Product Description

This text provides a simple account of classical number theory, as well as some of the historical background in which the subject evolved. It is intended for use in a one-semester, undergraduate number theory course taken primarily by mathematics majors and students preparing to be secondary school teachers. Although the text was written with this readership in mind, very few formal prerequisites are required. Much of the text can be read by students with a sound background in high school mathematics.

Product Details

• Amazon Sales Rank: #1350409 in Books
• Published on: 2001-11-01
• Original language: English
• Binding: Paperback
• 448 pages

From the Publisher
HISTORICAL EMPHASIS: The author has carefully placed the topics of number theory within the larger historical frame of mathematical development. Historical remarks are woven throughout the text along with theory, bringing out the point that number theory is developed piece by piece, with the work of each individual contributor built upon the research of many others. A student who is aware of how people of genius found their way slowly through the creative process may be less likely to be discouraged by his or her own difficulty with the subject.
EXTENSIVE EXERCISE SETS: More than 750 problems are an integral part of the text and range in difficulty from the purely mechanical to challenging theoretical questions. The computational exercises develop basic techniques and test understanding of concepts, while those of a theoretical nature give practice in constructing proofs.
NEW SECTIONS: Two new sections have been added to this edition: Section 6.4, An Application to the Calendar and Section 15.3, An Application to Factoring: Remote Coin-Flipping. Section 6.4 uses congruence theory to determine the day of the week on which a given date falls. Section 15.3 describes a number-theoretic protocol for flipping a fair coin over the telephone.
ADDITIONAL TOPIC COVERAGE: Additional topic coverage in this edition includes coverage of the quadratic sieve method with the factorization algorithms of Section 15.2. The material on Pell's equation has been expanded and clarified. A treatment of polyalphabetic ciphers, focusing on Hill's cipher, now appears in the section devoted to secrecy systems.
MODERN ADVANCES IN NUMBER THEORY: The resolution of certain challenging conjectures such as the confirmation of the composite nature of the Fermat number F24 is discussed in this edition, emphasizing the vitality of number theory as an area of research mathematics. In addition, certain numerical information has been updated in light of the latest finding.

Customer Reviews

Wonderful introduction to Number Theory
Having tried many books on the subject and being largely unimpressed, I was introduced to this little gem. This is quite possibly the best serious number theory book I have ever come across (The SUMS title is scattered and badly written by comparison). It lacks completeness but it has more than enough for most amateurs.
This book is also very suitable for undergraduate maths students in their early years,since number theory is rarely covered in class.There is more than enough here to keep any young mathematician happy in a world where most maths courses have a tendancy to skip over the queen of the field.

Clear but expensive
This is a good first textbook on number theory, the proofs are clear and you are guided through them well, also the book is laid out well including historical information on the subject. The thing is that for 40 pounds Id expect a textbook that would cover more, this book may just cover an undergrad course in number theory, but certainly wouldnt go any further. Its a good book, just overpriced for something you wont use beyond one 10 week course.