The Mathematical Foundations of Mixing the Linked Twist Maps as a Paradigm in Applications

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Mixing processes occur in many technological and natural applications, with length and time scales ranging from the very small to the very large. The diversity of problems can give rise to a diversity of approaches. Are there concepts that are central to all of them? Are there tools that allow for prediction and quantification? The authors show how a variety of flows in very different settings possess the characteristic of streamline crossing. This notion can be placed on firm mathematical footing via Linked Twist Maps (LTMs), which is the central organizing principle of this book. The authors discuss the definition and construction of LTMs, provide examples of specific mixers that can be analyzed in the LTM framework and introduce a number of mathematical techniques which are then brought to bear on the problem of fluid mixing. In a final chapter, they present a number of open problems and new directions. First book explaining new important ideas in our understanding of how fluids mix Authors are well-known book writers and leading researchers Starts with a broad, accessible and thought-provoking chapter, and ends with a collection of open problems

Set Theory and Foundations of Mathematics: An Introduction to Mathematical Logic Volume II: Foundations of Mathematics

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This book provides an introduction to mathematical logic and the foundations of mathematics. It will help prepare students for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra. The presentation of finite state and Turing machines leads to the Halting Problem and Gödel's Incompleteness Theorem, which have broad academic interest, particularly in computer science and philosophy. Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Introduction Contents: Preface About the Authors Introduction Propositional Logic Predicate Logic Models of Predicate Logic Boolean Algebras Computability Decidable and Undecidable Theories Algorithmic Randomness Nonstandard Numbers Foundations of Geometry Bibliography Index Readership: Advanced undergraduate or beginning graduate students interested in mathematical logic, mathematics, computer science, and philosophy.

FOUNDATIONS OF HIGHER MATHEMATICS (3版)

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書名：FOUNDATIONS OF HIGHER MATHEMATICS 3/E 作者：FLETCHER 出版社：Cengage Learning 出版日期：1995/11/00 ISBN：9780534951665 目錄 1. The Logic and Language of Proofs 2. Sets 3. Mathematical Induction 4. Relations and Orders 5. Functions 6. Combinatorial Proofs 7. Countable and Uncountable Sets 8. Introduction to Groups 9. Foundations of Advanced Calculus References / Selected Answers and Hints / Index