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Book Title | : | Basic Language of Mathematics |
| Edition | : | N/A | |
| Author(s) | : | Juan Jorge Schäffer | |
| Page | : | 321 Pages | |
| Year Published | : | 2014 | |
| Publisher | : | World Scientific Publishing Co. Pte. Ltd. | |
| ISBN | : | 978-9814596091 | |
| File Size | : | 2.55 MB | |
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Book Description:
This work is intended to provide a presentation (with some carefully chosen alternatives) of essential ingredients of mathematical discourse. It deals with concepts: set mapping, family, order, natural number, real number, finite and infinite sets, countability; with procedures: proof by induction, recursive definition, fixed-point theorem, and with some immediate applications. It concludes with a sketch of maximality axioms for infinite sets, with the Axiom of Choice and other useful equivalents.
The resulting account was designed to support a component of a comprehensive threesemester honors program, “Mathematical Studies”, conducted for years at Carnegie Mellon University, by the author with the inspiring partnership of Walter Noll.
The author owes special thanks to Ms Nancy J. Watson for her superb and tireless work on the preparation of the manuscript.
The author also records his appreciation of Ms Kwong Lai Fun of World Scientific for her unerring eye and tireless and insightful attention to every detail that have given this work its final polish.
This work is intended to provide a presentation (with some carefully chosen alternatives) of essential ingredients of mathematical discourse. It deals with concepts: set mapping, family, order, natural number, real number, finite and infinite sets, countability; with procedures: proof by induction, recursive definition, fixed-point theorem, and with some immediate applications. It concludes with a sketch of maximality axioms for infinite sets, with the Axiom of Choice and other useful equivalents.
The resulting account was designed to support a component of a comprehensive threesemester honors program, “Mathematical Studies”, conducted for years at Carnegie Mellon University, by the author with the inspiring partnership of Walter Noll.
The author owes special thanks to Ms Nancy J. Watson for her superb and tireless work on the preparation of the manuscript.
The author also records his appreciation of Ms Kwong Lai Fun of World Scientific for her unerring eye and tireless and insightful attention to every detail that have given this work its final polish.
| Table of Contents: | |
| Chapter 1 | SETS. |
| Chapter 2 | MAPPINGS. |
| Chapter 3 | PROPERTIES OF MAPPINGS. |
| Chapter 4 | FAMILIES. |
| Chapter 5 | RELATIONS. |
| Chapter 6 | ORDERED SETS. |
| Chapter 7 | COMPLETELY ORDERED SETS. |
| Chapter 8 | INDUCTION AND RECURSION. |
| Chapter 9 | THE NATURAL NUMBERS. |
| Chapter 10 | FINITE SETS. |
| Chapter 11 | FINITE SUMS. |
| Chapter 12 | COUNTABLE SETS. |
| Chapter 13 | SOME ALGEBRAIC STRUCTURES. |
| Chapter 14 | THE REAL NUMBERS: COMPLETE ORDERED FIELDS. |
| Chapter 15 | STHE REAL-NUMBER SYSTEM. |
| Chapter 16 | THE REAL NUMBERS: EXISTENCE. |
| Chapter 17 | INFINITE SETS. |
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