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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.
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, Horrocks 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.
"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.
Fundamentals of Contemporary Set Theory by K. J. Devlin Pdf
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.
The Joy of SET by Liz McMahon,Gary Gordon,Hannah Gordon,Rebecca Gordon Pdf
"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.
The Joy of Finite Mathematics by Chris P. Tsokos,Rebecca D. Wooten Pdf
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
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."
The ideal gift book on this flower that has seen a rise in popularity, illustrated with beautiful color photographsThe ultimate book for every flower lover"Dahlias have enriched my life. By making this book, I want to share my passion and show how versatile and special dahlias really are;" - Marlies Weijers"Everyone is capable of letting dahlias flower. And what we love the most is spreading the love for flowers with #spreadtheloveforflowers." - Linda van der SlotThe dahlia, a flower that was once thought of as old-fashioned, has surged in popularity over the past few years due to the development of new varieties and an uptick in appreciation from Royals and celebrities. They appear in a broad spectrum of beautiful colors and eccentric shapes, and thanks to their long flowering time they are garden crop favorites. This inspirational book explores every aspect of the dahlia from its history to its sustainable cultivation.
The Joy of Clojure by Chris Houser,Michael Fogus Pdf
Summary The Joy of Clojure, Second Edition is a deep look at the Clojure language. Fully updated for Clojure 1.6, this new edition goes beyond just syntax to show you the "why" of Clojure and how to write fluent Clojure code. You'll learn functional and declarative approaches to programming and will master the techniques that make Clojure so elegant and efficient. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the Technology The Clojure programming language is a dialect of Lisp that runs on the Java Virtual Machine and JavaScript runtimes. It is a functional programming language that offers great performance, expressive power, and stability by design. It gives you built-in concurrency and the predictable precision of immutable and persistent data structures. And it's really, really fast. The instant you see long blocks of Java or Ruby dissolve into a few lines of Clojure, you'll know why the authors of this book call it a "joyful language." It's no wonder that enterprises like Staples are betting their infrastructure on Clojure. About the Book The Joy of Clojure, Second Edition is a deep account of the Clojure language. Fully updated for Clojure 1.6, this new edition goes beyond the syntax to show you how to write fluent Clojure code. You'll learn functional and declarative approaches to programming and will master techniques that make Clojure elegant and efficient. The book shows you how to solve hard problems related to concurrency, interoperability, and performance, and how great it can be to think in the Clojure way. Appropriate for readers with some experience using Clojure or common Lisp. What's Inside Build web apps using ClojureScript Master functional programming techniques Simplify concurrency Covers Clojure 1.6 About the Authors Michael Fogus and Chris Houser are contributors to the Clojure and ClojureScript programming languages and the authors of various Clojure libraries and language features. Table of Contents PART 1 FOUNDATIONS Clojure philosophy Drinking from the Clojure fire hose Dipping your toes in the pool PART 2 DATA TYPES On scalars Collection types PART 3 FUNCTIONAL PROGRAMMING Being lazy and set in your ways Functional programming PART 4 LARGE-SCALE DESIGN Macros Combining data and code Mutation and concurrency Parallelism PART 5 HOST SYMBIOSIS Java.next Why ClojureScript? PART 6 TANGENTIAL CONSIDERATIONS Data-oriented programming Performance Thinking programs Clojure changes the way you think
The Joy of Mathematics by Alfred S. Posamentier,Robert Geretschläger,Charles Li,Christian Spreitzer Pdf
Wouldn't it be great if all school teachers (from kindergarten through high school) would share the joy of mathematics with their students, rather than focus only on the prescribed curriculum that will subsequently be tested? This book reveals some of the wonders of mathematics that are often missing from classrooms. Here's your chance to catch up with the math gems you may have missed. Using jargon-free language and many illustrations, the authors--all veteran math educators--explore five areas--arithmetic, algebra, geometry, probability, and the ways in which mathematics can reinforce common sense. Among other things, you'll learn "the rule of 72," which enables you to quickly determine how long it will take your bank account to double its value at a specific interest rate. Other handy techniques include an automatic algorithm for multiplying numbers mentally and a clever application that will allow you to convert from miles to kilometers (or the reverse) mentally. A delightful presentation of geometric novelties reveals relationships that could have made your study of geometry more fun and enlightening. In the area of probability there is a host of interesting examples: from the famous Monty-Hall problem to the counterintuitive probability of two people having the same birthday in a crowded room. Finally, the authors demonstrate how math will make you a better thinker by improving your organizing abilities and providing useful and surprising solutions to common mathematics problems. You'll come away with an appreciation for math you never thought possible and a true appreciation for this "queen of the sciences."
Elements of Logic via Numbers and Sets by D.L. Johnson Pdf
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.
'A brief but crucially important book' Marcus Chown In The Joy of Tax, tax campaigner Richard Murphy challenges almost every idea you have about tax. For him, tax is fundamentally about the ideas that shape the sort of society we want to live in, not technicalities. His intention is to demonstrate that there is indeed a joy in tax, and by embracing it we can create a fairer society and change the world for the better. Tax has been a feature of human society for a very long time. Almost no one gives tax a good press even though, as Richard Murphy argues, it has been fundamental to the development of democracy the world over. Whilst we may not like tax very much, in contrast it is clear that we really do like the public services which governments provide. So much so, in fact, that for most of the last 300 years, people have been more than happy for governments to run deficits by spending more than they raise in taxation. 2008 apparently changed all that. The issues of debt, deficits, cuts and austerity have dominated the political agenda ever since. Virtually every aspect of the government's finances and how to rearrange them in the forlorn hope of balancing the books has been discussed in great detail. Despite that, there has been almost no real discussion during this period about what tax is for and how it contributes to the creation of the society we aspire to.
