Series:

Problem Solving in Mathematics and Beyond

2 primary works

Book 17

Cover of Fate Of Schrodinger's Cat, The: Using Math And Computers To Explore The Counterintuitive
Can we correctly predict the flip of a fair coin more than half the time - or the decay of a single radioactive atom? Our intuition, based on a lifetime of experience, tells us that we cannot, as these are classic examples of what are known to be 50-50 guesses.But mathematics is filled with counterintuitive results - and this book discusses some surprising and entertaining examples. It is possible to devise experiments in which a flipped coin lands heads completely at random half the time, but we can also correctly predict when it will land heads more than half the time. The Fate of Schrodinger's Cat shows how high-school algebra and basic probability theory, with the invaluable assistance of computer simulations, can be used to investigate both the intuitive and the counterintuitive.This book explores fascinating and controversial questions involving prediction, decision-making, and statistical analysis in a number of diverse areas, ranging from whether there is such a thing as a 'hot hand' in shooting a basketball, to how we can successfully predict, more than half the time, the decay of the radioactive atom that determines the fate of Schrodinger's Cat.

Book 28

Cover of Seduced By Mathematics: The Enduring Fascination Of Mathematics
Seduction is not just an end result, but a process - and in mathematics, both the end results and the process by which those end results are achieved are often charming and elegant.This helps to explain why so many people - not just those for whom math plays a key role in their day-to-day lives - have found mathematics so seductive. Math is unique among all subjects in that it contains end results of amazing insight and power, and lines of reasoning that are clever, charming, and elegant. This book is a collection of those results and lines of reasoning that make us say, 'OMG, that's just amazing,' - because that's what mathematics is to those who love it. In addition, some of the stories about mathematical discoveries and the people who discovered them are every bit as fascinating as the discoveries themselves.This book contains material capable of being appreciated by students in elementary school - as well as some material that will probably be new to even the more mathematically sophisticated. Most of the book can be easily understood by those whose only math courses are algebra and geometry, and who may have missed the magic, enchantment, and wonder that is the special province of mathematics.