Mathematical Thinking: Problem-Solving and Proofs 2/e (絕)
- 20本以上，享 8.5折
售價
$
洽詢
- 一般書籍
- ISBN：9780132449021
- 作者：John P. D'Angelo
- 版次：2
- 年份：2000
- 出版商：Pearson Education
- 頁數/規格：412頁/平裝單色
書籍介紹
本書特色
目錄
Description
This text is designed to prepare students thoroughly in the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics-skills vital for success throughout the upperclass mathematics curriculum. The text offers both discrete and continuous mathematics, allowing instructors to emphasize one or to present the fundamentals of both. It begins by discussing mathematical language and proof techniques (including induction), applies them to easily-understood questions in elementary number theory and counting, and then develops additional techniques of proof via important topics in discrete and continuous mathematics. The stimulating exercises are acclaimed for their exceptional quality.
This text is designed to prepare students thoroughly in the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics-skills vital for success throughout the upperclass mathematics curriculum. The text offers both discrete and continuous mathematics, allowing instructors to emphasize one or to present the fundamentals of both. It begins by discussing mathematical language and proof techniques (including induction), applies them to easily-understood questions in elementary number theory and counting, and then develops additional techniques of proof via important topics in discrete and continuous mathematics. The stimulating exercises are acclaimed for their exceptional quality.
New to This Edition
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A clearly outlined transition course-Rearranges material to facilitate a clearly defined and more accessible transition course using Chs. 1-5, initial parts of Chs. 6,8 and Chs. 13-14.
＊ By narrowing the focus, makes it easy to present a course with rich content to beginning students in a transition course without overwhelming them. -
“Approaches to Problems”-In selected chapters. Summarizes key points and presents problem-solving strategies relevant to exercises.
＊ In the transition course, helps students organize their understanding of the chapter, avoid typical pitfalls, and learn ways to approach problems of moderate difficulty. -
A clearly outlined analysis course-Now contains an excellent course in analysis using Part I as background, touching briefly on Ch. 8, and covering Part IV in depth.
＊ Provides review reading on proof methods in Part I while being as thorough and accessible as introductory texts in Part IV. -
Expanded and improved selection of exercises-New, easier exercises check mastery of concepts; some difficult exercises are clarified.
＊ Enlarged selection of easier exercises provides greater encouragement for beginning students; clarifications make other exercises more accessible. -
Reorganization of material-Provides smoother development and clearer focus on essential material.
＊ Makes it easier for students to follow the mathematical development and how to know what assumption can be used when working problems. -
Definitions in bold-Terms being defined are in bold type with almost all definitions in numbered terms.
＊ Makes definitions easier for students to find. -
More accessible presentation-Some terse discussions expanded, examples added, and more computations placed in displays.
＊ Makes material easier for students to comprehend and conveys a greater sense of progress by making pages less dense.
Table of Contents
I. ELEMENTARY CONCEPTS
1. Numbers, Sets and Functions
2. Language and Proofs
3. Induction
4. Bijections and Cardinality
II. PROPERTIES OF NUMBERS
5. Combinatorial Reasoning
6. Divisibility
7. Modular Arithmetic
8. The Rational Numbers
III. DISCRETE MATHEMATICS
9. Probability
10. Two Principles of Counting
11. Graph Theory
12. Recurrence Relations
IV. CONTINUOUS MATHEMATICS
13. The Real Numbers
14. Sequences and Series
15. Continuous Functions
16. Differentiation
17. Integration
18. The Complex Numbers
I. ELEMENTARY CONCEPTS
1. Numbers, Sets and Functions
2. Language and Proofs
3. Induction
4. Bijections and Cardinality
II. PROPERTIES OF NUMBERS
5. Combinatorial Reasoning
6. Divisibility
7. Modular Arithmetic
8. The Rational Numbers
III. DISCRETE MATHEMATICS
9. Probability
10. Two Principles of Counting
11. Graph Theory
12. Recurrence Relations
IV. CONTINUOUS MATHEMATICS
13. The Real Numbers
14. Sequences and Series
15. Continuous Functions
16. Differentiation
17. Integration
18. The Complex Numbers
