The Joy of Finite Mathematics

The Joy of Finite Mathematics

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

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


The Joy of SET

The Joy of SET

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

"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.


Combinatorics of Finite Sets

Combinatorics of Finite Sets

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  • Author: Ian Anderson
  • Publisher: Courier Corporation
  • ISBN: 9780486422572
  • Category : Mathematics
  • Languages : en
  • Pages : 276

Among other subjects explored are the Clements-Lindström extension of the Kruskal-Katona theorem to multisets and the Greene-Kleitmen result concerning k-saturated chain partitions of general partially ordered sets. Includes exercises and solutions.


The Art of the Infinite

The Art of the Infinite

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  • Author: Robert Kaplan
  • Publisher: Bloomsbury Publishing USA
  • ISBN: 1608198693
  • Category : Mathematics
  • Languages : en
  • Pages : 417

Traces the development of mathematical thinking and describes the characteristics of the "republic of numbers" in terms of humankind's fascination with, and growing knowledge of, infinity.


Street-Fighting Mathematics

Street-Fighting Mathematics

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  • Author: Sanjoy Mahajan
  • Publisher: MIT Press
  • ISBN: 0262265591
  • Category : Education
  • Languages : en
  • Pages : 152

An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.


What Is Mathematics, Really?

What Is Mathematics, Really?

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  • Author: Reuben Hersh
  • Publisher: Oxford University Press
  • ISBN: 0199839395
  • Category : Mathematics
  • Languages : en
  • Pages : 369

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.


Applied Finite Mathematics

Applied Finite Mathematics

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  • Author:
  • Publisher:
  • ISBN: 9780495839606
  • Category : Mathematics
  • Languages : en
  • Pages : 413


Conceptual Mathematics

Conceptual Mathematics

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  • Author: F. William Lawvere
  • Publisher: Cambridge University Press
  • ISBN: 0521894859
  • Category : Mathematics
  • Languages : en
  • Pages : 409

This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.


Beyond Infinity

Beyond Infinity

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  • Author: Eugenia Cheng
  • Publisher: Profile Books
  • ISBN: 1782830812
  • Category : Mathematics
  • Languages : en
  • Pages : 191

SHORTLISTED FOR THE 2017 ROYAL SOCIETY SCIENCE BOOK PRIZE Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.


Finite-Dimensional Vector Spaces

Finite-Dimensional Vector Spaces

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  • Author: Paul R. Halmos
  • Publisher: Courier Dover Publications
  • ISBN: 0486822265
  • Category : Mathematics
  • Languages : en
  • Pages : 209

Classic, widely cited, and accessible treatment offers an ideal supplement to many traditional linear algebra texts. "Extremely well-written and logical, with short and elegant proofs." — MAA Reviews. 1958 edition.