Factorization and Primality Testing (Undergraduate Texts in Mathematics)

1989th Edition
ISBN-13: 978-0387970400, ISBN-10: 0387970401
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Book details

  1. ISBN-10
    0387970401
  2. ISBN-13
    978-0387970400
  3. Edition
    1989th
  4. Publisher
    Springer Verlag
  5. Publication date
    October 2, 1989
  6. Part of series
    Undergraduate Texts in Mathematics
  7. Language
    English
  8. Dimensions
    6.5 x 0.5 x 9.75 inches
  9. Print length
    237 pages
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Book overview

"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.

About the author

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David M. Bressoud
David M. Bressoud
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Product information

Publisher Springer Verlag
Publication date October 2, 1989
Edition 1989th
Language ‎English
Print length 237 pages
ISBN-10 0387970401
ISBN-13 978-0387970400
Item Weight ‎1.15 pounds
Dimensions 6.5 x 0.5 x 9.75 inches
Part of series Undergraduate Texts in Mathematics
Best Sellers Rank
Customer Reviews 4.5 out of 5 stars 7Reviews

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Customer reviews

4.5 out of 5 stars
7 global ratings

Top reviews from the United States

  • Andrew
    4.0 out of 5 starsVerified Purchase
    Old, but pertinent.
    Reviewed in the United States on October 4, 2009
    Format: Hardcover
    As far as I can tell this is the first edition of a book written in 1989, almost 20 years ago. Fortunately, the material is still relevant. The author does a good job of presenting the information in a precise manner that is understandable to the reader. Still you will see...
    As far as I can tell this is the first edition of a book written in 1989, almost 20 years ago. Fortunately, the material is still relevant. The author does a good job of presenting the information in a precise manner that is understandable to the reader. Still you will see that the largest Mersenne prime listed in the book is hopelessly out-of-date, and you will find some errors which were never corrected. May I request a second edition for this book as to make it up-to-date?
    7 people found this helpful
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  • Warrenkaos
    4.0 out of 5 starsVerified Purchase
    I like the jeans anad the fit
    Reviewed in the United States on April 9, 2018
    Format: Hardcover
    I like the jeans anad the fit. It is hard to find jeans that are "real" denim not the stretchy denim that most are these days. The legs are a little wide but I can live with it espacially in the trouser style.
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  • M.
    4.0 out of 5 starsVerified Purchase
    Good Book
    Reviewed in the United States on June 23, 2020
    Format: Hardcover
    Nice introductory text, but the pseudocode is pretty buggy---would definitely recommend checking the author's errata page before using the given algorithms.
    One person found this helpful
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  • true1987
    4.0 out of 5 stars
    Excellent Text on Factorization
    Reviewed in the United States on December 12, 2000
    Format: Hardcover
    This is one of the most compact and best organization of material on the subject of factorization and primality. Written by a promising author, this book explores factorization from the beginning to end, starting with the sieve of Eratosthenes and proceeding to much...
    This is one of the most compact and best organization of material on the subject of factorization and primality.
    Written by a promising author, this book explores factorization from the beginning to end, starting with the sieve of Eratosthenes and proceeding to much more complicated material. The book focuses on algorithms, and contains many useful ones, such as how to raise a number a to a power b, mod m. However, the primary focus of the book is factorization, so it contains algorithms for factorizations. They begin with trial division, then progress into Fermat's Algorithm and Pollard Rho. They eventually evolve into one of the strongest methods to date, Quadratic Sieve, and its child, Multiple Polynomial Quadratic Sieve.
    This book is certainly a must for amateurs who are exploring the subject.
    13 people found this helpful
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Top reviews from other countries

  • Steve Williams
    5.0 out of 5 starsVerified Purchase
    Simpler than some rivals and very useful
    Reviewed in the United Kingdom on February 24, 2023
    This has become, along with Hans Riesel's similarly entitled book and Richard Crandall / Carl Pomerance "Primes: A Computational Perspective", my main fall-back in developing implementations of algorithms useful in integer factorization. There are also e-books...
    This has become, along with Hans Riesel's similarly entitled book and Richard Crandall / Carl Pomerance "Primes: A Computational Perspective", my main fall-back in developing implementations of algorithms useful in integer factorization. There are also e-books in my possession by Samuel Wagstaff and Song Yan, as well as one by Henri Cohen, but in spite of their excellence a durable hardcover copy is indispensable for this sort of activity. David Bressoud's book precedes the others (except Cohen) and is aimed at undergraduates rather than graduates. Though I bought it later than the others it is a marvellous starting point for the amateur and auto-didact. The pseudocode for algorithms is a little strange after Crandall/Pomerance, whose solution of this problem is best, I feel. My copy was priced very reasonably at GBP22.00. I think I got a bargain!
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  • Anders
    5.0 out of 5 starsVerified Purchase
    Amazing book
    Reviewed in the United Kingdom on May 26, 2011
    This book explains factorization and theory about primes. It is very good, because it is easy to read. The explanations are well written, and in a lauguage that does not require you to be a master of mathematics. If you want to learn about things like dixons algorithm and...
    This book explains factorization and theory about primes. It is very good, because it is easy to read. The explanations are well written, and in a lauguage that does not require you to be a master of mathematics. If you want to learn about things like dixons algorithm and the quadratic sieve, then this book is well worth your money. I used the book when writing a report on this subject, and the book was a tremendous help.
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