazine which contains Olympiad level problems. The archived set of problems along with their solutions can be found at this link.
International Mathematics Competition for University students has problems more or less like the Putnam.
Vojtech-Jarnik is again a Undergraduate Mathematical Competition whose archived problems and solutions can be found at this link.
Problems in Elementary Number Theory by Hojoo Lee and Peter Vandendriessche has nice collection of problems in Number Theory.

Omnitic · Answer 14 · 2012-06-20 17:20:16Z UTC

0

There are a lot of books my the american mathematical society. But I think the best book is Mathematical Olympiad in China by Bin Xiong. Any advanced geometry book will also help you because geometry is an area which really improves with practice.

answered Jun 20 2012 at 17:20

Omnitic

community wiki

Koen S · Answer 15 · 2012-06-20 20:21:26Z UTC

0

I prepared my Mathematical Olympiad with "The Mathematical Olympiad Handbook" by A. Gardiner.

answered Jun 20 2012 at 20:21

Koen S

community wiki

Richard Eager · Answer 16 · 2012-10-08 15:06:51Z UTC

My favorite olympiad books were

"Winning Solutions" by Edward Lozansky and Cecil Rousseau

"Mathematical Miniatures" by Svetoslav Savchev and Titu Andreescu

"Geometry Unbound" by Kiran Kedlaya [online notes]

"Geometry Revisited" H. S. M. Coxeter and Samuel L. Greitzer

Notes by Po-Shen Loh http://www.math.cmu.edu/~ploh/olympiad.shtml

ex0du5 · Answer 17 · 2013-02-21 04:12:47Z UTC

Hardy and Williams have "The Red Book of Mathematical Problems" and "The Green Book of Mathematical Problems", with some good analysis, series, conbinatorics, and group theory.

de Souza and Silva have the more advanced "Berkeley Problems in Mathematics".

And finally, another one I leaned on in studying for the Putnam was Dixon's "Problems in Group Theory".

Although I do really like Polya and other's books on problem solving, I always found that I got more from them the more I actually worked through real problems. Others have mentioned actual problem books from the Olympiads and Putnam, which are of course great resources here as well.

Good books on problem solving / math olympiad

Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)

17 Answers

You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.