**Student Mathematical Library**

Volume: 84;
2017;
312 pp;
Softcover

MSC: Primary 11;

Print ISBN: 978-1-4704-3653-7

Product Code: STML/84

List Price: $52.00

Individual Member Price: $41.60

**Electronic ISBN: 978-1-4704-4125-8
Product Code: STML/84.E**

List Price: $52.00

Individual Member Price: $41.60

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# A Conversational Introduction to Algebraic Number Theory: Arithmetic Beyond \(\mathbb{Z}\)

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*Paul Pollack*

Gauss famously referred to mathematics as the “queen of the
sciences” and to number theory as the “queen of
mathematics”. This book is an introduction to algebraic
number theory, meaning the study of arithmetic in finite extensions of
the rational number field \(\mathbb{Q}\). Originating in the
work of Gauss, the foundations of modern algebraic number theory are
due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book
lays out basic results, including the three “fundamental
theorems”: unique factorization of ideals, finiteness of the
class number, and Dirichlet's unit theorem. While these theorems are
by now quite classical, both the text and the exercises allude
frequently to more recent developments.

In addition to traversing the main highways, the book reveals some
remarkable vistas by exploring scenic side roads. Several topics
appear that are not present in the usual introductory texts. One
example is the inclusion of an extensive discussion of the theory of
elasticity, which provides a precise way of measuring the failure of
unique factorization.

The book is based on the author's notes from a course delivered at
the University of Georgia; pains have been taken to preserve the
conversational style of the original lectures.

#### Readership

Undergraduate and graduate students interested in algebraic number theory.