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Putnam and Beyond Paperback – August 23, 2007

by Razvan Gelca (Author), Titu Andreescu (Author)

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Putnam and Beyond takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis in one and several variables, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research.

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Product Details

Paperback: 798 pages
Publisher: Springer; 2007 edition (August 23, 2007)
Language: English
ISBN-10: 0387257659
ISBN-13: 978-0387257655
Product Dimensions: 7 x 1.8 x 9.4 inches
Shipping Weight: 3.6 pounds (View shipping rates and policies)
Average Customer Review: 4.2 out of 5 stars See all reviews (5 customer reviews)
Amazon Best Sellers Rank: #179,003 in Books (See Top 100 in Books)
- #13 in Books > Science & Math > Mathematics > Pure Mathematics > Combinatorics
- #34 in Books > Science & Math > Mathematics > Pure Mathematics > Discrete Mathematics
- #45 in Books > Science & Math > Mathematics > Pure Mathematics > Number Theory

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Customer Reviews

4.2 out of 5 stars

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Most Helpful Customer Reviews

22 of 23 people found the following review helpful

An excellent high-level compilation of problems and problem-solving strategies

By nilkn on August 8, 2009

Format: Paperback

There are many books on problem solving. The majority are aimed at junior high and high school students preparing for either the International Mathematical Olympiad or national IMO selection tests (the American Mathematics Contests in the United States, such as the USAMO). A select few, such as Problem Solving through Problems by Loren Larson, are aimed at university students preparing for university competitions. This book, as the title suggests, belongs to this latter category, and it has a particular emphasis on the sorts of problems that occur on the Putnam exams.

This book is generally written at a higher level than most other problem solving books. Many problem solving books place a great emphasis on geometry. Just as the Putnam exam generally replaces synthetic geometry with analysis and abstract and linear algebra (although there are exceptions), so this book replaces the traditional focus on geometry with a focus on analysis and algebra. That said, there is an entire chapter on geometry, but it does not discuss synthetic geometry, instead focusing on vectors, the geometry of the complex plane, analytic geometry, and some special topics that are especially relevant to college mathematics (integrals in geometry, some higher-level results such as the fact that all conics are rational curves, and a brief but still substantive survey of trigonometric substitutions).

Putnam and Beyond discusses many areas of college mathematics that are likely to appear on the Putnam exam but would never appear on the IMO, such as abstract algebra, linear algebra, and real analysis (with a very tiny bit of complex analysis).

That said, this book still does overlap a bit with many other problem solving books.Read more ›

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6 of 7 people found the following review helpful

Very useful collection of Putnam-like math problems

By Chee Lim Cheung on July 10, 2008

Format: Paperback

This book consists of a very useful collection of Putnam-like math problems. Putnam and Beyond is organized for self-study by undergraduate and graduate students who wish to try a lot of competitive math problems.It is also useful for teachers who are preparing their bright students for IMO type (or higher) math competitions. However the book assumes a level of mathematical maturity and prior mathematical knowledge that not many college students possess. Another very useful book for math competitions is The IMO Compendium.

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2 of 2 people found the following review helpful

Has flaws in it.

By Abhi on May 16, 2014

Format: Paperback

It has a rich collection of problems but has flaws. Most of the solutions are correct. It might be highly desirable for a lot of people to posses this book simply based on the fact that it has solutions. But honestly, most problems from famous books like the Art and Craft of Problem Solving by Paul Zeitz have solutions on the internet.

An example in this book is problem 818. The answer is simply wrong. 7^x mod(9) = 4 does not imply that x is even.

Prof. Andrescu has an errata published on his website for this book and you might want to refer to it in case you buy this book. I know that he is a genius and some of his books are really good. This one has some flaws and it puts me off whenever Math books have LOGICAL flaws (not typos mind you) in the solutions that are given at the end. It shows that the author was careless especially when there are multiple LOGICAL flaws.

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Great book! The only thin is make sure you've ...

By Marco campos on August 5, 2015

Format: Paperback Verified Purchase

Great book! The only thin is make sure you've taken up to Real Analysis if you really want to get the full understanding of the content but if you have then definately get this for the Putnam!

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2 of 3 people found the following review helpful

Ivan Borsenco

By Ivan Borsenco on December 31, 2008

Format: Paperback

An excellent book! I found some nice classical and some non-standard methods for solving problems.

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