Essentials of Mathematics: Introduction to Theory, Proof, and the Professional Culture (Mathematical Association of America Textbooks)

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As a youngster, I loved baseball and read everything I could about how to play the game. Each book that I read started with the line, "You must first learn the fundamentals." This also applies to mathematics, where there is a small set of axioms, definitions and theorems that form the basis of most of what else can be learned. Many teachers have started applying this approach to their teaching of mathematics and are beginning to offer a class in the fundamentals of mathematics early in the undergraduate curriculum. This book is an introduction to the fundamentals, as well as the theory and philosophy of mathematics.
The coverage begins with a basic explanation of what mathematics is, what kind of people do mathematics and some of the ways in which it is split into categories. Chapter one is a survey of the fundamentals of logic and chapter two covers set theory. Each of the next four chapters contains a brief coverage of the sets of numbers in increasing order of containment. The natural numbers are described in chapter three, the rational numbers in chapter four, the real numbers in chapter five and the complex numbers in chapter six. The explanations are well-done and a large number of exercises that advance your understanding are included.
Written in a style well within the knowledge base of the beginning undergraduate math major, this is a book that can be used in courses in the fundamentals of mathematics. The highly motivated individual could also use it in a plan of self-study.

Published in the recreational mathematics e-mail newsletter, reprinted with permission.


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Essentials of Mathematics: Introduction to Theory, Proof, and the Professional Culture (Mathematical Association of America Textbooks) Overviews

Essentials of Mathematics is designed as both a textbook and outside reading for college students who want to prepare themselves for mathematics courses beyond the first-year level. The mathematical content includes logic, set theory and a theoretical development of the number systems, giving students practice at proving mathematical statements. There are no answers in the book, but a separate manual provides instructor support. The book makes an excellent reference for students beginning to take courses in which proofs play a major role. In addition to the course material, there are narratives on the nature of mathematics and the mathematics profession. These sections can be read without help or guidance.

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