Mathematical Thinking: Problem-Solving and Proofs

John P. D'Angelo/ Douglas B. West

ISBN 10: 0130144126 / ISBN 13: 9780130144126

Published by Prentice Hall, 1999

About this Item

2nd sub edition. 412 pages. 9.50x6.50x1.00 inches. In Stock.

Seller Inventory # 0130144126

Bibliographic Details

• Title: Mathematical Thinking: Problem-Solving and Proofs
• Publisher: Prentice Hall
• Publication Date: 1999
• Language: English
• ISBN 10: 0130144126
• ISBN 13: 9780130144126
• Binding: Hardcover
• Edition: 2nd Edition
• Condition: Brand New

About this title

Synopsis

This survey of both discrete and continuous mathematics focuses on the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics, rather than on rote symbolic manipulation. Coverage begins with the fundamentals of mathematical language and proof techniques (such as induction); then applies them to easily-understood questions in elementary number theory and counting; then develops additional techniques of proofs via fundamental topics in discrete and continuous mathematics. Topics are addressed in the context of familiar objects; easily-understood, engaging examples; and over 700 stimulating exercises and problems, ranging from simple applications to subtle problems requiring ingenuity. ELEMENTARY CONCEPTS. Numbers, Sets and Functions. Language and Proofs. Properties of Functions. Induction. PROPERTIES OF NUMBERS. Counting and Cardinality. Divisibility. Modular Arithmetic. The Rational Numbers. DISCRETE MATHEMATICS. Combinatorial Reasoning. Two Principles of Counting. Graph Theory. Recurrence Relations. CONTINUOUS MATHEMATICS. The Real Numbers. Sequences and Series. Continuity. Differentiation. Integration. The Complex Numbers. For anyone interested in learning how to understand and write mathematical proofs, or a reference for college professors and high school teachers of mathematics.