Elements of Advanced Mathematic
1st Edition
Published on 21. April 1995
Book
Hardback
180 pages
978-0-8493-8491-2 (ISBN)
Description
Clearly written and easy to understand, The Elements of Advanced Mathematics covers logic, set theory, methods of proof, and axiomatic structures, providing an excellent grounding in analytical thinking. It facilitates the transition from elementary mathematics, generally characterized by problem-solving techniques, to advanced mathematics, characterized by theory, rigor, and proofs. This text clearly identifies and explains the components and methods of advanced mathematics. Each chapter contains exercises designed to assist the reader in understanding the material.
More details
Language
English
Place of publication
Bosa Roca
United States
Publishing group
Taylor & Francis Inc
Target group
College/higher education
Audience
Students learning how to read and write mathematical proofs in transition courses
Dimensions
Height: 235 mm
Width: 156 mm
Weight
510 gr
ISBN-13
978-0-8493-8491-2 (9780849384912)
Schweitzer Classification
Other editions
New editions
Steven G. Krantz
The Elements of Advanced Mathematics, Second Edition
Book
01/2002
2nd Edition
CRC Press
€69.51
Article exhausted; check for reprint
Content
Basic Logic: Principles of Logic. Truth. "And" and "Or". "Not". "If-Then". Contrapositive, Converse, and "Iff". Quantifiers. Truth and Provability. Exercises.
Methods of Proof: What is a Proof? Direct Proof. Proof by Contradiction. Proof by Induction. Exercises.
Set Theory: Undefinable Terms. Elements of Set Theory. Venn Diagrams. Further Ideas in Elementary Set Theory. Indexing and Extended Set Operations. Exercises.
Relations and Functions: Relations . Order Relations. Functions. Combining Functions. Cantor's Notion of Cardinality. Exercises.
Axioms of Set Theory, Paradoxes, and Rigor: Axioms of Set Theory. The Axiom of Choice. Set Theory and Arithmetic. Exercises.
Number Systems: Preliminary Remarks. The Natural Number System. The Integers. The Rational Numbers. The Real Number System. The Complex Numbers. The Quaternions, the Cayley Numbers, and Beyond. Exercises.
Examples of Axiomatic Theories: Group Theory. Euclidean and Non-Euclidean Geometry. Exercises. Bibliography. Index.
Methods of Proof: What is a Proof? Direct Proof. Proof by Contradiction. Proof by Induction. Exercises.
Set Theory: Undefinable Terms. Elements of Set Theory. Venn Diagrams. Further Ideas in Elementary Set Theory. Indexing and Extended Set Operations. Exercises.
Relations and Functions: Relations . Order Relations. Functions. Combining Functions. Cantor's Notion of Cardinality. Exercises.
Axioms of Set Theory, Paradoxes, and Rigor: Axioms of Set Theory. The Axiom of Choice. Set Theory and Arithmetic. Exercises.
Number Systems: Preliminary Remarks. The Natural Number System. The Integers. The Rational Numbers. The Real Number System. The Complex Numbers. The Quaternions, the Cayley Numbers, and Beyond. Exercises.
Examples of Axiomatic Theories: Group Theory. Euclidean and Non-Euclidean Geometry. Exercises. Bibliography. Index.