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...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
San Diego, Calif. :
Academic Press,
©2002.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | Includes index. |
| Beschreibung: | 1 online resource (xviii, 304 pages) : illustrations |
| ISBN: | 9780080496474 0080496474 1281012076 9781281012074 9786611012076 6611012079 |
Internformat
MARC
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| 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 | ||
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| 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. | ||
| 650 | 0 | |a Proof theory. |0 http://id.loc.gov/authorities/subjects/sh85107437 | |
| 650 | 0 | |a Logic, Symbolic and mathematical. |0 http://id.loc.gov/authorities/subjects/sh85078115 | |
| 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 | |
| 758 | |i has work: |a Mathematical thinking and writing (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFQV7q9v4pmWkbQBtFcqpK |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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| _version_ | 1816881652404584449 |
| adam_text | |
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| author | Maddox, Randall B. |
| author_GND | http://id.loc.gov/authorities/names/n2001016887 |
| author_facet | Maddox, Randall B. |
| author_role | |
| author_sort | Maddox, Randall B. |
| author_variant | r b m rb rbm |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA9 |
| callnumber-raw | QA9.54 .M34 2002eb |
| callnumber-search | QA9.54 .M34 2002eb |
| callnumber-sort | QA 19.54 M34 42002EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| 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 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 |
| ctrlnum | (OCoLC)166269238 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn166269238 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:16:07Z |
| institution | BVB |
| isbn | 9780080496474 0080496474 1281012076 9781281012074 9786611012076 6611012079 |
| language | English |
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| publisher | Academic Press, |
| record_format | marc |
| spelling | Maddox, Randall B. http://id.loc.gov/authorities/names/n2001016887 Mathematical thinking and writing : a transition to abstract mathematics / Randall B. Maddox. San Diego, Calif. : Academic Press, ©2002. 1 online resource (xviii, 304 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes index. Print version record. 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 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. English. Proof theory. http://id.loc.gov/authorities/subjects/sh85107437 Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Théorie de la preuve. Logique symbolique et mathématique. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Logic, Symbolic and mathematical fast Proof theory fast has work: Mathematical thinking and writing (Text) https://id.oclc.org/worldcat/entity/E39PCFQV7q9v4pmWkbQBtFcqpK https://id.oclc.org/worldcat/ontology/hasWork Print version: Maddox, Randall B. Mathematical thinking and writing. San Diego, Calif. : Academic Press, ©2002 0124649769 9780124649767 (DLC) 2001091290 (OCoLC)48536718 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=195523 Volltext |
| spellingShingle | Maddox, Randall B. Mathematical thinking and writing : a transition to abstract mathematics / 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 Proof theory. http://id.loc.gov/authorities/subjects/sh85107437 Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Théorie de la preuve. Logique symbolique et mathématique. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Logic, Symbolic and mathematical fast Proof theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85107437 http://id.loc.gov/authorities/subjects/sh85078115 |
| title | Mathematical thinking and writing : a transition to abstract mathematics / |
| title_auth | Mathematical thinking and writing : a transition to abstract mathematics / |
| title_exact_search | Mathematical thinking and writing : a transition to abstract mathematics / |
| title_full | Mathematical thinking and writing : a transition to abstract mathematics / Randall B. Maddox. |
| title_fullStr | Mathematical thinking and writing : a transition to abstract mathematics / Randall B. Maddox. |
| title_full_unstemmed | Mathematical thinking and writing : a transition to abstract mathematics / Randall B. Maddox. |
| title_short | Mathematical thinking and writing : |
| title_sort | mathematical thinking and writing a transition to abstract mathematics |
| title_sub | a transition to abstract mathematics / |
| topic | Proof theory. http://id.loc.gov/authorities/subjects/sh85107437 Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Théorie de la preuve. Logique symbolique et mathématique. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Logic, Symbolic and mathematical fast Proof theory fast |
| topic_facet | Proof theory. Logic, Symbolic and mathematical. Théorie de la preuve. Logique symbolique et mathématique. MATHEMATICS Infinity. MATHEMATICS Logic. Logic, Symbolic and mathematical Proof theory |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=195523 |
| work_keys_str_mv | AT maddoxrandallb mathematicalthinkingandwritingatransitiontoabstractmathematics |