Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics

Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics

Author: Robert B. Banks

Publisher: Princeton University Press

Published: 2012-05-02

Total Pages: 302

ISBN-13: 1400843030

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Have you ever daydreamed about digging a hole to the other side of the world? Robert Banks not only entertains such ideas but, better yet, he supplies the mathematical know-how to turn fantasies into problem-solving adventures. In this sequel to the popular Towing Icebergs, Falling Dominoes (Princeton, 1998), Banks presents another collection of puzzles for readers interested in sharpening their thinking and mathematical skills. The problems range from the wondrous to the eminently practical. In one chapter, the author helps us determine the total number of people who have lived on earth; in another, he shows how an understanding of mathematical curves can help a thrifty lover, armed with construction paper and scissors, keep expenses down on Valentine's Day. In twenty-six chapters, Banks chooses topics that are fairly easy to analyze using relatively simple mathematics. The phenomena he describes are ones that we encounter in our daily lives or can visualize without much trouble. For example, how do you get the most pizza slices with the least number of cuts? To go from point A to point B in a downpour of rain, should you walk slowly, jog moderately, or run as fast as possible to get least wet? What is the length of the seam on a baseball? If all the ice in the world melted, what would happen to Florida, the Mississippi River, and Niagara Falls? Why do snowflakes have six sides? Covering a broad range of fields, from geography and environmental studies to map- and flag-making, Banks uses basic algebra and geometry to solve problems. If famous scientists have also pondered these questions, the author shares the historical details with the reader. Designed to entertain and to stimulate thinking, this book can be read for sheer personal enjoyment.


Digital Dice

Digital Dice

Author: Paul Nahin

Publisher: Princeton University Press

Published: 2013-03-24

Total Pages: 288

ISBN-13: 1400846110

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Some probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to get numerical answers to difficult probability problems without having to solve complicated mathematical equations. Popular-math writer Paul Nahin challenges readers to solve twenty-one difficult but fun problems, from determining the odds of coin-flipping games to figuring out the behavior of elevators. Problems build from relatively easy (deciding whether a dishwasher who breaks most of the dishes at a restaurant during a given week is clumsy or just the victim of randomness) to the very difficult (tackling branching processes of the kind that had to be solved by Manhattan Project mathematician Stanislaw Ulam). In his characteristic style, Nahin brings the problems to life with interesting and odd historical anecdotes. Readers learn, for example, not just how to determine the optimal stopping point in any selection process but that astronomer Johannes Kepler selected his second wife by interviewing eleven women. The book shows readers how to write elementary computer codes using any common programming language, and provides solutions and line-by-line walk-throughs of a MATLAB code for each problem. Digital Dice will appeal to anyone who enjoys popular math or computer science. In a new preface, Nahin wittily addresses some of the responses he received to the first edition.


Excursions in Number Theory

Excursions in Number Theory

Author: Charles Stanley Ogilvy

Publisher: Courier Corporation

Published: 1988-01-01

Total Pages: 196

ISBN-13: 9780486257785

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Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. No special training is needed, just high school mathematics and an inquisitive mind. "A splendidly written, well selected and presented collection. I recommend the book unreservedly to all readers." — Martin Gardner.


Applications of Differential Equations in Engineering and Mechanics

Applications of Differential Equations in Engineering and Mechanics

Author: Kam Tim Chau

Publisher: CRC Press

Published: 2019-01-08

Total Pages: 831

ISBN-13: 042989435X

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This second of two comprehensive reference texts on differential equations continues coverage of the essential material students they are likely to encounter in solving engineering and mechanics problems across the field - alongside a preliminary volume on theory. This book covers a very broad range of problems, including beams and columns, plates, shells, structural dynamics, catenary and cable suspension bridge, nonlinear buckling, transports and waves in fluids, geophysical fluid flows, nonlinear waves and solitons, Maxwell equations, Schrodinger equations, celestial mechanics and fracture mechanics and dynamics. The focus is on the mathematical technique for solving the differential equations involved. All readers who are concerned with and interested in engineering mechanics problems, climate change, and nanotechnology will find topics covered in this book providing valuable information and mathematics background for their multi-disciplinary research and education.


Mathematics in Nature

Mathematics in Nature

Author: John Adam

Publisher: Princeton University Press

Published: 2011-10-02

Total Pages: 408

ISBN-13: 1400841011

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From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature. Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathematics can be used to formulate and solve puzzles observed in nature and to interpret the solutions. In the process, it teaches such topics as the art of estimation and the effects of scale, particularly what happens as things get bigger. Readers will develop an understanding of the symbiosis that exists between basic scientific principles and their mathematical expressions as well as a deeper appreciation for such natural phenomena as cloud formations, halos and glories, tree heights and leaf patterns, butterfly and moth wings, and even puddles and mud cracks. Developed out of a university course, this book makes an ideal supplemental text for courses in applied mathematics and mathematical modeling. It will also appeal to mathematics educators and enthusiasts at all levels, and is designed so that it can be dipped into at leisure.


How to Guard an Art Gallery

How to Guard an Art Gallery

Author: T.S. Michael

Publisher: JHU Press

Published: 2009-09-01

Total Pages: 273

ISBN-13: 0801897041

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An “accessible and engaging” tool for understanding the branch of mathematics that is so crucial to modern computer science, using real-life problems (Mathematical Reviews). What is the maximum number of pizza slices one can get by making four straight cuts through a circular pizza? How does a computer determine the best set of pixels to represent a straight line on a computer screen? How many people at a minimum does it take to guard an art gallery? Discrete mathematics has the answer to these—and many other—questions of picking, choosing, and shuffling. T. S. Michael’s gem of a book brings this vital but tough-to-teach subject to life using examples from the real world and popular culture. Each chapter uses one problem—such as slicing a pizza—to detail key concepts about counting numbers and arranging finite sets. Michael takes a different perspective in tackling each of eight problems and explains them in differing degrees of generality, showing in the process how the same mathematical concepts appear in varied guises and contexts. In doing so, he imparts a broader understanding of the ideas underlying discrete mathematics and helps readers appreciate and understand mathematical thinking and discovery. This book explains the basic concepts of discrete mathematics and demonstrates how to apply them in largely nontechnical language. The explanations and formulas can be grasped with a basic understanding of linear equations.


MATH BRIDGES TO A BETTER FUTURE:

MATH BRIDGES TO A BETTER FUTURE:

Author: James Elander

Publisher: Xlibris Corporation

Published: 2023-09-05

Total Pages: 208

ISBN-13: 1669876284

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From ER to E.T.

From ER to E.T.

Author: Rajeev Bansal

Publisher: John Wiley & Sons

Published: 2017-01-04

Total Pages: 222

ISBN-13: 1118458176

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This book covers the study of electromagnetic wave theory and describes how electromagnetic technologies affect our daily lives. From ER to ET: How Electromagnetic Technologies Are Changing Our Lives explores electromagnetic wave theory including its founders, scientific underpinnings, ethical issues, and applications through history. Utilizing a format of short essays, this book explains in a balanced, and direct style how electromagnetic technologies are changing the world we live in and the future they may create for us. Quizzes at the end of each chapter provide the reader with a deeper understanding of the material. This book is a valuable resource for microwave engineers of varying levels of experience, and for instructors to motivate their students and add depth to their assignments. In addition, this book: Presents topics that investigate all aspects of electromagnetic technology throughout history Explores societal and global issues that relate to the field of electrical engineering (emphasized in current ABET accreditation criteria) Includes quizzes relevant to every essay and answers which explain technical perspectives Rajeev Bansal, PhD, is a professor of Electrical and Computer Engineering at the University of Connecticut. He is a member of IEEE and the Connecticut Academy of Science and Engineering. He is a Fellow of the Electromagnetics Academy. His editing credits include Fundamentals of Engineering Electromagnetics and Engineering Electromagnetics: Applications. Dr. Bansal contributes regular columns to IEEE Antennas and Propagation Magazine and IEEE Microwave Magazine.