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Chapter Zero: Fundamental Notions of Abstract Mathematics (2nd Edition) - Carol Schumacher
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Carol Schumacher:
Chapter Zero: Fundamental Notions of Abstract Mathematics (2nd Edition) - Livres de poche

2000, ISBN: 0201437244

ID: 14068003274

[EAN: 9780201437249], Neubuch, [PU: Pearson], Mathematics|General, Mathematics|Logic, Education|Decision-Making & Problem Solving, Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: 0. Introduction-an Essay Mathematical Reasoning. Deciding What to Assume. What Is Needed to Do Mathematics? Chapter Zero 1. Logic. True or False. Thought Experiment: True or False. Statements and Predicates. Quantification. Mathematical Statements. Mathematical Implication. Direct Proofs. Compound Statements and Truth Tables. Learning from Truth Tables. Tautologies. What About the Converse? Equivalence and Rephrasing. Negating Statements. Existence Theorems. Uniqueness Theorems. Examples and Counter Examples. Direct Proof. Proof by Contrapositive. Proof by Contradiction. Proving Theorems: What Now? Problems. Questions to Ponder 2. Sets. Sets and Set Notation. Subsets. Set Operations. The Algebra of Sets. The Power Set. Russell's Paradox. Problems. Questions to Ponder. 3. Induction. Mathematical Induction. Using Induction. Complete Induction. Questions to Ponder. 4. Relations. Relations. Orderings. Equivalence Relations. Graphs. Coloring Maps. Problems. Questions to Ponder. 5. Functions. Basic Ideas. Composition and Inverses. Images and Inverse Images. Order Isomorphisms. Sequences. Sequences with Special Properties. Subsequences. Constructing Subsequences Recursively. Binary Operations. Problems. Questions to Ponder 6. Elementary Number Theory. Natural Numbers and Integers. Divisibility in the Integers. The Euclidean Algorithm. Relatively Prime Integers. Prime Factorization. Congruence Modulo n. Divisibility Modulo n. Problems. Questions to Ponder. 7. Cardinality. Galileo's Paradox. Infinite Sets. Countable Sets. Beyond Countability. Comparing Cardinalities. The Continuum Hypothesis. Problems. Questions to Ponder. 8. The Real Numbers. Constructing the Axioms. Arithmetic. Order. The Least Upper Bound Axiom. Sequence Convergence in R. Problems. Questions to Ponder. A. Axiomatic Set Theory. Elementary Axioms. The Axiom of Infinity. Axioms of Choice and Substitution. B. Constructing R. From N to Z. From Z to Q. From Q to R. Index.

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Chapter Zero: Fundamental Notions of Abstract Mathematics (2nd Edition) - Carol Schumacher
Livre non disponible
(*)
Carol Schumacher:
Chapter Zero: Fundamental Notions of Abstract Mathematics (2nd Edition) - Livres de poche

ISBN: 0201437244

[SR: 399669], Paperback, [EAN: 9780201437249], Pearson, Pearson, Book, [PU: Pearson], Pearson, This book is designed for the sophomore/junior level Introduction to Advanced Mathematics course. Written in a modified R.L. Moore fashion, it offers a unique approach in which readers construct their own understanding. However, while readers are called upon to write their own proofs, they are also encouraged to work in groups. There are few finished proofs contained in the text, but the author offers “proof sketches” and helpful technique tips to help readers as they develop their proof writing skills. This book is most successful in a small, seminar style class.   Logic, Sets, Induction, Relations, Functions, Elementary Number Theory, Cardinality, The Real Numbers   For all readers interested in abstract mathematics.<, 13950, Logic, 226698, Pure Mathematics, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 468218, Mathematics, 491542, Algebra & Trigonometry, 491544, Calculus, 491546, Geometry, 491548, Statistics, 468216, Science & Mathematics, 465600, New, Used & Rental Textbooks, 2349030011, Specialty Boutique, 283155, Books

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Chapter Zero: Fundamental Notions of Abstract Mathematics (2nd Edition) - Carol Schumacher
Livre non disponible
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Carol Schumacher:
Chapter Zero: Fundamental Notions of Abstract Mathematics (2nd Edition) - Livres de poche

ISBN: 0201437244

[SR: 399669], Paperback, [EAN: 9780201437249], Pearson, Pearson, Book, [PU: Pearson], Pearson, This book is designed for the sophomore/junior level Introduction to Advanced Mathematics course. Written in a modified R.L. Moore fashion, it offers a unique approach in which readers construct their own understanding. However, while readers are called upon to write their own proofs, they are also encouraged to work in groups. There are few finished proofs contained in the text, but the author offers “proof sketches” and helpful technique tips to help readers as they develop their proof writing skills. This book is most successful in a small, seminar style class.   Logic, Sets, Induction, Relations, Functions, Elementary Number Theory, Cardinality, The Real Numbers   For all readers interested in abstract mathematics.<, 13950, Logic, 226698, Pure Mathematics, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 468218, Mathematics, 491542, Algebra & Trigonometry, 491544, Calculus, 491546, Geometry, 491548, Statistics, 468216, Science & Mathematics, 465600, New, Used & Rental Textbooks, 2349030011, Specialty Boutique, 283155, Books

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Chapter Zero: Fundamental Notions of Abstract Mathematics (2nd Edition) - Carol Schumacher
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Carol Schumacher:
Chapter Zero: Fundamental Notions of Abstract Mathematics (2nd Edition) - Livres de poche

ISBN: 0201437244

[SR: 489441], Paperback, [EAN: 9780201437249], Pearson, Pearson, Book, [PU: Pearson], Pearson, This book is designed for the sophomore/junior level Introduction to Advanced Mathematics course. Written in a modified R.L. Moore fashion, it offers a unique approach in which readers construct their own understanding. However, while readers are called upon to write their own proofs, they are also encouraged to work in groups. There are few finished proofs contained in the text, but the author offers “proof sketches” and helpful technique tips to help readers as they develop their proof writing skills. This book is most successful in a small, seminar style class.   Logic, Sets, Induction, Relations, Functions, Elementary Number Theory, Cardinality, The Real Numbers   For all readers interested in abstract mathematics.<, 13950, Logic, 226698, Pure Mathematics, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 468218, Mathematics, 491542, Algebra & Trigonometry, 491544, Calculus, 491546, Geometry, 491548, Statistics, 468216, Science & Mathematics, 465600, New, Used & Rental Textbooks, 2349030011, Specialty Boutique, 283155, Books

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Chapter Zero: Fundamental Notions of Abstract Mathematics (2nd Edition) - Carol Schumacher
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Carol Schumacher:
Chapter Zero: Fundamental Notions of Abstract Mathematics (2nd Edition) - Livres de poche

ISBN: 0201437244

[SR: 489441], Paperback, [EAN: 9780201437249], Pearson, Pearson, Book, [PU: Pearson], Pearson, This book is designed for the sophomore/junior level Introduction to Advanced Mathematics course. Written in a modified R.L. Moore fashion, it offers a unique approach in which readers construct their own understanding. However, while readers are called upon to write their own proofs, they are also encouraged to work in groups. There are few finished proofs contained in the text, but the author offers “proof sketches” and helpful technique tips to help readers as they develop their proof writing skills. This book is most successful in a small, seminar style class.   Logic, Sets, Induction, Relations, Functions, Elementary Number Theory, Cardinality, The Real Numbers   For all readers interested in abstract mathematics.<, 13950, Logic, 226698, Pure Mathematics, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 468218, Mathematics, 491542, Algebra & Trigonometry, 491544, Calculus, 491546, Geometry, 491548, Statistics, 468216, Science & Mathematics, 465600, New, Used & Rental Textbooks, 2349030011, Specialty Boutique, 283155, Books

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Détails sur le livre
Chapter Zero: Fundamental Notions of Abstract Mathematics
Auteur:

Schumacher, Carol

Titre:

Chapter Zero: Fundamental Notions of Abstract Mathematics

ISBN:

Chapter Zero is designed for the undergraduate level Introduction to AdvancedMathematics course. Written in a modified R.L. Moore fashion, it offers a unique approach in which students construct their own understandings. However, while students are called upon to write their own proofs, they are also encouraged to work in groups. There are few finished proofs contained in the text, but the author offers 'proof sketches' and helpful technique tips to help students as they develop their proof writing skills. This book is most successful in a small, seminar style class. *NEW - Coverage of Isomorphisms and Graph Theory. *Exercise sections have been improved by smoothing out the grade of difficulty. *Proof Sketches. Woven throughout the early chapters of the text, these sketches assist students with proof techniques. *Logic is used as a tool for analyzing the content of mathematical assertions and for constructing valid mathematical proofs. *Rigorous axiomatic treatment of set theory is introduced in Appendices A and B (which are written in the same style as the texts chapters.)

Informations détaillées sur le livre - Chapter Zero: Fundamental Notions of Abstract Mathematics


EAN (ISBN-13): 9780201437249
ISBN (ISBN-10): 0201437244
Version reliée
Livre de poche
Date de parution: 2000
Editeur: ADDISON WESLEY PUB CO INC
192 Pages
Poids: 0,363 kg
Langue: eng/Englisch

Livre dans la base de données depuis 04.06.2007 07:07:19
Livre trouvé récemment le 12.02.2017 21:59:25
ISBN/EAN: 0201437244

ISBN - Autres types d'écriture:
0-201-43724-4, 978-0-201-43724-9


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