Product Details

• Amazon Sales Rank: #25048 in Books
• Published on: 2003-05-12
• Original language: English
• Number of items: 1
• Binding: Paperback
• 218 pages

Synopsis
While most mathematical textbooks are devoted to the proof of true statements, this text focuses on counterexamples for proving statements are false. The 13 chapters cover differentiation, Riemann integration, sequences, infinite series, sets of real numbers, functions of two variables, and metric and topological spaces. Originally published by Hol

Customer Reviews

Test the limits !
In my teaching of the basic tools of mathematical analysis; and even going back to my student days, I noticed the hurdle that separates the beautiful definitions from the `messy' examples. Often students tell me that the theory looks so easy, `but how do we construct an example to illustrate the limits of the theory?' -----A counter example?
Part of the difficulty is that the definitions involve quantifiers; and how do you check the quantifier `for all' ? And on top of that, there are the axioms of set theory: the axiom of choice, or one of its equivalent variants.

The lovely little book by Gelbaum-Olmsted was a savior to many of us when we started out in math, and it appeared first in 1961. But I had almost forgotten about it until by accident (while browsing in the bookstore) I stumbled over a new edition of it about a year ago, a lovely Dover reprinted edition. And so affordable !

In all the other books you learn about the wonderful things that are true about convergence, sets on the line or in the plane, modern variants of the so called Fundamental Theorem of Calculus, and in Gelbaum-Olmstead you learn the things that aren't true. And then there are all the lovely Cantor constructions, The Devil's Staircase, space filling curves, and much more; beautiful, but little known constructions going back to Lebesgue, and some to Riemann.

But more importantly the book gives students an edge when they have to do the assigned exercises in your analysis course. Many told me that the book is a 'secret weapon'.

Palle Jorgensen, October 2004.