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Brief Description:
"Dover (2013) republication of the edition originally published by the Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1961"--Page 4 of cover.
Marc Notes:
Dover (2013) republication of the edition originally published by the Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1961--Page 4 of cover.
Table of Contents:
Chapter 1. Introduction -- 1-1. Our program of study -- 1-2. How numbers developed -- 1-3. The mathematician's view of the development of numbers -- 1-4. A word to the reader -- 1-5. Numbers and numerals -- Chapter 2. The Natural Numbers -- 2-1. Introduction -- 2-2. Axioms -- 2-3. Using the axioms -- 2-4. Subtraction and division -- 2-5. Arithmetic in other bases -- 2-6. Structure and isomorphism -- Chapter 3. Sets, Variables, and Statement Forms -- 3-1. Sets -- 3-2. Subsets -- 3-3. Variables and statement forms -- 3-4. Unions, intersections, differences, and products -- Chapter 4. Mappings and Operations -- 4-1. Mapping of a set into a set -- 4-2. Mappings of a set onto a set -- 4-3. One-to-one mappings -- 4-4. Operations on a set -- 4-5. Mathematical systems -- Chapter 5. Groups -- 5-1. Definition of a group. Examples -- 5-2. Inherent properties of a group -- 5-3. Permutation groups -- 5-4. Isomorphisms -- Chapter 6. Relations and Partitions -- 6-1. Relations on a set -- 6-2. Properties of relations -- 6-3. Equivalence relations -- 6-4. Partitions -- 6-5. Order relations -- Chapter 7. The Integers -- 7-1. The relation fu on ∼ N N -- 7-2. The operations (+) and ⊗ on I -- 7-3. The commutativity and associativity of (+) and ⊗ -- 7-4. The number system {I; (+), } -- 7-5. A new notation for the integers -- 7-6. Subtraction and division -- 7-7. A simplified notation for the integers -- 7-8. Integral domains -- 7-9. Congruences -- 7-10. Conclusion -- Chapter 8. The Rational Numbers -- 8-1. Constructing the rationals -- 8-2. The operations + and on the rationals -- 8-3. The commutative and associative laws -- 8-4. Subtraction and division -- 8-5. The cancellation laws -- 8-6. The fractions -- 8-7. Ordering the rationals -- 8-8. Fields -- Chapter 9. The Real Numbers -- 9-1. Introduction -- 9-2. Repeating decimals -- 9-3. Irrational numbers -- 9-4. Sequences of rationals -- 9-5. The real numbers -- 9-6. The infinite decimals -- 9-7. Countability -- 9-8. Completeness of the reals -- Index.
Biographical Note:
John Edward Hafstrom was a Professor of Mathematics and Engineering at the University of Minnesota, Duluth.
Publisher Marketing:
An in-depth survey of some of the most readily applicable essentials of modern mathematics, this concise volume is geared toward undergraduates of all backgrounds as well as future math majors. By focusing on relatively few fundamental concepts, the text delves deeply enough into each subject to challenge students and to offer practical applications.
The opening chapter introduces the program of study and discusses how numbers developed. Subsequent chapters explore the natural numbers; sets, variables, and statement forms; mappings and operations; groups; relations and partitions; integers; and rational and real numbers. Prerequisites include high school courses in elementary algebra and plane geometry.
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