{"product_id":"the-foundations-of-mathematics-9780470085011","title":"The Foundations of Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eFinally 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePART I  \u003cp\u003eChapter 1: LANGUAGE, LOGIC, AND SETS\u003cbr\u003e 1.1 Logic and Language\u003cbr\u003e 1.2 Implication\u003cbr\u003e 1.3 Quantifiers and Definitions\u003cbr\u003e 1.4 Introduction to Sets\u003cbr\u003e 1.5 Introduction to Number Theory\u003cbr\u003e 1.6 Additional Set Theory\u003cbr\u003e Definitions from Chapter 1\u003cbr\u003e Algebraic and Order Properties of Number Systems\u003c\/p\u003e \u003cp\u003eChapter 2: PROOFS\u003cbr\u003e 2.1 Proof Format I: Direct Proofs\u003cbr\u003e 2.2 Proof Format II: Contrapositive and Contradition\u003cbr\u003e 2.3 Proof Format III: Existence, Uniqueness, Or\u003cbr\u003e 2.4 Proof Format IV: Mathematical Induction\u003cbr\u003e The Fundamental Theorem of Arithmetic\u003cbr\u003e 2.5 Further Advice and Practice in Proving\u003cbr\u003e Proof Formats\u003c\/p\u003e \u003cp\u003eChapter 3: FUNCTIONS\u003cbr\u003e 3.1 Definitions\u003cbr\u003e 3.2 Composition, One-to-One, Onto, and Inverses\u003cbr\u003e 3.3 Images and Pre-Images of Sets\u003cbr\u003e Definitions from Chapter 3\u003c\/p\u003e \u003cp\u003eChapter 4: RELATIONS\u003cbr\u003e 4.1 Relations\u003cbr\u003e 4.2 Equivalence Relations\u003cbr\u003e 4.3 Partitions and Equivalence Relations\u003cbr\u003e 4.4 Partial Orders\u003cbr\u003e Definitions from Chapter 4\u003c\/p\u003e \u003cp\u003ePART II\u003c\/p\u003e \u003cp\u003eChapter 5: INFINTE SETS\u003cbr\u003e 5.1 The Sizes of Sets\u003cbr\u003e 5.2 Countable Sets\u003cbr\u003e 5.3 Uncountable Sets\u003cbr\u003e 5.4 The Axiom of Choice and Its Equivalents\u003cbr\u003e Definitions from Chapter 5\u003c\/p\u003e \u003cp\u003eChapter 6: INTRODUCTION TO DISCRETE MATHEMATICS\u003cbr\u003e 6.1 Graph Theory\u003cbr\u003e 6.2 Trees and Algorithms\u003cbr\u003e 6.3 Counting Principles I\u003cbr\u003e 6.4 Counting Principles II\u003cbr\u003e Definitions from Chapter 6\u003c\/p\u003e \u003cp\u003eChapter 7: INTRODUCTION TO ABSTRACT ALGEBRA\u003cbr\u003e 7.1 Operations and Properties\u003cbr\u003e 7.2 Groups\u003cbr\u003e Groups in Geometry\u003cbr\u003e 7.3 Rings and Fields\u003cbr\u003e 7.4 Lattices\u003cbr\u003e 7.5 Homomorphisms\u003cbr\u003e Definitions from Chapter 7\u003c\/p\u003e \u003cp\u003eChapter 8: INTRODUCTION TO ANALYSIS\u003cbr\u003e 8.1 Real Numbers, Approximations, and Exact Values\u003cbr\u003e Zeno’s Paradoxes\u003cbr\u003e 8.2 Limits of Functions\u003cbr\u003e 8.3 Continuous Functions and Counterexamples\u003cbr\u003e Counterexamples in Rational Analysis\u003cbr\u003e 8.4 Sequences and Series\u003cbr\u003e 8.5 Discrete Dynamical Systems\u003cbr\u003e The Intermediate Value Theorem\u003cbr\u003e Definitions for Chapter 8\u003c\/p\u003e \u003cp\u003eChapter 9: METAMATHEMATICS AND THE PHILOSOPHY OF MATHEMATICS\u003cbr\u003e 9.1 Metamathematics\u003cbr\u003e 9.2 The Philosophy of Mathematics\u003cbr\u003e Definitions for Chapter 9\u003c\/p\u003e \u003cp\u003eAppendix: THE GREEK ALPHABET\u003cbr\u003e Answers: SELECTED ANSWERS\u003c\/p\u003e \u003cp\u003eIndex\u003cbr\u003e List of Symbols\u003cbr\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402281394519,"sku":"9780470085011","price":209.66,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470085011.jpg?v=1730479936","url":"https:\/\/bookcurl.com\/products\/the-foundations-of-mathematics-9780470085011","provider":"Book Curl","version":"1.0","type":"link"}