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Şaban Alaca

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Introductory Algebraic Number Theory 1st Edition

by Saban Alaca (Author)

4.6 11 ratings

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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.

ISBN-10

0521540119
ISBN-13

978-0521540117
Edition

1st
Publisher

Cambridge University Press
Publication date

January 5, 2010
Language

English
Dimensions

6.69 x 1.01 x 9.61 inches
Print length

448 pages
See all details

Jeffrey Stopple
20
Paperback
22 offers from $18.68

Editorial Reviews

Review

'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

'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 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

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

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

Publisher ‏ : ‎ Cambridge University Press; 1st edition (January 5, 2010)
Language ‏ : ‎ English
Paperback ‏ : ‎ 448 pages
ISBN-10 ‏ : ‎ 0521540119
ISBN-13 ‏ : ‎ 978-0521540117
Item Weight ‏ : ‎ 1.71 pounds
Dimensions ‏ : ‎ 6.69 x 1.01 x 9.61 inches

Best Sellers Rank: #3,148,874 in Books (See Top 100 in Books)
- #803 in Number Theory (Books)
- #9,939 in Mathematics (Books)
- #143,745 in Unknown

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4.6 11 ratings

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G. Sanders

review of text

Reviewed in the United States on November 24, 2010

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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.

5 people found this helpful

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Amazon Customer

4 stars means I like it. I would love it if I didn't ...

Reviewed in the United States on April 11, 2017

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4 stars means I like it. I would love it if I didn't already know basic ring theory and galois theory. The development mixes algebraic numbers with the pure algebraic ideas, so I couldn't skip the early stuff. I agree with most reviews, especially the length of proofs. However, if your abstract algebra is weak, I don't know if there is a better book out there. Any reader who is new to algebraic number theory, regardless of how impressive your background is, will appreciate the worked examples. I certainly did.

One person found this helpful

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exp{ix}

Great Introduction to Alg. Number Theory

Reviewed in the United States on May 20, 2012

Verified Purchase

I was very pleased when I received this book two months ago. I highly recommend it for a student who is studying algebraic number theory (ANT) for the first time. It contains a complete and concise introduction to ANT. Each section of the book is very well written, the proofs are presented nicely and there are many useful examples that illustrate the theory that is presented in each section. The end of each chapter contains a wealth of exercises which help one get a good grasp of the material presented in each section.

This book is appropriate for first year graduate or senior level undergrad students who have completed introductory courses in number theory, linear algebra, and abstract algebra. It makes an excellent self study book for one interested in ANT as me.

This is such a beautiful book; it should have been produced in hardcover as the cover wears with multiple uses. The business of college bookstores gauging students with extremely high costs for textbooks is the reason. However I laminated the cover on mine with some clear tape and it is holding up just fine.

3 people found this helpful

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Cliente Amazon

Pone muchos ejemplos

Reviewed in the United States on May 5, 2019

Verified Purchase

Estoy empezando a estudiarlo todavía. Pero hasta ahora, lo visto, pone muchos ejemplos que son muy aclaratorios y dan sentido al contenido tan abstracto. Para aprovecharlo bien hace falta tener cierta base. No obstante, por ahora, el mejor que he encontrado sobre esta materia con diferencia.

One person found this helpful

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J. Katz

Superb introductory book

Reviewed in the United States on November 2, 2012

This book is an outstanding introduction to algebraic number theory for upper-level undergraduates. The authors have done a great job keeping prerequisites to a minimum: some linear algebra and one semester of undergraduate algebra should suffice. (No Galois theory is assumed.) Proofs are crystal clear, and plenty of examples are given.

I do agree with a previous reviewer that sometimes the text is *too* simple: when a simple theorem has a long proof, you wonder whether you are missing something subtle! But this is easy to gloss over.

2 people found this helpful

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T-Lex

Interesting Content, Iffy Presentation

Reviewed in the United States on September 5, 2013

Verified Purchase

I used this textbook for a special studies class for advanced undergraduates. The content is interesting and doable for anyone who has had Number Theory, but especially straightforward if you have had Abstract Algebra. While I think the range and progression of topics is solid, the presentation was a bit off. For instance, there would be a three page proof of a complicated concept, but very few practical problem solving examples. I believe the author's intention was to leave those for the reader in the forms of exercises, however I find that approach to be unhelpful at times.

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A. Curtis

Grab bag of good and bad

Reviewed in the United States on November 7, 2004

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.

27 people found this helpful

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