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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.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 049 | |a UAMI | ||
| 100 | 1 | |a Maddox, Randall B. | |
| 245 | 1 | 0 | |a Mathematical thinking and writing : |b a transition to abstract mathematics / |c Randall B. Maddox. |
| 260 | |a San Diego, Calif. : |b Academic Press, |c ©2002. | ||
| 300 | |a 1 online resource (xviii, 304 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 500 | |a Includes index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 7.8 Ring Morphisms7.9 Quotient Rings; Index | |
| 520 | |a 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. | ||
| 546 | |a English. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Proof theory. | |
| 650 | 0 | |a Logic, Symbolic and mathematical. | |
| 650 | 6 | |a Théorie de la preuve. | |
| 650 | 6 | |a Logique symbolique et mathématique. | |
| 650 | 7 | |a MATHEMATICS |x Infinity. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Logic. |2 bisacsh | |
| 650 | 7 | |a Logic, Symbolic and mathematical |2 fast | |
| 650 | 7 | |a Proof theory |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Maddox, Randall B. |t Mathematical thinking and writing. |d San Diego, Calif. : Academic Press, ©2002 |z 0124649769 |z 9780124649767 |w (DLC) 2001091290 |w (OCoLC)48536718 |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=195523 |z Texto completo |
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