Elements of advanced mathematics. (2012)

• Record Type: Book
• Further Information: Note: Steven G. Krantz.
• Other Names: Krantz, Steven G (Steven George), 1951-
• Contents: Basic Logic; Principles of Logic; Truth; "And" and "Or"; "Not"; "If-Then"; Contrapositive, Converse, and "Iff"; Quantifiers; Truth and Provability Methods of Proof; What Is a Proof?; Direct Proof; Proof by Contradiction; Proof by Induction; Other Methods of Proof Set Theory; Undefinable Terms; Elements of Set Theory; Venn Diagrams; Further Ideas in Elementary Set Theory; Indexing and Extended Set Operations Relations and Functions; Relations; Order Relations; Functions; Combining Functions; Cantor’s Notion of Cardinality Axioms of Set Theory, Paradoxes, and Rigor; Axioms of Set Theory; The Axiom of Choice; Independence and Consistency; Set Theory and Arithmetic Number Systems; The Natural Number System; The Integers; The Rational Numbers; The Real Number System; The Nonstandard Real Number System; The Complex Numbers; The Quaternions, the Cayley Numbers, and Beyond More on the Real Number System; Introductory Remark; Sequences; Open Sets and Closed Sets; Compact Sets; The Cantor Set A Glimpse of Topology; What Is Topology?; First Definitions; Mappings; The Separation Axioms; Compactness Theoretical Computer Science; Introductory Remarks; Primitive Recursive Functions; General Recursive Functions; Description of Boolean Algebra; Axioms of Boolean Algebra; Theorems in Boolean Algebra; Illustration of the Use of Boolean Logic; The Robbins Conjecture The P/NP Problem; Introduction; The Complexity of a Problem; Comparing Polynomial and Exponential Complexity; Polynomial Complexity; Assertions That Can Be Verified in Polynomial Time; Nondeterministic Turing Machines; Foundations of NP-Completeness; Polynomial Equivalence; Definition of NP-Completeness Examples of Axiomatic Theories; Group Theory; Euclidean and Non-Euclidean Geometry Zero-Knowledge Proofs; Basics and Background; Preparation for RSA; The RSA System Enunciated; The RSA Encryption System Explicated; Zero-Knowledge Proofs Solutions to Selected Exercises Bibliography Index Exercises appear at the end of each chapter.
• Edition: 3rd ed
• Publisher Details: Boca Raton : Chapman and Hall/CRC
• Publication Date: 2012
• Extent: 1 online resource (xvi, 351 pages), illustrations
• Subjects: 510; Mathematics; MATHEMATICS -- General; MATHEMATICS -- Algebra -- General; MATHEMATICS -- Set Theory; Mathematics; Mathematische Logik; Mengenlehre; Zahlentheorie; Theoretische Informatik; Electronic books
• Languages: English
• ISBNs: 9781439898352; 1439898359
• Related ISBNs: 9781439898345; 1439898340
• Notes: Note: Includes bibliographical references and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.