Introductory Algebraic Number Theory [Paperback]

Saban Alaca (Author), Kenneth S. Williams (Author)

Book Description

ISBN-10: 0521540119 | ISBN-13: 978-0521540117 | Publication Date: November 17, 2003

Suitable for senior undergraduates and beginning graduate students in mathematics, this book is an introduction to algebraic number theory at an elementary level. Prerequisites are kept to a minimum, and numerous examples illustrating the material occur throughout the text. References to suggested readings and to the biographies of mathematicians who have contributed to the development of algebraic number theory are provided at the end of each chapter. Other features include over 320 exercises, an extensive index, and helpful location guides to theorems in the text.

Editorial Reviews

Review

'The overall presentation makes the book suitable for a course for advanced undergraduate students.' Zentralblatt MATH

'Learning algebraic number theory is about the least abstract way to learn about important aspects of commutative ring theory, as well as being beautiful in its own right too. This text is ideally suited to the learner of both of these, with clear writing, a plentiful supply of examples and exercises, and a good range of 'suggested reading'. ... I look forward to reading and learning from this book in greater detail. The features which make it attractive are worth listing: the intrinsic fascination of the results; the balance between clearn theory and dirty calculation (the latter essential for developing familiarity with the local terrain, the former for appreciating an arial view of the whole route); the balance between calculation dependent upon the depth of theory and those details dependent on simple algebraic and trigonometric identities and results from elementary number theory; a very full quota of exercises and further reading.' The Mathematical Gazette

'This is a very good textbook on algebraic number theory for beginners. ... Its most appealing feature is the very large number of examples it contains. Their abundance provides a lot of hands-on experience and has the power to transform the reader's understanding of basic notions into active knowledge.' Monatshefte für Mathematik

'This book provides a nice introduction to classical parts of algebraic number theory.... The text is written in a lively style and can be read without any prerequisites. Therefore the book is very suitable for graduate students starting mathematics courses or mathematicians interested in introductory reading in algebraic number theory. The book presents a welcome addition to the existing literature.' EMS Newsletter

Book Description

This book provides an introduction to algebraic number theory suitable for senior undergraduates and beginning graduate students in mathematics. The material is presented in a straightforward, clear and elementary fashion, and the approach is hands on, with an explicit computational flavor. Prerequisites are kept to a minimum, and numerous examples illustrating the material occur throughout the text. References to suggested readings and to the biographies of mathematicians who have contributed to the development of algebraic number theory are given at the end of each chapter. There are over 320 exercises, an extensive index, and helpful location guides to theorems and lemmas in the text.

Product Details

• Paperback: 448 pages
• Publisher: Cambridge University Press (November 17, 2003)
• Language: English
• ISBN-10: 0521540119
• ISBN-13: 978-0521540117
• Product Dimensions: 9.9 x 7.1 x 1.2 inches
• Shipping Weight: 1.7 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #241,574 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

23 of 23 people found the following review helpful:

3.0 out of 5 stars Grab bag of good and bad, November 7, 2004

By 

A. Curtis (Wyoming, USA) - See all my reviews
(REAL NAME)   

This review is from: Introductory Algebraic Number Theory (Paperback)

Strengths:
1. Easy reading, detailed proofs
2. Covered required algebra background (modules, ideals, Dedekind domains, etc)
3. Many, many examples

Weaknesses:
1. Too detailed in some cases
2. Does not develop more advanced ideas that actually make the material easier
3. Poor index
4. Examples are often too simple

This book takes the reader through the required algebra background and moves them into the realm of using these abstract algebraic construction to study the theory of numbers. The book is aimed at upper-level undergraduates, so it's easy reading. Sometimes too easy reading, as proofs are often long-winded and contain many trivial details. In some instances, I wanted all those details, often it was simply annoying.

The real strength of this book lies in the many explicit examples. It was worth the price for these examples, as most higher-level books offer few examples.

The index is terrible, but the additional reading section at the end of each chapter is a nice addition.

Overall, I learned a lot from this book, but would have liked to have the authors approached the material at a little bit higher level. For instance, instead of using complex conjugates extensively, I would have preferred introducing a mapping to the complex conjugates (say sigma) for use in most proofs.

2 of 2 people found the following review helpful:

5.0 out of 5 stars review of text, November 24, 2010

By 

G. Sanders "Charlie Sanders" (Corpus Christi, TX) - See all my reviews
(REAL NAME)   

Amazon Verified Purchase

This review is from: Introductory Algebraic Number Theory (Paperback)

There are only 2 genuine introductory texts to algebraic number theory---this book and the one by Stewart and Tall. The latter is not as inclusive as the present text. This text abounds in examples. Unlike the other reviewer, I do not find them tedious, but explicit instead. Both Williams and Saban are specialists in cubic equations, and the text is interestingly flavored with this expertise. There is a very detailed, and theoretic, introduction to Minkowski bounds, class group numbers, units of general number fields, and factoring in a tower of domains. As an amateur mathematician, I am grateful to both authors for setting down their insights in a readable and graspable manner. They invite the reader to accompany them on an exciting journey into a beautiful realm of mathematics. This text will enable the reader to tackle, later on, a more formidable book like "Algebraic Number Theory" by Mollin. For example, a problem found on page 10 of Mollin's book is found on page 136 of this text. If one has any hope to master Mollin's deep meditation on ideals, one would first need to become fluent in Williams' and Saban's presentation of them.