{"product_id":"mathematical-proofs-a-transition-to-advanced-mathematics-9781292040646","title":"Mathematical Proofs A Transition to Advanced","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003e0. Communicating Mathematics\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eLearning Mathematics\u003c\/p\u003e \u003cp\u003eWhat Others Have Said About Writing\u003c\/p\u003e \u003cp\u003eMathematical Writing\u003c\/p\u003e \u003cp\u003eUsing Symbols\u003c\/p\u003e \u003cp\u003eWriting Mathematical Expressions\u003c\/p\u003e \u003cp\u003eCommon Words and Phrases in Mathematics\u003c\/p\u003e \u003cp\u003eSome Closing Comments About Writing\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e1. Sets\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1. Describing a Set\u003c\/p\u003e \u003cp\u003e1.2. Subsets\u003c\/p\u003e \u003cp\u003e1.3. Set Operations\u003c\/p\u003e \u003cp\u003e1.4. Indexed Collections of Sets\u003c\/p\u003e \u003cp\u003e1.5. Partitions of Sets\u003c\/p\u003e \u003cp\u003e1.6. Cartesian Products of Sets\u003c\/p\u003e \u003cp\u003eExercises for Chapter 1\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e2. Logic\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1. Statements\u003c\/p\u003e \u003cp\u003e2.2. The Negation of a Statement\u003c\/p\u003e \u003cp\u003e2.3. The Disjunction and Conjunction of Statements\u003c\/p\u003e \u003cp\u003e2.4. The Implication\u003c\/p\u003e \u003cp\u003e2.5. More On Implications\u003c\/p\u003e \u003cp\u003e2.6. The Biconditional\u003c\/p\u003e \u003cp\u003e2.7. Tautologies and Contradictions\u003c\/p\u003e \u003cp\u003e2.8. Logical Equivalence\u003c\/p\u003e \u003cp\u003e2.9. Some Fundamental Properties of Logical Equivalence\u003c\/p\u003e \u003cp\u003e2.10. Quantified Statements\u003c\/p\u003e \u003cp\u003e2.11. Characterizations of Statements\u003c\/p\u003e \u003cp\u003eExercises for Chapter 2\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e3. Direct Proof and Proof by Contrapositive\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1. Trivial and Vacuous Proofs\u003c\/p\u003e \u003cp\u003e3.2. Direct Proofs\u003c\/p\u003e \u003cp\u003e3.3. Proof by Contrapositive\u003c\/p\u003e \u003cp\u003e3.4. Proof by Cases\u003c\/p\u003e \u003cp\u003e3.5. Proof Evaluations\u003c\/p\u003e \u003cp\u003eExercises for Chapter 3\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e4. More on Direct Proof and Proof by Contrapositive\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1. Proofs Involving Divisibility of Integers\u003c\/p\u003e \u003cp\u003e4.2. Proofs Involving Congruence of Integers\u003c\/p\u003e \u003cp\u003e4.3. Proofs Involving Real Numbers\u003c\/p\u003e \u003cp\u003e4.4. Proofs Involving Sets\u003c\/p\u003e \u003cp\u003e4.5. Fundamental Properties of Set Operations\u003c\/p\u003e \u003cp\u003e4.6. Proofs Involving Cartesian Products of Sets\u003c\/p\u003e \u003cp\u003eExercises for Chapter 4\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e5. Existence and Proof by Contradiction\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1. Counterexamples\u003c\/p\u003e \u003cp\u003e5.2. Proof by Contradiction\u003c\/p\u003e \u003cp\u003e5.3. A Review of Three Proof Techniques\u003c\/p\u003e \u003cp\u003e5.4. Existence Proofs\u003c\/p\u003e \u003cp\u003e5.5. Disproving Existence Statements\u003c\/p\u003e \u003cp\u003eExercises for Chapter 5\u003c\/p\u003e \u003cp\u003e\u003cb\u003e \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6. Mathematical Induction\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 The Principle of Mathematical Induction\u003c\/p\u003e \u003cp\u003e6.2 A More General Principle of Mathematical Induction\u003c\/p\u003e \u003cp\u003e6.3 Proof By Minimum Counterexample\u003c\/p\u003e \u003cp\u003e6.4 The Strong Principle of Mathematical Induction\u003c\/p\u003e \u003cp\u003eExercises for Chapter 6\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e7. Prove or Disprove\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Conjectures in Mathematics\u003c\/p\u003e \u003cp\u003e7.2 Revisiting Quantified Statements\u003c\/p\u003e \u003cp\u003e7.3 Testing Statements\u003c\/p\u003e \u003cp\u003eExercises for Chapter 7\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e8. Equivalence Relations\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Relations\u003c\/p\u003e \u003cp\u003e8.2 Properties of Relations\u003c\/p\u003e \u003cp\u003e8.3 Equivalence Relations\u003c\/p\u003e \u003cp\u003e8.4 Properties of Equivalence Classes\u003c\/p\u003e \u003cp\u003e8.5 Congruence Modulo \u003ci\u003en\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.6 The Integers Modulo \u003ci\u003en\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eExercises for Chapter 8\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e9. Functions\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 The Definition of Function\u003c\/p\u003e \u003cp\u003e9.2 The Set of All Functions from \u003ci\u003eA\u003c\/i\u003e to \u003ci\u003eB\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.3 One-to-one and Onto Functions\u003c\/p\u003e \u003cp\u003e9.4 Bijective Functions\u003c\/p\u003e \u003cp\u003e9.5 Composition of Functions\u003c\/p\u003e \u003cp\u003e9.6 Inverse Functions\u003c\/p\u003e \u003cp\u003e9.7 Permutations\u003c\/p\u003e \u003cp\u003eExercises for Chapter 9\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e10. Cardinalities of Sets\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Numerically Equivalent Sets\u003c\/p\u003e \u003cp\u003e10.2 Denumerable Sets\u003c\/p\u003e \u003cp\u003e10.3 Uncountable Sets\u003c\/p\u003e \u003cp\u003e10.4 Comparing Cardinalities of Sets\u003c\/p\u003e \u003cp\u003e10.5 The Schröder-Bernstein Theorem\u003c\/p\u003e \u003cp\u003eExercises for Chapter 10\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e11. Proofs in Number Theory\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Divisibility Properties of Integers\u003c\/p\u003e \u003cp\u003e11.2 The Division Algorithm\u003c\/p\u003e \u003cp\u003e11.3 Greatest Common Divisors\u003c\/p\u003e \u003cp\u003e11.4 The Euclidean Algorithm\u003c\/p\u003e \u003cp\u003e11.5 Relatively Prime Integers\u003c\/p\u003e \u003cp\u003e11.6 The Fundamental Theorem of Arithmetic\u003c\/p\u003e \u003cp\u003e11.7 Concepts Involving Sums of Divisors\u003c\/p\u003e \u003cp\u003eExercises for Chapter 11\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e12. Proofs in Calculus\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Limits of Sequences\u003c\/p\u003e \u003cp\u003e12.2 Infinite Series\u003c\/p\u003e \u003cp\u003e12.3 Limits of Functions\u003c\/p\u003e \u003cp\u003e12.4 Fundamental Properties of Limits of Functions\u003c\/p\u003e \u003cp\u003e12.5 Continuity\u003c\/p\u003e \u003cp\u003e12.6 Differentiability\u003c\/p\u003e \u003cp\u003eExercises for Chapter 12\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e13. Proofs in Group Theory\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1\u003c\/p\u003e","brand":"Pearson Education Limited","offers":[{"title":"Default Title","offer_id":48866510963031,"sku":"9781292040646","price":70.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781292040646.jpg?v=1722279006","url":"https:\/\/bookcurl.com\/products\/mathematical-proofs-a-transition-to-advanced-mathematics-9781292040646","provider":"Book Curl","version":"1.0","type":"link"}