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Introduction to Abstract Mathematics by Robert J. Bond and William J. Keane (1999, Hardcover)
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Introduction to Abstract Mathematics by Robert J. Bond; William J. Keane Missing dust jacket; Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More, Spend Less
- Buy It NowIntroduction to Abstract Mathematics by Robert J. Bond; William J. Keane
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About this product
Product Identifiers
PublisherBrooks/Cole
ISBN-100534950507
ISBN-139780534950507
eBay Product ID (ePID)964979
Product Key Features
Number of Pages352 Pages
LanguageEnglish
Publication NameIntroduction to Abstract Mathematics
Publication Year1999
SubjectGeneral
TypeTextbook
AuthorRobert J. Bond, William J. Keane
Subject AreaMathematics
FormatHardcover
Dimensions
Item Weight24.9 Oz
Item Length9.8 in
Item Width7.9 in
Additional Product Features
Edition Number1
Intended AudienceCollege Audience
LCCN98-037192
Dewey Edition21
IllustratedYes
Dewey Decimal510
Table Of ContentPREFACE FOR THE INSTRUCTOR / INTRODUCTION TO THE STUDENT 1. MATHEMATICAL REASONING Introduction: Early Greek Mathematicians / Statements / Compound Statements / Implications / Contrapositive and Converse 2. SETS Sets and Subsets / Combining Sets / Collections of Sets 3. FUNCTIONS Definition and Basic Properties / Surjective and Injective Functions / Composition and Invertible Functions 4. BINARY OPERATIONS AND RELATIONS Binary Operations / Equivalence Reactions 5. THE INTEGERS Axioms and Basic Properties / Induction / The Division Algorithm and the Greatest Common Divisors / Primes and Unique Factorization / Congruences / Generalizing a Theorem 6. INFINITE SETS Introduction / Countable Sets / Uncountable Sets, Cantor's Theorem, and the Schroeder-Bernstein Theorem / Collections of Sets 7. THE REAL AND COMPLEX NUMBERS Fields / The Real Numbers / The Complex Numbers 8. POLYNOMIALS Polynomials / Unique Factorization / Polynomials over C, R, and Q / ANSWERS AND HINTS TO SELECTED EXERCISES / INDEX
SynopsisThe goal of this book is to show students how mathematicians think and to glimpse some of the fascinating things they think about. Bond and Keane develop students' ability to do abstract mathematics by teaching the form of mathematics in the context of real and elementary mathematics. Students learn the fundamentals of mathematical logic; how to read and understand definitions, theorems, and proofs; and how to assimilate abstract ideas and communicate them in written form. Students will learn to write mathematical proofs coherently and correctly.
