About this product

Product Identifiers

PublisherAddison-Wesley Longman, Incorporated

ISBN-100201710900

ISBN-139780201710908

eBay Product ID (ePID)2190762

Product Key Features

Number of Pages384 Pages

LanguageEnglish

Publication NameMathematical Proofs : a Transition to Advanced Mathematics

Publication Year2002

SubjectLogic

TypeTextbook

AuthorPing Zhang, Gary Chartrand, Albert D. Polimeni

Subject AreaMathematics

FormatHardcover

Dimensions

Item Height0.6 in

Item Weight23.4 Oz

Item Length9.6 in

Item Width7.7 in

Additional Product Features

Intended AudienceCollege Audience

LCCN2001-055322

Dewey Edition23

IllustratedYes

Dewey Decimal511.3/6

Table Of Content0. Communicating Mathematics. Learning Mathematics. What Others Have Said About Writing. Mathematical Writing. Using Symbols. Writing Mathematical Expressions. Common Words and Phrases in Mathematics. Some Closing Comments About Writing. 1. Sets. Describing a Set. Special Sets. Subsets. Set Operations. Indexed Collections of Sets. Partitions of Sets. Cartesian Products of Sets. 2. Logic. Statements. The Negation of a Statement. The Disjunction and Conjunction of Statements. The Implication. More On Implications. The Biconditional. Tautologies and Contradictions. Logical Equivalence. Some Fundamental Properties of Logical Equivalence. Characterizations of Statements. Quantified Statements and Their Negations. 3. Direct Proof and Proof by Contrapositive. Trivial and Vacuous Proofs. Direct Proofs. Proof by Contrapositive. Proof by Cases. Proof Evaluations. 4. More on Direct Proof and Proof by Contrapositive. Proofs Involving Divisibility of Integers. Proofs Involving Congruence of Integers. Proofs Involving Real Numbers. Proofs Involving Sets. Fundamental Properties of Set Operations. Proofs Involving Cartesian Products of Sets. 5. Proof by Contradiction. Proof by Contradiction. Examples of Proof by Contradiction. The Three Prisoners Problem. Other Examples of Proof by Contradiction. The Irrationality of A2. A Review of the Three Proof Techniques. 6. Prove or Disprove. Conjectures in Mathematics. A Review of Quantifiers. Existence Proofs. A Review of Negations of Quantified Statements. Counterexamples. Disproving Stateme

SynopsisThis text is designed to prepare students for the more abstract mathematics courses that follow calculus. It introduces students to proof techniques and advises them on how to write proofs of their own., Mathematical Proofs is designed to prepare students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise providing solid introductions to relations, functions, and cardinalities of sets.

LC Classification NumberQA9.54.C48 2002