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Set theory and the continuum hypothesis
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Paul J. Cohen
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Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity
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Loren R Graham, Jean-Michel Kantor
In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping - ...
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The Nuts and Bolts of Proofs
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Antonella Cupillari
This book leads readers through a progressive explanation of what mathematical proofs are, why they are important, and how they work, along with a presentation of basic techniques used to construct proofs. The Second Edition presents more examples, more exercises, a more complete treatment of mathematical induction and set theory, and it ...
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An Introduction to Mathematical Reasoning
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Peter Eccles
The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory, topics which include many ...
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The Joy of Sets: Fundamentals of Contemporary Set Theory
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Keith J Devlin
This book is intended to provide an account of those parts of contemporary set theory that are relevant to other areas of pure mathematics. Intended for advanced undergraduates and beginning graduate students, the text is written in an easy-going style, with a minimum of formalism. The book begins with a review of "naive" set theory; it then ...
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Schaum's Outline of Set Theory and Related Topics
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Seymour Lipschutz, Ph.D.
If you want top grades and thorough understanding of set theory and related topics, this powerful study tool is the best tutor you can have! It takes you step-by-step through the subject and gives you 530 accompanying related problems with fully worked solutions. You also get plenty of practice problems to do on your own, working at your own speed ...
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A Concise Introduction to Pure Mathematics
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Martin W Liebeck (Editor)
"A Concise Introduction to Pure Mathematics, Second Edition" provides a robust bridge between high school and university mathematics, expanding upon basic topics in ways that will interest first-year students in mathematics and related fields and stimulate further study. Divided into 22 short chapters, this textbook offers a selection of exercises ...
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Dave's Down-To-Earth Rock Shop
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Stuart J Murphy
As they consider sorting their rock collection by color, size, type, and hardness, Josh and Amy learn that the same objects can be organized in many different ways.
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Set Theory: The Third Millennium Edition, Revised and Expanded
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Thomas Jech
Set Theory has experienced a rapid development in recent years, with major advances in forcing, inner models, large cardinals and descriptive set theory. The present book covers each of these areas, giving the reader an understanding of the ideas involved. It can be used for introductory students and is broad and deep enough to bring the reader ...
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Fuzzy Set Theory - And Its Applications
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Hans-Jurgen Zimmermann
Since its inception, the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of fuzzy technology can be found in artificial intelligence, computer science, control engineering, decision theory, expert systems, logic, management science, operations research, robotics, and others. Theoretical advances have ...
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The Pea and the Sun: A Mathematical Paradox
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Leonard M Wapner
Take an apple and cut it into five pieces. Would you believe that these five pieces can be reassembled in such a manner that would to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the Sun by breaking something so small as a pea into a finite number of pieces and putting it ...
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Introduction to Mathematical Logic
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Elliott Mendelson
This classic in the field is a compact introduction to some of the basic topics of mathematical logic. Major changes in this edition include a new section on semantic trees; an expanded chapter on Axiomatic Set Theory; and full coverage of effective computability, where Turing computability is now the central notion and diagrams (flow-charts) are ...
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In Search of Infinity
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N. Ya Vilenkin, Hardy Grant (Editor), Abe Shenitzer (Translator)
The concept of infinity has been for hundreds of years one of the most fascinating and elusive ideas to tantalize the minds of scholars and lay people alike. The theory of infinite sets lies at the heart of much of mathematics, yet is has produced a series of paradoxes that have led many scholars to doubt the soundness of its foundations. The ...
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The Philosophy of Set Theory: An Historical Introduction to Cantor's Paradise
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Mary Tiles
This volume offers a guided tour of modern mathematics' Garden of Eden, beginning with perspectives on the finite universe and classes and Aristotelian logic. Author Mary Tiles further examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more. 1989 ...
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Notes on Set Theory
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Yiannis N Moschovakis
The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. At the same time, it is often viewed as a foundation of mathematics so that in the most prevalent, current mathematical practice "to make a notion precise" simply means "to define it in set theory." This book ...
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Introduction to the theory of sets
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Joseph Breuer
Set theory permeates much of contemporary mathematical thought. This text for undergraduates offers a natural introduction, developing the subject through observations of the physical world. Its progressive development leads from finite sets to cardinal numbers, infinite cardinals, and ordinals. Exercises appear throughout the text, with answers ...
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Classic Set Theory for Guided Independent Study
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by
Derek Goldrei
Designed for undergraduate students of set theory, "Classic Set Theory" presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes: The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbers; Defining natural numbers in terms of ...
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Logic, Induction and Sets
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Thomas Forster
This is an introduction to logic and the axiomatization of set theory from a unique standpoint. Philosophical considerations, which are often ignored or treated casually, are here given careful consideration, and furthermore the author places the notion of inductively defined sets (recursive datatypes) at the centre of his exposition resulting in ...
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Axiomatic Set Theory
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Paul Bernays
A historical introduction by A. A. Fraenkel to the original Zermelo-Fraenkel form of set-theoretic axiomatics, plus Paul Bernays' independent presentation of a formal system of axiomatic set theory.
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The Continuum and Other Types of Serial Order
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Edward V Huntington
Based on the Dedekind-Cantor ordinal theory, this classic presents the best systematic elementary account of modern theory of the continuum as a type of serial order. 119 footnotes. 1917 edition.
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Set Theory
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Felix Hausdorff
This work is a translation into English of the third edition of the classic German language work "Mengenlehre" by Felix Hausdorff published in 1937.From the Preface (1937): 'The present book has as its purpose an exposition of the most important theorems of the theory of sets, along with complete proofs, so that the reader should not find it ...
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Set Theory for the Working Mathematician
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Krzysztof Ciesielski
This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra. The book begins with a tour of the basics of set theory, culminating in a proof of Zorn's Lemma and a ...
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Set Theory and Its Logic, Revised Edition
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Professor W V Quine
This is an extensively revised edition of Mr. Quine's introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are ...
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An Outline of Set Theory
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James M Henle
An innovative problem-oriented introduction to set theory, this volume is intended for undergraduate courses in which students work in groups on projects and present their solutions to the class. The three-part treatment consists of problems, hints for their solutions, and complete answers. 1986 edition.
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Seaweed Soup
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by
Frank Remkiewicz
To feed all of his friends, Turtle has to mix and match the cups and bowls, and spoons. As more guests arrive, readers can learn about matching sets and the correpsondence between different groups of objects. Full-color illustrations.
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