Customer Reviews

Elementary Number Theory in Nine Chapters

5 star:		(2)
4 star:		(1)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

For its freshness and originality of exposition and material, I give this book 5 stars despite some minor weaknesses noted below.

The book covers classical material in an unconventional manner; for example, it adopts the historical approach, begins with polygonal numbers and number sequences, and contains much recreational material, aside from the "serious" classical results. It also treats some applied aspects of number theory such as public-key cryptography. There is an abundance of problems, ranging from easy and computional to challenging. Solutions are provided.

Some strengths of the book are:
1. Strong continuity of topics and motivation behind the ideas and theorems.
2. Extensive coverage of recreational and "fun" number theory, and computer developments.
3. Historical approach: the book begins with the earliest number theory, that is, polygonal numbers and prime numbers; it has a lot of historical references and anecdotes, and gives some credits to the contributions of China, Iran, etc.
4. Many numerical examples and some neat algorithms, for example, Sanderson's algorithm to express the gcd of two numbers as a linear combination of these numbers, and heuristic methods for Diophantine equations and the Chinese Remainder Theorem.
5. Very clear and entertaining introduction to cryptology and its history.

Some weaknesses of the book are:
1. There are a considerable number of minor typographical errors, but nothing you can't correct yourself.
2. A little long (about 400 pages)--I prefer more conciseness in a textbook--but then it has a lot of history in it....

Overall, this is a very good number theory textbook for classroom use or self-study.

I took Dr. Tattersall's number theory class in the fall of 1998, for which we used a bound draft of this text. Its composition matches his frenetic and exhilarating lecture style, both in the presentation of the material and the frequent side-trips into math history. If you are math-mad, it's worth buying for fun, and if you must buy it for a class, it's worth hanging onto after that last exam. Good stuff!

Never has a course of study gotten me so interested in mathematics as this course by Dr. Tattersall. This particual book has given me incredible insight into the fascinating world of numbers and has enabled me to think about mathematics as both a historical progression and a personal endeavor. It envolopes the student and holds on right through the semester.

PS. If there were any mistakes in the table of prime numbers don't come looking for me!