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All the Mathematics You Missed: But Need to Know for Graduate School

1 rating: 3.0
A book by Thomas A. Garrity

"This book will fill an interesting niche in a library collection...it should be used by browsing students interested in making sure that they are prepared for success in their graduate programs." Choice    "All the Mathematics You … see full wiki

Author: Thomas A. Garrity
Publisher: Cambridge University Press
1 review about All the Mathematics You Missed: But Need...

Logic is conspicuously absent, otherwise a reasonable survey

  • Jan 13, 2007
While there is some truth to both segments of the title, in my experience there is also a great deal that can be disputed. Many of the topics that Garrity discusses in the book are standard fare in an undergraduate mathematics major. Chapter one is a recapitulation and summary of a basic course in linear algebra, certainly not something that any math major would have missed. The topic of chapter two is epsilon and delta real analysis, the mainstay of first year calculus. Chapter three covers calculus of vector-values functions, a primary topic of third semester calculus. Finally, the basics of abstract algebra, groups, rings and fields, are covered in chapter eleven. Therefore, four of the sixteen chapters describe topics that no math major could have missed.
Some of the other chapters cover topics that may or may not be requirements for completion of a major:

*) Chapter 4 point set topology
*) Chapter 8 geometry
*) Chapter 14 differential equations
*) Chapter 15 combinatorics and probability

However, it is most unlikely that anyone could receive a math major without taking at least two of these courses.
My disputes with the second part of the title are twofold. The first is that the topic may not be needed in graduate school. Chapter thirteen covers Fourier analysis and chapter sixteen algorithms. I am not convinced that graduate students really need to know either of these topics. My second point of dispute is that some of these topics are the basic topics that you study in graduate school. Stokes' Theorem, differential forms, curvature for curves and surfaces, complex analysis, countability and the axiom of choice and Lebesgue integration are all described at a level that I consider to be above the undergraduate.
Putting these criticisms aside, this book is a good survey of most of the topics that you would be expected to master in graduate school. The one conspicuous absence is any mention of logic. The word proposition or even the word logic does not appear in the index, and this is a topic that is needed in graduate school. To me, this is a glaring and unfortunate oversight.

Published in Journal of Recreational Mathematics, reprinted with permission.

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