The Joy of Sets PDF Download

Author: Keith Devlin
Publisher: Springer Science & Business Media
ISBN: 146120903X
Category : Mathematics
Languages : en
Pages : 204

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Book Description
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: Chris Horrocks
Publisher: Reaktion Books
ISBN: 1780237839
Category : History
Languages : en
Pages : 283

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Book Description
It is a modern activity, one of the primary ways we consume information and entertainment, something we’ll do over dinner, at a bar, or even standing on the street peering into a store window—watch TV. Many of us spend countless hours in front of the tube, and even those of us who have proudly eliminated it from our lives can probably still rattle off the names of today’s most popular shows. But for as crucial as television viewing is in modern culture, the television set itself, as a ubiquitous object in our environment, rarely captures our attention—turn one off and it seems to all but disappear. In this book, Chris Horrocks tells the story of the television set, exploring its contradictory presence in our lives as both a material object and a conveyor of illusory images. Horrocks begins in the nineteenth century and television’s prehistory as a fantastic, futuristic concept. He follows the television’s journey from its strange roots in spiritualism, imperialism, and Victorian experiments in electro-magnetism to the contested accounts of its actual invention, looking at the work of engineering pioneers such as Philo Farnsworth and John Logie Baird. Unboxing sets all across the world, he details how it arrived as an essential consumer product and began to play an extraordinary role as a bridge between public and private life. Horrocks describes how the console and cabinet themselves expressed status and good taste and how their designs drew on cultural phenomena such as the space race and the avant-garde. He discusses how we have both loved it for what it can provide and reviled it as a sinister object literally controlling our thoughts, and he shows how it has figured in other cultural realms, such as the work of artists like Wolf Vostell and Nam June Paik. Finally, Horrock laments the death of the cathode ray tube and the emergence of the flat-screen, which has reduced the presence of the television as a significant material object. Altogether, The Joy of Sets brings this most elusive object into crystal-clear critical and historical focus.

Author: Liz McMahon
Publisher: Princeton University Press
ISBN: 0691192324
Category : Games & Activities
Languages : en
Pages : 320

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Book Description
"Have you ever played the addictive card game SET? Have you ever wondered about the connections between games and mathematics? . . . The Joy of SET takes readers on a fascinating journey into this seemingly simple card game and reveals its surprisingly deep and diverse mathematical dimensions. Absolutely no mathematical background is necessary to enjoy this book - all you need is a sense of curiosity and adventure. Originally invented in 1974 by Marsha Falco and officially released in 1991, SET has gained a widespread, loyal following. SET's eighty-one cards consist of one, two, or three symbols of different shapes (diamond, oval, squiggle), shadings (solid, striped, open), and colors (green, purple, red). In order to win, players must identify 'sets' of three cards for which each characteristic is the same - or different - on all the cards. SET's strategic and unique design opens connections to a plethora of mathematical disciplines, including geometry, modular arithmetic, combinatorics, probability, linear algebra, and computer simulations. The Joy of SET looks at these areas as well as avenues for further mathematical exploration. As the authors show, the relationship between SET and mathematics runs in both directions - playing this game has generated new mathematics, and the math has led to new questions about the game itself."--Provided by publisher.

Author: Keith J. Devlin
Publisher: Springer
ISBN: 9783540940944
Category : Mengenlehre
Languages : en
Pages : 192

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Book Description
"This book provides 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 develops the Zermelo-Fraenkel axioms of the theory, showing how they arise naturally from a rigorous answer to the question, "what is a set?" After discussing the ordinal and cardinal numbers, the book then delves into contemporary set theory, covering such topics as: the Borel hierarchy, stationary sets and regressive functions, and Lebesgue measure. Two chapters present an extension of the Zermelo-Fraenkel theory, discussing the axiom of constructibility and the question of provability in set theory. A final chapter presents an account of an alternative conception of set theory that has proved useful in computer science, the non-well-founded set theory of Peter Aczel"--Back cover.

Author: K. J. Devlin
Publisher: Springer Science & Business Media
ISBN: 1468400843
Category : Mathematics
Languages : en
Pages : 191

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Book Description
This book is intended to provide an account of those parts of contemporary set theory which are of direct relevance to other areas of pure mathematics. The intended reader is either an advanced level undergraduate, or a beginning graduate student in mathematics, or else an accomplished mathematician who desires or needs a familiarity with modern set theory. The book is written in a fairly easy going style, with a minimum of formalism (a format characteristic of contemporary set theory) • In Chapter I the basic principles of set theory are developed in a "naive" tl manner. Here the notions of "set I II union " , "intersection", "power set" I "relation" I "function" etc. are defined and discussed. One assumption in writing this chapter has been that whereas the reader may have met all of these concepts before, and be familiar with their usage, he may not have considered the various notions as forming part of the continuous development of a pure subject (namely set theory) • Consequently, our development is at the same time rigorous and fast. Chapter II develops the theory of sets proper. Starting with the naive set theory of Chapter I, we begin by asking the question "What is a set?" Attempts to give a rLgorous answer lead naturally to the axioms of set theory introduced by Zermelo and Fraenkel, which is the system taken as basic in this book.

Author: Chris P. Tsokos
Publisher: Academic Press
ISBN: 0128029854
Category : Mathematics
Languages : en
Pages : 556

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Book Description
The Joy of Finite Mathematics: The Language and Art of Math teaches students basic finite mathematics through a foundational understanding of the underlying symbolic language and its many dialects, including logic, set theory, combinatorics (counting), probability, statistics, geometry, algebra, and finance. Through detailed explanations of the concepts, step-by-step procedures, and clearly defined formulae, readers learn to apply math to subjects ranging from reason (logic) to finance (personal budget), making this interactive and engaging book appropriate for non-science, undergraduate students in the liberal arts, social sciences, finance, economics, and other humanities areas. The authors utilize important historical facts, pose interesting and relevant questions, and reference real-world events to challenge, inspire, and motivate students to learn the subject of mathematical thinking and its relevance. The book is based on the authors’ experience teaching Liberal Arts Math and other courses to students of various backgrounds and majors, and is also appropriate for preparing students for Florida’s CLAST exam or similar core requirements. Highlighted definitions, rules, methods, and procedures, and abundant tables, diagrams, and graphs, clearly illustrate important concepts and methods Provides end-of-chapter vocabulary and concept reviews, as well as robust review exercises and a practice test Contains information relevant to a wide range of topics, including symbolic language, contemporary math, liberal arts math, social sciences math, basic math for finance, math for humanities, probability, and the C.L.A.S.T. exam Optional advanced sections and challenging problems are included for use at the discretion of the instructor Online resources include PowerPoint Presentations for instructors and a useful student manual

Author: Steven Henry Strogatz
Publisher: Houghton Mifflin Harcourt
ISBN: 0547517653
Category : Mathematics
Languages : en
Pages : 333

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Book Description
A delightful tour of the greatest ideas of math, showing how math intersects with philosophy, science, art, business, current events, and everyday life, by an acclaimed science communicator and regular contributor to the "New York Times."

Author: D.L. Johnson
Publisher: Springer Science & Business Media
ISBN: 1447106032
Category : Mathematics
Languages : en
Pages : 179

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Book Description
In mathematics we are interested in why a particular formula is true. Intuition and statistical evidence are insufficient, so we need to construct a formal logical proof. The purpose of this book is to describe why such proofs are important, what they are made of, how to recognize valid ones, how to distinguish different kinds, and how to construct them. This book is written for 1st year students with no previous experience of formulating proofs. Dave Johnson has drawn from his considerable experience to provide a text that concentrates on the most important elements of the subject using clear, simple explanations that require no background knowledge of logic. It gives many useful examples and problems, many with fully-worked solutions at the end of the book. In addition to a comprehensive index, there is also a useful `Dramatis Personae` an index to the many symbols introduced in the text, most of which will be new to students and which will be used throughout their degree programme.

Author: Reuben Hersh
Publisher: Oxford University Press
ISBN: 0198027362
Category : Mathematics
Languages : en
Pages : 368

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Book Description
Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

Author: D.C. Goldrei
Publisher: Routledge
ISBN: 1351460609
Category : Mathematics
Languages : en
Pages : 300

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Book Description
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 numbersDefining natural numbers in terms of setsThe potential paradoxes in set theoryThe Zermelo-Fraenkel axioms for set theoryThe axiom of choiceThe arithmetic of ordered setsCantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.