A Transition to Advanced Mathematics ( ADM )

Publication series :ADM

Author: Doug Smith;Maurice Eggen;Richard St. Andre  

Publisher: Cengage‎

Publication year: 2011

E-ISBN: 9781133385691

P-ISBN(Paperback): 9780495562023

Subject: O1 Mathematics

Keyword: 数学

Language: ENG

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Description

A TRANSITION TO ADVANCED MATHEMATICS helps students make the transition from calculus to more proofs-oriented mathematical study. The most successful text of its kind, the 7th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically—to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors place continuous emphasis throughout on improving students' ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. Students will come away with a solid intuition for the types of mathematical reasoning they'll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems.教学资源:教师手册、Exercise Migration from 6th Edition。 教学资源目前仅能提供给老师,获取方式如下: 1. 邮箱获取:将教辅需求发邮件至asia.infochina@cengage.com 2. 电话获取:010-83435111 3. 微信获取:关注我们的公众号,会由客服人员答疑解惑 公众号名称:圣智教育服务中心 微信号:Cengage_Learning 4. QQ获取:加入我们的QQ群 群名称:圣智教育服务中心 群号:658668132

Chapter

1.2 Conditionals and Biconditionals

1.3 Quantifiers

1.4 Basic Proof Methods Ⅰ

1.5 Basic Proof Methods Ⅱ

1.6 Proofs Involving Quantifiers

1.7 Additional Examples of Proofs

CHAPTER 2 Set Theory

2.1 Basic Concepts of Set Theory

2.2 Set Operations

2.3 Extended Set Operations and Indexed Families of Sets

2.4 Mathematical Induction

2.5 Equivalent Forms of Induction

2.6 Principles of Counting

CHAPTER 3 Relations and Partitions

3.1 Cartesian Products and Relations

3.2 Equivalence Relations

3.3 Partitions

3.4 Ordering Relations

3.5 Graphs

CHAPTER 4 Functions

4.1 Functions as Relations

4.2 Constructions of Functions

4.3 Functions That Are Onto;One-to-One Functions

4.4 One-to-One Correspondences and Inverse Functions

4.5 Images of Sets

4.6 Sequences

CHAPTER 5 Cardinality

5.1 Equivalent Sets;Finite Sets

5.2 Infinite Sets

5.3 Countable Sets

5.4 The Ordering of Cardinal Numbers

5.5 Comparability of Cardinal Numbers and the Axiom of Choice

CHAPTER 6 Concepts of Algebra

6.1 Algebraic Structures

6.2 Groups

6.3 Subgroups

6.4 Operation Preserving Maps

6.5 Rings and Fields

CHAPTER 7 Concepts of Analysis

7.1 Completeness of the Real Numbers

7.2 The Heine-Borel Theorem

7.3 The Bolzano-Weierstrass Theorem

7.4 The Bounded Monotone Sequence Theorem

7.5 Equivalents of Completeness

Answers to Selected Exercises

Index

LIST OF SYMBOLS

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