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David M Bressoud
Springer

Factorization and Primality Testing

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AuthorDavid M Bressoud
PublisherSpringer
PublishedJun 14 2001
Book FormatHardcover
ISBN-139780387970400
Dimensions9.5 X 6.42 X 0.79 inches
Weight 1.09 pounds
BISAC
CategoriesMathematics > Number Theory
LanguageEnglish

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Book Description

About binomial theorems I'm teeming with a lot of news, With many cheerful facts about the square on the hypotenuse. - William S. Gilbert (The Pirates of Penzance, Act I) The question of divisibility is arguably the oldest problem in mathematics. Ancient peoples observed the cycles of nature: the day, the lunar month, and the year, and assumed that each divided evenly into the next. Civilizations as separate as the Egyptians of ten thousand years ago and the Central American Mayans adopted a month of thirty days and a year of twelve months. Even when the inaccuracy of a 360-day year became apparent, they preferred to retain it and add five intercalary days. The number 360 retains its psychological appeal today because it is divisible by many small integers. The technical term for such a number reflects this appeal. It is called a smooth number. At the other extreme are those integers with no smaller divisors other than 1, integers which might be called the indivisibles. The mystic qualities of numbers such as 7 and 13 derive in no small part from the fact that they are indivisibles. The ancient Greeks realized that every integer could be written uniquely as a product of indivisibles larger than 1, what we appropriately call prime numbers. To know the decomposition of an integer into a product of primes is to have a complete description of all of its divisors.

Author Bio

David Bressoud is Director of the Conference Board of the Mathematical Sciences. He is now Dewitt Wallace Professor Emeritus at Macalester College, having served on the faculty from 1994 to 2020.

He is also a former President of the Mathematical Association of America, a Fellow of the American Mathematical Society, and a Fellow of the American Association for the Advancement of Science. He served in the Peace Corps, teaching math and science at the Clare Hall School in Antigua, West Indies before studying with Emil Grosswald at Temple University and then teaching at Penn State for 17 years.

He chaired the Department of Mathematics and Computer Science at Macalester from 1995 until 2001. He has held visiting positions at the Institute for Advanced Study, the University of Wisconsin-Madison, the University of Minnesota, Université Louis Pasteur (Strasbourg, France), and the State College Area High School.

David has received the MAA Gung and Hu Award for Distinguished Service to Mathematics, the MAA Distinguished Teaching Award (Allegheny Mountain Section), the MAA Beckenbach Book Award for Proofs and Confirmations, and has been a Pólya Lecturer and a Leitzel Lecturer for the MAA. He is a recipient of Macalester's Jefferson Award. He has published over sixty research articles in number theory, combinatorics, special functions, and mathematics education. His other books include Factorization and Primality Testing, Second Year Calculus from Celestial Mechanics to Special Relativity, A Radical Approach to Real Analysis (now in 2nd edition), A Radical Approach to Lebesgue's Theory of Integration, Calculus Reordered: A History of the Big Ideas, A Course in Computational Number Theory (with Wagon), and Calculus: Graphical, Numerical, Algebraic (with Demana, Waits, Kennedy, & Boardman).

David has chaired the MAA special interest group, Teaching Advanced High School Mathematics as well as the AP Calculus Development Committee and has served as Director of the FIPSE-sponsored program Quantitative Methods for Public Policy and PI for two NSF-sponsored national studies of Calculus: Characteristics of Successful Programs in College Calculus (NSF #0910240) and Progress through Calculus (NSF #1430540).

A native of Pennsylvania, David lives in Saint Paul, Minnesota with his wife, Jan.

Source: davidbressoud.org

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Factorization and Primality Testing

Mathematics

Number Theory

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