Doing Mathematics An Introduction to Proofs and Problem-Solving

Name: Doing Mathematics An Introduction to Proofs and Problem-Solving
Price: 30.82 USD
Availability: InStock
ISBN: 9780495108160

ISBN-10: 0495108162

ISBN-13: 9780495108160

Edition: 2nd 2007 (Revised)

Authors: Steven Galovich

List price: $125.95

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This book introduces students to the process of doing mathematics and prepares them to succeed in higher-level mathematics courses. By discussing proof techniques, problem solving methods, and the understanding of mathematical ideas, the book provides a solid foundation for students majoring in mathematics, science, and engineering. Students will learn to grasp the underlying concepts of a subject and how to apply these concepts to solving problems. While being able to understand and reproduce proofs of theorems, they will also gain the ability to comprehend the connections among the important concepts and techniques of each subject. This book is intended for a course on proofs and…

Book details

List price: $125.95
Edition: 2nd
Copyright year: 2007
Publisher: Brooks/Cole
Publication date: 7/7/2006
Binding: Paperback
Pages: 336
Size: 6.50" wide x 9.00" long x 0.50" tall
Weight: 0.990
Language: English



Preface



Solving Problems



How to Solve It



Understanding the Problem



Thinking Logically



Propositional Calculus



Sets



Predicates and Quantifiers



Proving Theorems



Direct Proof



Indirect Proof



Mathematical Induction



Case Analysis



Attacking the Problem/Proof



Looking Back



Sets and Relations



Sets and Set Operations



Relations



Functions



Equivalence Relations



Number Systems and Well-Defined Operations



The Real and Complex Numbers



Cardinality



Equinumerous Sets



Finite Sets



Denumerable Sets



Uncountable Sets



Cardinality and the Cantor-Bernstein Theorem



Discrete Structures



Fundamental Combinatorial Principles



Permutations and Combinations



Binomial Coefficients and the Binomial Theorem



Recurrence Relations



Algebraic Properties of the Integers



Doing Mathematics



Controlling Your Thinking



Attitudes and Beliefs



Problems


References


Hints and Solutions to Selected Exercises


Index