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Mathematical Problems and Proofs: Combinatorics, Number Theory, and Geometry [Hardcover]

by Branislav Kisacanin
5.0 out of 5 stars  See all reviews (1 customer review)

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Book Description

October 31, 1998 0306459671 978-0306459672 1999
A gentle introduction to the highly sophisticated world of discrete mathematics, Mathematical Problems and Proofs presents topics ranging from elementary definitions and theorems to advanced topics -- such as cardinal numbers, generating functions, properties of Fibonacci numbers, and Euclidean algorithm. This excellent primer illustrates more than 150 solutions and proofs, thoroughly explained in clear language. The generous historical references and anecdotes interspersed throughout the text create interesting intermissions that will fuel readers' eagerness to inquire further about the topics and some of our greatest mathematicians. The author guides readers through the process of solving enigmatic proofs and problems, and assists them in making the transition from problem solving to theorem proving.
At once a requisite text and an enjoyable read, Mathematical Problems and Proofs is an excellent entrée to discrete mathematics for advanced students interested in mathematics, engineering, and science.


Product Details

  • Hardcover: 220 pages
  • Publisher: Springer; 1999 edition (October 31, 1998)
  • Language: English
  • ISBN-10: 0306459671
  • ISBN-13: 978-0306459672
  • Product Dimensions: 9.2 x 6.4 x 0.8 inches
  • Shipping Weight: 1.1 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #517,913 in Books (See Top 100 in Books)

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18 of 18 people found the following review helpful
5.0 out of 5 stars A Basketful of Gems January 5, 2003
Format:Hardcover
This is a very interesting book. If you have mastered the bare essentials of set theory (through the upside down A for "for all" and the backwards E for "there exists"), AND either 1) the bare essentials of combinatorics (through Pascal's triangle), or 2) the bare essentials of number theory (through the definition of the Moebius function and the statement of the Chinese Remainder theorem), or 3) the bare essentials of geometry (through the law of cosines), AND if you are very talented in mathematics, then this book is a "MUST READ". It matters not whether you are a high school student or a professional mathematician. You will find new and fruitful insights and quite a few interesting problems in this book. For the beginner, there are several tantalizing (but somewhat oversimplified) references to advanced topics such as Paul Cohen's proof of the independence of the continuum hypotheses and Wiles' proof of Fermat's last theorem. For the professional there are footnotes with references to little known and suprising results obtained in the 20th century. But, unlike the claims in the "editorial review", this book neither prepares you to read the literaure nor is it a store house of exercises which will help you take your problem solving abilities to the next level. The "editorial review" is "off", but the book is "right on". Only the title is unfortunate. Where it will help the career mathematician is in the "beer hall" or "coffee house" or "tea time" discussions with other mathematicians. It is just chock full of beautiful little "gems" which can be shared with one's friends. This is the kind of beautiful stuff that makes mathematics truly interesting and exciting and though I have searched for a book like this for the last 35 years, this is by far the best in its class which I have found. Dr. John Aiken, Jan 5, 2003.
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