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Foundations of Mathematics by Thomas Q. Sibley (2008, Hardcover)
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About this product
Product Identifiers
PublisherWiley & Sons, Incorporated, John
ISBN-100470085010
ISBN-139780470085011
eBay Product ID (ePID)60669340
Product Key Features
Number of Pages408 Pages
Publication NameFoundations of Mathematics
LanguageEnglish
Publication Year2008
SubjectHistory & Philosophy, Logic
TypeTextbook
AuthorThomas Q. Sibley
Subject AreaMathematics
FormatHardcover
Dimensions
Item Height1.1 in
Item Weight24.1 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceCollege Audience
LCCN2011-282213
Dewey Edition22
TitleLeadingThe
IllustratedYes
Dewey Decimal510
Table Of ContentPART I Chapter 1: LANGUAGE, LOGIC, AND SETS 1.1 Logic and Language 1.2 Implication 1.3 Quantifiers and Definitions 1.4 Introduction to Sets 1.5 Introduction to Number Theory 1.6 Additional Set Theory Definitions from Chapter 1 Algebraic and Order Properties of Number Systems Chapter 2: PROOFS 2.1 Proof Format I: Direct Proofs 2.2 Proof Format II: Contrapositive and Contradition 2.3 Proof Format III: Existence, Uniqueness, Or 2.4 Proof Format IV: Mathematical Induction The Fundamental Theorem of Arithmetic 2.5 Further Advice and Practice in Proving Proof Formats Chapter 3: FUNCTIONS 3.1 Definitions 3.2 Composition, One-to-One, Onto, and Inverses 3.3 Images and Pre-Images of Sets Definitions from Chapter 3 Chapter 4: RELATIONS 4.1 Relations 4.2 Equivalence Relations 4.3 Partitions and Equivalence Relations 4.4 Partial Orders Definitions from Chapter 4 PART II Chapter 5: INFINTE SETS 5.1 The Sizes of Sets 5.2 Countable Sets 5.3 Uncountable Sets 5.4 The Axiom of Choice and Its Equivalents Definitions from Chapter 5 Chapter 6: INTRODUCTION TO DISCRETE MATHEMATICS 6.1 Graph Theory 6.2 Trees and Algorithms 6.3 Counting Principles I 6.4 Counting Principles II Definitions from Chapter 6 Chapter 7: INTRODUCTION TO ABSTRACT ALGEBRA 7.1 Operations and Properties 7.2 Groups Groups in Geometry 7.3 Rings and Fields 7.4 Lattices 7.5 Homomorphisms Definitions from Chapter 7 Chapter 8: INTRODUCTION TO ANALYSIS 8.1 Real Numbers, Approximations, and Exact Values Zeno's Paradoxes 8.2 Limits of Functions 8.3 Continuous Functions and Counterexamples Counterexamples in Rational Analysis 8.4 Sequences and Series 8.5 Discrete Dynamical Systems The Intermediate Value Theorem Definitions for Chapter 8 Chapter 9: METAMATHEMATICS AND THE PHILOSOPHY OF MATHEMATICS 9.1 Metamathematics 9.2 The Philosophy of Mathematics Definitions for Chapter 9 Appendix: THE GREEK ALPHABET Answers: SELECTED ANSWERS Index List of Symbols
SynopsisThe Foundations of Mathematics provides a careful introduction to proofs in mathematics, along with basic concepts of logic, set theory and other broadly used areas of mathematics. The concepts are introduced in a pedagogically effective manner without compromising mathematical accuracy and completeness. Thus, in Part I students explore concepts before they use them in proofs. The exercises range from reading comprehension questions and many standard exercises to proving more challenging statements, formulating conjectures and critiquing a variety of false and questionable proofs. The discussion of metamathematics, including Gödel's Theorems, and philosophy of mathematics provides an unusual and valuable addition compared to other similar texts, Finally there's an easy-to-follow book that will help readers succeed in the art of proving theorems. Sibley not only conveys the spirit of mathematics but also uncovers the skills required to succeed. Key definitions are introduced while readers are encouraged to develop an intuition about these concepts and practice using them in problems. With this approach, they'll gain a strong understanding of the mathematical language as they discover how to apply it in order to find proofs., The Foundations of Mathematics provides a careful introduction to proofs in mathematics, along with basic concepts of logic, set theory and other broadly used areas of mathematics. The concepts are introduced in a pedagogically effective manner without compromising mathematical accuracy and completeness. Thus, in Part I students explore concepts before they use them in proofs. The exercises range from reading comprehension questions and many standard exercises to proving more challenging statements, formulating conjectures and critiquing a variety of false and questionable proofs. The discussion of metamathematics, including G del's Theorems, and philosophy of mathematics provides an unusual and valuable addition compared to other similar texts, Finally theres an easy-to-follow book that will help readers succeed in the art of proving theorems. Sibley not only conveys the spirit of mathematics but also uncovers the skills required to succeed. Key definitions are introduced while readers are encouraged to develop an intuition about these concepts and practice using them in problems.
LC Classification NumberQA39.3.S53 2009
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