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.
Synopsis
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.
Synopsis
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.
Table of Contents
PrefacePart 1. Starting PointsChapter 1. Logic, Language and MathematicsChapter 2. The Foundations of MathematicsPart 2. The Strategic Attack in MathematicsChapter 3. A Formally Informal Theory of SetsChapter 4. Topology and Connected SetsChapter 5. FunctionsChapter 6. Counting the InfiniteChapter 7. Equivalence RelationsChapter 8. Continuity, Connectedness and CompactnessAppendix AIndex