The Joy of Finite Mathematics


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




The Joy of SET


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.




Finite Mathematics


Book Description




The Art of the Infinite


Book Description

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.




The Joy of X


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."







Finite Mathematics


Book Description




What Is Mathematics, Really?


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.




The Joys of Haar Measure


Book Description

From the earliest days of measure theory, invariant measures have held the interests of geometers and analysts alike, with the Haar measure playing an especially delightful role. The aim of this book is to present invariant measures on topological groups, progressing from special cases to the more general. Presenting existence proofs in special cases, such as compact metrizable groups, highlights how the added assumptions give insight into just what the Haar measure is like; tools from different aspects of analysis and/or combinatorics demonstrate the diverse views afforded the subject. After presenting the compact case, applications indicate how these tools can find use. The generalisation to locally compact groups is then presented and applied to show relations between metric and measure theoretic invariance. Steinlage's approach to the general problem of homogeneous action in the locally compact setting shows how Banach's approach and that of Cartan and Weil can be unified with good effect. Finally, the situation of a nonlocally compact Polish group is discussed briefly with the surprisingly unsettling consequences indicated. The book is accessible to graduate and advanced undergraduate students who have been exposed to a basic course in real variables, although the authors do review the development of the Lebesgue measure. It will be a stimulating reference for students and professors who use the Haar measure in their studies and research.




Finite Mathematics


Book Description