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A Survey of Arithmetic

by Steven K. Atiyah

410 pages; quality trade paperback (softcover); illustrated; catalogue #05-0042; ISBN 1-4120-5147-9; US$44.95, C$56.00, EUR36.40, £25.23

A Survey of Arithmetic is a book that contains all the basic information that is needed to prepare you for the ensuing math courses like algebra, calculus, etc....

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About the Book      About the Author      Excerpts      Catalogue Information

About the Book

The title of this book describes very well its content. The first three chapters deal primarily with the laws and operations of arithmetic---the laws of exponents; common fractions, decimal fractions, and percentages; the rules of divisibility 2 through 12 and beyond; finding the GCD and LCM; using the Euclidean algorithm to find the GCD of two large positive integers; finding the number of positive divisors of a given integer; determining whether a given positive integer is prime or composite, or whether it is rational or irrational; and many many other basic rules and components of arithmetic.

The theory of sets is covered in chapter 4. Also covered here is the principle of duality, the binomial expansion theorem, and a demonstration showing that a repeating decimal is a rational number.

Chapter 5 discusses the properties of the real numbers. Many rules of arithmetic which are normally accepted without challenge, are proven here.

In chapter 6, numbers are expressed in expanded form, i.e., in powers of ten, and the processes of addition, subtraction, multiplication, and division are carried out using these expanded forms to justify the process of place-value carry-overs.

Mensuration, dimensional analysis, and measurement are discussed in chapter 7. The British and metric systems are introduced, and a bridge between them is established. The meaning of accurate, and precise measurements is given; and the greatest possible error, and relative error of measurements are explained.

In chapter 8, arithmetic, geometric, and other patterns of sequences are investigated. Numbers to bases other than base ten are discussed.

Application problems in probability and consumer math are given in the last chapter. These include simple and compound interest laws; percent mark-ups and mark-downs; annulityl; combination and permutation, and permutation of things where some are identical; and multistage experiments with tree diagrams.

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About the Author

A Ph.D in Math Education with emphasis in statistical methods; a Master's and beyond in Theoretical and Applied Mathematics; and a B.S. in Chemical Engineering with emphasis on petroleum refining engineering. The author retired from the Old Dominion University in December of 2000 after 36 years of teaching undergraduate and graduate courses in mathematics. The author is presently teaching part time for Old Dominion University and Tidewater Community College.

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Excerpts

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Catalogue Information

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