Introductory Concepts for Abstract Mathematics | 
 enlarge | Author: Kenneth E. Hummel
Publisher: Chapman & Hall/CRC
Category: Book
List Price: $79.95
Buy New: $79.30
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Rating:  1 reviews
Sales Rank: 918194
Media: Hardcover
Edition: 1
Pages: 344
Number Of Items: 1
Shipping Weight (lbs): 1.5
Dimensions (in): 9.1 x 6.3 x 1
ISBN: 1584881348
Dewey Decimal Number: 510
EAN: 9781584881346
Publication Date: March 23, 2000
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Condition: BRAND NEW
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| Editorial Reviews:
Product Description
Beyond calculus, the world of mathematics grows increasingly abstract and places new and challenging demands on those venturing into that realm. As the focus of calculus instruction has become increasingly computational, it leaves many students ill prepared for more advanced work that requires the ability to understand and construct proofs. Introductory Concepts for Abstract Mathematics helps readers bridge that gap. It teaches them to work with abstract ideas and develop a facility with definitions, theorems, and proofs. They learn logical principles, and to justify arguments not by what seems right, but by strict adherence to principles of logic and proven mathematical assertions - and they learn to write clearly in the language of mathematics The author achieves these goals through a methodical treatment of set theory, relations and functions, and number systems, from the natural to the real. He introduces topics not usually addressed at this level, including the remarkable concepts of infinite sets and transfinite cardinal numbers Introductory Concepts for Abstract Mathematics takes readers into the world beyond calculus and ensures their voyage to that world is successful. It imparts a feeling for the beauty of mathematics and its internal harmony, and inspires an eagerness and increased enthusiasm for moving forward in the study of mathematics.
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| Customer Reviews:
Worth the price! July 28, 2002
Charlie Johnson (Minnetonka, MN USA)
4 out of 4 found this review helpful
I have used this text for a Foundations in Mathematics course, and have subsequently found this book among the best that I have read. It would also be good for self-study, as most of the answers are included in the back--which is essential for a good self-study book at this level of Mathematics. Other books I would recommend are: Morash's "Bridge to Abstract mathematics"; "200% of nothing", "An introduction to mathematical reasoning";and "A transition to higher mathematics". Books I would recommend you don't use for self-study are: How to prove it: a structured approach, and any book which doesn't include solutions. (Once one is comfortable with writing and reading proofs, and with higher math in general, then solutions are not always needed.) This book will introduce the reader to many of the topics that one will find in Abstract Algebra and Real analysis: upper and lower bounds, least upper bound, real number system, epsilon-delta proofs, a little number theory, the uncountability of the reals, trans-finite cardinal arithmetic; also has a nice section on the controversial axiom of choice . On the whole, I would recommed this book.
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