Mathematical thinking and writing : a transition to abstract mathematics / Randall B. Maddox.

Format:

Book

Author/Creator:

Maddox, Randall B.

Language:

English

Subjects (All):

Proof theory.

Logic, Symbolic and mathematical.

Physical Description:

1 online resource (323 p.)

Place of Publication:

San Diego, Calif. : Academic Press, c2002.

Language Note:

English

Summary:

The ability to construct proofs is one of the most challenging aspects of the world of mathematics. It is, essentially, the defining moment for those testing the waters in a mathematical career. Instead of being submerged to the point of drowning, readers of Mathematical Thinking and Writing are given guidance and support while learning the language of proof construction and critical analysis. Randall Maddox guides the reader with a warm, conversational style, through the task of gaining a thorough understanding of the proof process, and encourages inexperienced mathematicians to step

Contents:

Cover; Contents; Why Read This Book?; Preface; Chapter 0. Notation and Assumptions; 0.1 Set Terminology and Notation; 0.2 Assumptions; Part I: Foundations of Logic and Proof Writing; Chapter 1. Logic; 1.1 Introduction to Logic; 1.2 If-Then Statements; 1.3 Universal and Existential Quantifiers; 1.4 Negations of Statements; Chapter 2. Beginner-Level Proofs; 2.1 Proofs Involving Sets; 2.2 Indexed Families of Sets; 2.3 Algebraic and Ordering Properties of R; 2.4 The Principle of Mathematical Induction; 2.5 Equivalence Relations: The Idea of Equality; 2.6 Equality, Addition, and Multiplication inQ

2.7 The Division Algorithm and Divisibility2.8 Roots and irrational numbers; 2.9 Relations In General; Chapter 3. Functions; 3.1 Definitions and Terminology; 3.2 Composition and Inverse Functions; 3.3 Cardinality of Sets; 3.4 Counting Methods and the Binomial Theorem; Part II: Basic Priniciples of Analysis; Chapter 4. The Real Numbers; 4.1 The Least Upper Bound Axiom; 4.2 Sets in R; 4.3 Limit Points and Closure of Sets; 4.4 Compactness; 4.5 Sequences in R; 4.6 Convergence of Sequences; 4.7 The Nested Interval Property; 4.8 Cauchy Sequences; Chapter 5. Functions of a Real Variable

5.1 Bounded and Monotone Functions5.2 Limits and Their Basic Properties; 5.3 More on Limits; 5.4 Limits Involving Infinity; 5.5 Continuity; 5.6 Implications of Continuity; 5.7 Uniform Continuity; Part III: Basic Principles of Algebra; Chapter 6. Groups; 6.1 Introduction to Groups; 6.2 Generated and Cyclic Subgroups; 6.3 Integers Modulo n and Quotient Groups; 6.4 Permutation Groups and Normal Subgroups; 6.5 Group Morphisms; Chapter 7. Rings; 7.1 Rings and Subrings; 7.2 Ring Properties and Fields; 7.3 Ring Extensions; 7.4 Ideals; 7.5 Integral Domains; 7.6 UFDs and PIDs; 7.7 Euclidean Domains

7.8 Ring Morphisms7.9 Quotient Rings; Index

Notes:

Includes index.

ISBN:

1-281-01207-6

9786611012076

0-08-049647-4

OCLC:

476069793