This helpful workbook-style """"bridge"""" book introduces students to the foundations of advanced mathematics, spanning the gap between a practically oriented calculus sequence and subsequent courses in algebra and analysis with a more theoretical slant. Part 1 focuses on logic and number systems, providing the most basic tools, examples, and motivation for the manner, method, and concerns of higher mathematics. Part 2 covers sets, relations, functions, infinite sets, and mathematical proofs and reasoning. Author Dennis Sentilles also discusses the history and development of mathematics as well as the reasons behind axiom systems and their uses. He assumes no prior knowledge of proofs or logic, and he takes an intuitive approach that builds into a formal development. Advanced undergraduate students of mathematics and engineering will find this volume an excellent source of instruction, reinforcement, and review.
By:
Dennis Sentilles
Imprint: Dover
Country of Publication: United States
Dimensions:
Height: 234mm,
Width: 164mm,
Spine: 20mm
Weight: 580g
ISBN: 9780486482194
ISBN 10: 0486482197
Series: Dover Books on Mathema 1.4tics
Pages: 387
Publication Date: 18 August 2011
Audience:
College/higher education
,
Professional and scholarly
,
Primary
,
Undergraduate
Format: Paperback
Publisher's Status: Unspecified
Preface Part 1. Starting Points Chapter 1. Logic, Language and Mathematics Chapter 2. The Foundations of Mathematics Part 2. The Strategic Attack in Mathematics Chapter 3. A Formally Informal Theory of Sets Chapter 4. Topology and Connected Sets Chapter 5. Functions Chapter 6. Counting the Infinite Chapter 7. Equivalence Relations Chapter 8. Continuity, Connectedness and Compactness Appendix A Index
