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Mathematical thinking and writing : a transition to abstract mathematics /
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 giv...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
San Diego, Calif. :
Academic Press,
©2002.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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 Alegbra; 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