Class Field Theory (Universitext) [Paperback]

Nancy Childress (Author)

Book Description

Publication Date: November 24, 2008 | ISBN-10: 0387724893 | ISBN-13: 978-0387724898 | Edition: 1st Edition. 2nd Printing.

Class field theory brings together the quadratic and higher reciprocity laws of Gauss, Legendre, and others, and vastly generalizes them. This book provides an accessible introduction to class field theory. It takes a traditional approach in that it attempts to present the material using the original techniques of proof, but in a fashion which is cleaner and more streamlined than most other books on this topic. It could be used for a graduate course on algebraic number theory, as well as for students who are interested in self-study. The book has been class-tested, and the author has included lots of challenging exercises throughout the text.

Editorial Reviews

Review

From the reviews: "This book has grown out of lectures on the subject by the author. … it must have been fun for both the author presenting these courses on class field theory and the students taking them and eager to learn the subject. … list of contents may give a good impression of how class field theory is developed in this book. … each chapter is commenced by a short introduction describing what is going on next. I enjoyed seeing explicit examples and nice applications … ." (Jürgen Ritter, Mathematical Reviews, Issue 2009 i) "Class field theory studies abelian extensions of number fields and their completions. … The clarity of the exposition and the many exercises ranging from routine to quite challenging problems make the book perfect for a first introduction to class field theory." (Franz Lemmermeyer, Zentralblatt MATH, Vol. 1165, 2009) “In a fast ride, running half the length of many competing volumes, Childress (Arizona State) employs a balanced mix of standard tools for a remarkably honed introduction … . Good to read alongside fleshier accounts; probably more accessible … . Summing Up: Recommended. Upper-division undergraduates through researchers/faculty.” (D. V. Feldman, Choice, Vol. 47 (3), November, 2009)

From the Back Cover

Class field theory, the study of abelian extensions of algebraic number fields, is one of the largest branches of algebraic number theory. It brings together the quadratic and higher reciprocity laws of Gauss, Legendre, and others, and vastly generalizes them. Some of its consequences (e.g., the Chebotarev density theorem) apply even to nonabelian extensions.   This book is an accessible introduction to class field theory. It takes a traditional approach in that it presents the global material first, using some of the original techniques of proof, but in a fashion that is cleaner and more streamlined than most other books on this topic.   It could be used for a graduate course on algebraic number theory, as well as for students who are interested in self-study. The book has been class-tested, and the author has included exercises throughout the text.   Professor Nancy Childress is a member of the Mathematics Faculty at Arizona State University.

Product Details

• Paperback: 226 pages
• Publisher: Springer; 1st Edition. 2nd Printing. edition (November 24, 2008)
• Language: English
• ISBN-10: 0387724893
• ISBN-13: 978-0387724898
• Product Dimensions: 9.1 x 6 x 0.5 inches
• Shipping Weight: 11.2 ounces (View shipping rates and policies)
• Amazon Best Sellers Rank: #1,694,626 in Books (See Top 100 in Books)

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