Fundamentals Of Set And Number Theory
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Author | : Valeriy K. Zakharov |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 448 |
Release | : 2018-02-05 |
Genre | : Mathematics |
ISBN | : 3110550946 |
This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics.The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Fundamentals of the theory of classes, sets, and numbers Characterization of all natural models of Neumann – Bernays – Godel and Zermelo – Fraenkel set theories Local theory of sets as a foundation for category theory and its connection with the Zermelo – Fraenkel set theory Compactness theorem for generalized second-order language
Author | : Joseph Breuer |
Publisher | : Courier Corporation |
Total Pages | : 130 |
Release | : 2012-08-09 |
Genre | : Mathematics |
ISBN | : 0486154874 |
This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.
Author | : Richard Friedberg |
Publisher | : Courier Corporation |
Total Pages | : 241 |
Release | : 2012-07-06 |
Genre | : Mathematics |
ISBN | : 0486152693 |
This witty introduction to number theory deals with the properties of numbers and numbers as abstract concepts. Topics include primes, divisibility, quadratic forms, and related theorems.
Author | : Sean Morris |
Publisher | : Cambridge University Press |
Total Pages | : 221 |
Release | : 2018-12-13 |
Genre | : History |
ISBN | : 110715250X |
Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.
Author | : Oystein Ore |
Publisher | : Courier Corporation |
Total Pages | : 404 |
Release | : 2012-07-06 |
Genre | : Mathematics |
ISBN | : 0486136434 |
Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.
Author | : Keith Devlin |
Publisher | : Springer Science & Business Media |
Total Pages | : 204 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 146120903X |
This text covers the parts of contemporary set theory relevant to other areas of pure mathematics. After a review of "naïve" set theory, it develops the Zermelo-Fraenkel axioms of the theory before discussing the ordinal and cardinal numbers. It then delves into contemporary set theory, covering such topics as the Borel hierarchy and Lebesgue measure. A final chapter presents an alternative conception of set theory useful in computer science.
Author | : Bernd S. W. Schröder |
Publisher | : Wiley |
Total Pages | : 0 |
Release | : 2010-08-16 |
Genre | : Mathematics |
ISBN | : 9780470551387 |
An accessible introduction to abstract mathematics with an emphasis on proof writing Addressing the importance of constructing and understanding mathematical proofs, Fundamentals of Mathematics: An Introduction to Proofs, Logic, Sets, and Numbers introduces key concepts from logic and set theory as well as the fundamental definitions of algebra to prepare readers for further study in the field of mathematics. The author supplies a seamless, hands-on presentation of number systems, utilizing key elements of logic and set theory and encouraging readers to abide by the fundamental rule that you are not allowed to use any results that you have not proved yet. The book begins with a focus on the elements of logic used in everyday mathematical language, exposing readers to standard proof methods and Russell's Paradox. Once this foundation is established, subsequent chapters explore more rigorous mathematical exposition that outlines the requisite elements of Zermelo-Fraenkel set theory and constructs the natural numbers and integers as well as rational, real, and complex numbers in a rigorous, yet accessible manner. Abstraction is introduced as a tool, and special focus is dedicated to concrete, accessible applications, such as public key encryption, that are made possible by abstract ideas. The book concludes with a self-contained proof of Abel's Theorem and an investigation of deeper set theory by introducing the Axiom of Choice, ordinal numbers, and cardinal numbers. Throughout each chapter, proofs are written in much detail with explicit indications that emphasize the main ideas and techniques of proof writing. Exercises at varied levels of mathematical development allow readers to test their understanding of the material, and a related Web site features video presentations for each topic, which can be used along with the book or independently for self-study. Classroom-tested to ensure a fluid and accessible presentation, Fundamentals of Mathematics is an excellent book for mathematics courses on proofs, logic, and set theory at the upper-undergraduate level as well as a supplement for transition courses that prepare students for the rigorous mathematical reasoning of advanced calculus, real analysis, and modern algebra. The book is also a suitable reference for professionals in all areas of mathematics education who are interested in mathematical proofs and the foundation upon which all mathematics is built.
Author | : |
Publisher | : Univalent Foundations |
Total Pages | : 484 |
Release | : |
Genre | : |
ISBN | : |
Author | : Charles C Pinter |
Publisher | : Courier Corporation |
Total Pages | : 259 |
Release | : 2014-07-23 |
Genre | : Mathematics |
ISBN | : 0486497089 |
"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--
Author | : Paul Halmos |
Publisher | : |
Total Pages | : 98 |
Release | : 2019-06 |
Genre | : |
ISBN | : 9781950217014 |
Written by a prominent analyst Paul. R. Halmos, this book is the most famous, popular, and widely used textbook in the subject. The book is readable for its conciseness and clear explanation. This emended edition is with completely new typesetting and corrections. Asymmetry of the book cover is due to a formal display problem. Actual books are printed symmetrically. Please look at the paperback edition for the correct image. The free PDF file available on the publisher's website www.bowwowpress.org