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A Bridge to Advanced Mathematicsby Dennis Sentilles
Synopses & Reviews
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.
This helpful "bridge" book offers students the foundations they need to understand advanced mathematics. The two-part treatment provides basic tools and covers sets, relations, functions, mathematical proofs and reasoning, more. 1975 edition.
This helpful "bridge" book offers students the foundations they need to understand advanced mathematics, spanning the gap between practically oriented and theoretically orientated courses. Part 1 provides the most basic tools, examples, and motivation for the manner, method, and material of higher mathematics. Part 2 covers sets, relations, functions, infinite sets, and mathematical proofs and reasoning. 1975 edition.
Table of Contents
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
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