Schumer P.D. Mathematical Journeys

Hoboken: Wiley-Interscience, 2004. - 199p.Mathematics is more than just a large set of problems. Perhaps more than any other thing, it is about ideas, often from a seed planted by a basic human physical need, but in most cases, the original germ appeared in the mind of a human. Two basic principles make the ideas of mathematics different from the abstractions in other areas. The first is that those of mathematics can be resolved. And once they are resolved, the issue is settled forever. As I often tell my math students, the only way this result can ever be rendered false is by somehow modifying the definitions of the terms. The second is that the results of mathematics almost always prove to be useful. It is said that Albert Einstein was continuously incredulous at how the mathematics he needed for relativity already existed, but was considered little more than a curiosity. In this book Schumer captures a great deal of the grandeur of mathematics as well as the historical context when some of the great mathematical ideas germinated and grew to maturity. My favorite chapter was the one about Paul Erdös, a man with a great sense of humor, incredible mathematical talent, an odd sense of humility and whose impact on the mathematical world is probably greater than that of anyone else, including Euclid. While there is no question that the codification of geometry done by Euclid has had a profound effect for millennia, Erdös was personally involved in many careers. Those touched by his genius continue to spread the mathematical seeds imparted by his many symbiotic relationships. Other topics include the green chicken problem solving contest, the Josephus problem, basic games such as Nim and Wythoff's game; Mersenne primes and number theory; Fermat primes, magic and Latin squares; the consequences of rolling unusual dice, a history of the computation of pi, primality testing and Pascal's triangle. Schumer writes with a great deal of wit, precision and humor, yet employs very little excess verbiage. The highest level of mathematics needed to understand the descriptions is that of number theory and combinatorics. A set of problems is given at the end of each chapter and solutions are included in an appendix. This is a book that could be used as a text for a course in the history of mathematics. With such a broad range of topics, it would allow any instructor to demonstrate the breadth of mathematics as well as give some background on the personalities that helped form it into what we have today. It can also be read just for enjoyment, and if you were to use it as a textbook, some of the people, instructor included, would find that it serves you well in both capacities.Let’s Get Cooking: A Variety of Mathematical Ingredients
The Green Chicken Contest
The Josephus Problem: Please Choose Me Last
Nim and Wythoff’s Game: Or How to Get Others to Pay Your Bar Bill
Mersenne Primes, Perfect Numbers, and Amicable Pairs
The Harmonic Series...and Less
Fermat Primes, the Chinese Remainder Theorem, and Lattice Points
Tic-Tac-Toe, Magic Squares, and Latin Squares
Mathematical Variations on Rolling Dice
Pizza Slicing, Map Coloring, Pointillism, and Jack-in-the-Box
Episodes in the Calculation of Pi
A Sextet of Scintillating Problems
Primality Testing Below a Quadrillion
Erd¨os Number Zero
Choosing Stamps to Mail a Letter, Let Me Count the Ways
Pascal Potpourri
Appendix: Comments and Solutions to Problems Worth Considering