The coin exchange problem: The minimal transversal method in Numerical semigroups - Softcover

Leher, Eli

Softcover

ISBN 10: 3639143264 ISBN 13: 9783639143263

Publisher: VDM Verlag, 2009

Synopsis

Suppose our monetary system used only coins of the values 5 and 8. Which bills could we exchange using only these coins? How many sums are impossible to get? More generally, let a,b,...,n be natural numbers (the values of the coins). The set of all natural combinations of these numbers is a numerical semigroup. Our goal is to determine the structure of this semigroup. This question, known as the coin exchange problem or the Frobenius problem, captured the imagination of many mathematicians ever since it was first proposed by Sylvester in 1884. If we use only 2 kinds of coins, the answer is quite simple, but the case of 3 or more turns out to be much more complicated and interesting. This book presents the problem in a clear and vivid way, and shows an ingenious simple method to solve it. The main parameters of the problem, including the Frobenius number and genus, are explained and discussed. Finally, the book presents the surprising link between numerical semigroups and cyclotomic polynomials. The subject, as well as the clever solution and clear presentation, make this book a delight to anyone interested in mathematics, professionals and amateurs alike.

About this title

About the Author

Born in Israel in 1971. Currently teaches mathematics at Tel Aviv University, where he got his Ph.D in 2007. Main mathematical interests: Probability, Algebra and Number Theory. Chairperson of the Coordinating Forum of the Junior Academic Stuff Associations in Israel. Author of "I love Tamir" a non-mathematical novel.

Edition details

• Publisher: VDM Verlag
• Publication date: 2009
• Language: English
• ISBN 10: 3639143264
• ISBN 13: 9783639143263
• Binding: Paperback
• Number of pages: 92