Elementary Number Theory in Nine Chapters 2nd Edition by James J. Tattersall (PDF)

Description

This textbook is intended to serve as a one-semester introductory course in number theory and in this second edition it has been revised throughout and many new exercises have been added. Historical perspective is included and emphasis is given to some of the subject’s applied aspects; in particular the field of cryptography is highlighted. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler, and to fully illustrate the properties of numbers and concepts developed in the text, a wealth of exercises have been included. It is assumed that the reader will have ‘pencil in hand’ and ready access to a calculator or computer. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐As I am not a professional mathematician, I would only offer my opinion that in places this text is unnecessarily terse. If fair, that criticism is probably offset by the fact that this book is meant to be used in a college class where presumably the author or another professor would offer supplementary explanation. I purchased this book to augment my understanding of the Chinese Remainder Theorem (CRT), which does not disappoint but would profit from sidebar explanations or problems as in the antiquated Keedy/Bittinger texts in calculus. That said, all chapters and sections should probably be thoroughly reviewed in the order presented prior to delving in particular sub-sections. I will persevere with this text if perhaps seeking occasional third party help to illumine the author’s examples. The book is manufactured beautifully, though not in sewn signatures, which may limit the lifetime of the book with the marginal notes that the author suggests.

⭐A fascinating book for both undergraduate and graduate math students looking for a broad variety of number theory topics. Topics are also placed in historical perspective–a real plus, in my estimation. Secondary school teachers will also find this book to be an inspiration for topics that are suitable for advanced high school students.

⭐Good !

⭐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.

⭐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!

⭐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!

⭐As expected

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