Overview

TRANSITION TO ADVANCED MATHEMATICS bridges the gap between calculus and advanced math in at least three ways. First, it guides students to think precisely and to express themselves mathematically-to analyze a situation, extract pertinent facts, and draw appropriate conclusions. Second, it provides a firm foundation of the basic concepts and methods needed for continued work. Finally, it provides introductions to concepts of modern algebra and analysis in sufficient depth to capture some of their spirit and characteristics. The text will improve the student's ability to think and write in a mature mathematical fashion and provide a solid understanding of the material most useful for advanced courses.

Full Product Details

Author:   Douglas Smith ,  Maurice Eggen ,  Richard St.Andre
Publisher:   Cengage Learning, Inc
Imprint:   Brooks/Cole
Edition:   International ed
Dimensions:   Width: 18.50cm , Height: 1.50cm , Length: 22.90cm
Weight:   0.568kg
ISBN:  

9780534410193

ISBN 10:   0534410197
Pages:   360
Publication Date:   01 September 2004
Audience:   General/trade ,  College/higher education ,  General ,  Tertiary & Higher Education
Replaced By:   9780495826705
Format:   Paperback
Publisher's Status:   Active
Availability:   Temporarily unavailable  
The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you.

Table of Contents

1. LOGIC AND PROOFS. Propositions and Connectives. Conditionals and Biconditionals. Quantifiers. Basic Proof Methods I. Basic Proof Methods II. Proofs Involving Quantifiers. Additional Examples of Proofs (optional). 2. SET THEORY. Basic Notions of Set Theory. Set Operations. Extended Set Operations and Indexed Families of Sets. Induction. Equivalent Forms of Induction. Principles of Counting (optional). 3. RELATIONS. Cartesian Products and Relations. Equivalence Relations. Partitions. Ordering Relations (optional). Graphs of Relations (optional). 4. FUNCTIONS. Functions as Relations. Constructions of Functions. Functions That Are Onto; One-to-One Functions. Induced Set Functions. Sequences as Functions (optional). 5. CARDINALITY. Equivalent Sets; Finite Sets. Infinite Sets. Countable Sets. The Ordering of Cardinal Numbers. Comparability of Cardinal Numbers and the Axiom of Choice (optional). 6. CONCEPTS OF ALGEBRA: GROUPS (optional). Algebraic Structures. Groups. Examples of Groups. Subgroups. 7. CONCEPTS OF ANALYSIS: COMPLETENESS OF THE REAL NUMBERS (optional). Ordered Field Properties of the Real Numbers. The Heine-Borel Theorem. The Bolzano-Weierstrass Theorem. The Bounded Monotone Sequence Theorem. Equivalents of Completeness. Answers to Exercises. Index. List of Symbols.

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