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Advanced Number Theory

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Synopses & Reviews

Publisher Comments:

"A very stimulating book ... in a class by itself." — American Mathematical Monthly

Advanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. Moreover, the book abounds with numerical examples and more concrete, specific theorems than are found in most contemporary treatments of the subject.

The book is divided into three parts. Part I is concerned with background material — a synopsis of elementary number theory (including quadratic congruences and the Jacobi symbol), characters of residue class groups via the structure theorem for finite abelian groups, first notions of integral domains, modules and lattices, and such basis theorems as Kronecker's Basis Theorem for Abelian Groups.

Part II discusses ideal theory in quadratic fields, with chapters on unique factorization and units, unique factorization into ideals, norms and ideal classes (in particular, Minkowski's theorem), and class structure in quadratic fields. Applications of this material are made in Part III to class number formulas and primes in arithmetic progression, quadratic reciprocity in the rational domain and the relationship between quadratic forms and ideals, including the theory of composition, orders and genera. In a final concluding survey of more recent developments, Dr. Cohn takes up Cyclotomic Fields and Gaussian Sums, Class Fields and Global and Local Viewpoints.

In addition to numerous helpful diagrams and tables throughout the text, appendices, and an annotated bibliography, Advanced Number Theory also includes over 200 problems specially designed to stimulate the spirit of experimentation which has traditionally ruled number theory.

Synopsis:

Eminent mathematician/teacher approaches algebraic number theory from historical standpoint. Demonstrates how concepts, definitions, and theories have evolved during last two centuries. Features over 200 problems and specific theorems. Includes numerous graphs and tables.

Synopsis:

Eminent mathematician/teacher approaches algebraic number theory from historical standpoint. Demonstrates how concepts, definitions, theories have evolved during last 2 centuries. Features over 200 problems and specific theorems. Includes numerous graphs and tables.


Product Details

ISBN:
9780486640235
Author:
Cohn, Harvey
Publisher:
Dover Publications
Author:
Mathematics
Location:
New York :
Subject:
Mathematics
Subject:
Number Theory
Subject:
Modern mathematics
Subject:
General Mathematics
Subject:
Mathematics-Number Theory
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
no. 30
Publication Date:
19800831
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
288
Dimensions:
8.25 x 5.63 in 0.72 lb

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Related Subjects

Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Number Theory
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics
Science and Mathematics » Mathematics » Topology
Young Adult » General

Advanced Number Theory New Trade Paper
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Product details 288 pages Dover Publications - English 9780486640235 Reviews:
"Synopsis" by ,
Eminent mathematician/teacher approaches algebraic number theory from historical standpoint. Demonstrates how concepts, definitions, and theories have evolved during last two centuries. Features over 200 problems and specific theorems. Includes numerous graphs and tables.

"Synopsis" by , Eminent mathematician/teacher approaches algebraic number theory from historical standpoint. Demonstrates how concepts, definitions, theories have evolved during last 2 centuries. Features over 200 problems and specific theorems. Includes numerous graphs and tables.


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