Problems in Algebraic Number Theory (Graduate Texts in Mathematics) [Hardcover]

Jody Esmonde (Author), J. Esmonde (Author), M. RAM Murty (Author)

Book Description

ISBN-10: 0387986170 | ISBN-13: 978-0387986173 | Publication Date: December 1998

Asking how one does mathematical research is like asking how a composer creates a masterpiece. No one really knows. It is clear, however, that problem solving plays an important role in the training of the research mind. In fact, it would not be an exaggeration to say that the ability to do research is essentially the art of asking the 'right'questions. And indeed, the approach taken here is based on the principle that questions focus the mind. This book is a collection of approximately 500 problems in algebraic number theory, systematically arranged to reveal the evolution of concepts and ideas of the subject. Some are easy and straightforward, others difficult. However, they have all been arranged with a didactic purpose in mind and are completely solved. This text is suitable for a first course in algebraic number theory with minimal supervision by the instructor. The exposition also facilitates independent study, however, and any student who has taken a basic course in calculus, linear algebra and abstract algebra should be able to work through these problems on his/her own.

Editorial Reviews

Review

From the reviews of the second edition: "Problems in Algebraic Number Theory is intended to be used by the students for independent study of the subject. It provides the reader with a large collection of problems (about 500) … . The reviewer thinks that the authors have done a fantastic job choosing the problems, which are perfectly arranged so the students can progressively move from topic to topic … . the book is an excellent resource for the instructor and the student as a companion to any algebraic number theory course." (Álvaro Lozano-Robledo, MathDL, May, 2005) "This second edition is an expanded and revised version of the first edition. In particular, it contains an extra chapter on density theorems and L-Functions highlighting some of the analytic aspects of algebraic number theory. … the reviewer is certain that many students will benefit from this pathway into the fascinating realm of algebraic number theory." (Zentralblatt für Didaktik der Mathematik, August, 2005) "This is the second edition of Problems in algebraic number theory. ... errors have been corrected … . The decision to expand the book by including a chapter on density theorems is most welcome." (Franz Lemmermeyer, Zentralblatt MATH, Vol. 1055) "This is the second edition of an unusual introduction to algebraic number theory. … each chapter is written in straightforward textbook style. All chapters contain a very large number of problems. … it presents a good way of acquiring a working knowledge of basic algebraic number theory by using it for independent study or as supplementary reading." (Ch. Baxa, Monatshefte für Mathematik, Vol. 149 (4), 2006) --This text refers to an alternate Hardcover edition.

From the Back Cover

From Reviews of the First Edition: This book provides a problem-oriented first course in algebraic number theory. ... The authors have done a fine job in collecting and arranging the problems. Working through them, with or without help from a teacher, will surely be a most efficient way of learning the theory. Many of the problems are fairly standard, but there are also problems of a more original type. This makes the book a useful supplementary text for anyone studying or teaching the subject. ... This book deserves many readers and users. - T. Metsänkylä , Mathematical Reviews The book covers topics ranging from elementary number theory (such as the unique factorization of integers or Fermat's little theorem) to Dirichlet's theorem about primes in arithmetic progressions and his class number formula for quadratic fields, and it treats standard material such as Dedekind domains, integral bases, the decomposition of primes not dividing the index, the class group, the Minkowski bound and Dirichlet's unit theorem ... the reviewer is certain that many students will benefit from this pathway into the fascinating realm of algebraic number theory. - Franz Lemmermeyer, Zentralblatt This second edition is an expanded and revised version of the first edition. In particular, it contains an extra chapter on density theorems and $L$-functions highlighting some of the analytic aspects of algebraic number theory. --This text refers to an alternate Hardcover edition.

Product Details

• Hardcover: 376 pages
• Publisher: Springer (December 1998)
• Language: English
• ISBN-10: 0387986170
• ISBN-13: 978-0387986173
• Product Dimensions: 9.5 x 6.4 x 0.8 inches
• Shipping Weight: 1.3 pounds
• Average Customer Review: 4.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #3,747,317 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

6 of 8 people found the following review helpful:

5.0 out of 5 stars Amazing!!, December 16, 2004

By 

Katie (Canada) - See all my reviews

This review is from: Problems in Algebraic Number Theory (Graduate Texts in Mathematics) (Hardcover)

Best book of it's kind that I've ever read. I found it to be extremely helpful. I even read it at night before I go to bed because its so entertaining. I thoroughly enjoyed it and would recommend it to anyone who is studying this.

7 of 10 people found the following review helpful:

3.0 out of 5 stars Won't become a classic., May 27, 2003

By A Customer

This review is from: Problems in Algebraic Number Theory (Graduate Texts in Mathematics) (Hardcover)

A problem book is always helpful to students. But this one is sloppy. Besides the supplementary problems at the end of each chapter, most problems are boring or break-ups of theorems, and there isn't much enlightment or warmth or lucidity in presentation of the materials. I do find though, the author's other book, "Problems in analytic number theory", is far superior to this one.

4 of 6 people found the following review helpful:

4.0 out of 5 stars Excellent book on problems, February 22, 2006

By 

Physicsmind "Physicswish" (CA United States) - See all my reviews

This review is from: Problems in Algebraic Number Theory (Graduate Texts in Mathematics) (Hardcover)

This is a very useful book for anyone studying number theory. It's especially helpful for amatuer mathematicians learning on their own. This one is the same as the older edition with more hints and more detailed explanation. But WOULDN'T IT BE GREAT TO LEAVE A little room for the readers to think on their own?! You will reap the benefit from thinking hard as well as working hard!