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53 of 57 people found the following review helpful
Excellent Foundational Text
on October 11, 1997
I have the fifth edition of the text, which is now in its eight edition. This is an excellent book, and it is very entertaining to read--a description that does not fit many mathematics textbooks. Although geared for students without much math background, it is an enjoyable read for all, with its engaging sidebars, its sense of the history, and believe it or not, a sense of humor (for instance, a problem requiring you to create a Venn diagram for the topics of country songs--truckers, prison and love).
A a philosopher, it is refreshing that the first 100 pages are devoted to set theory and logic--something that is not focused on often enough in basic courses. Most topics are likewise presented with a philosophical angle--for example, the first page points out the problems with defining "set." Utlimately, all definitions of set are circular--does this make "set" undisputably axiomatic? These kinds of problems are at least implied throughout the text. The effect is as deligtful as it is rare. You are not given the sense that the subject matter is complete, instead you are inspired to solve the dilemmas. While the incompleteness and conundrums are common knowledge to mathematics graduate students, they are not frequently imparted to students taking basic courses.
That is a shame. When I was in high school, I felt turned off from math--as did many of my friends, because it was presented as a dry, static subject. Memorizing formulas and theorems was like memorizing the Gettysburg Address. Mathematical Ideas does the opposite--it shows an open door for creative problem solving and makes you hungry to explore.