A Course in Algebraic Number Theory by Robert B. Ash
A Course in Algebraic Number Theory - Table of Contents
1. Introduction
2. Norms, Traces, and Discriminants
3. Dedekind Domains
4. Factorization of Prime Ideals in Extensions
5. The Ideal Class Group
6. The Dirichlet Unit Theorem
7. Cyclotomic Extensions
8. Factorization of Prime Ideals in Galois Extensions
9. Local Fields
A. Quadratic Reciprocity via Gauss Sums
B. Extension of Absolute Values
C. The Different
What You Will Learn in A Course in Algebraic Number Theory
"Robert B. Ash" is an American mathematician and longtime professor at the "University of Illinois at Urbana–Champaign", known for his clear teaching style and well-structured lecture notes in "algebra" and "number theory". Throughout his academic career, he focused on making advanced mathematical topics accessible to students through careful explanations and logical progression. His materials are widely respected for balancing rigor with readability, especially at the graduate level.
His book "A Course in Algebraic Number Theory" originated as university lecture notes and was later shared freely for educational use. The text introduces fundamental ideas such as number fields, "Dedekind domains", ideals, and unique factorization, guiding readers step by step through the core theory. It is especially valued by students for its systematic approach and abundance of explanations that support independent study.
Today, the book remains a popular reference for learners and educators seeking a solid foundation in algebraic number theory. Its availability as a free academic resource has made it widely cited and linked across educational websites. Ash’s work reflects a strong commitment to open education and continues to support students entering advanced areas of modern mathematics.
Book Details & Specifications
Title:
A Course in Algebraic Number Theory by Robert B. Ash
Publisher:
Dover
Year:
2010
Pages:
108
Type:
PDF
Language:
English
ISBN-10 #:
0486477541
ISBN-13 #:
978-0486477541
License:
External Educational Resource
Amazon:
Amazon
About the Author: Robert B. Ash
The author
Robert B. Ash
is an American mathematician and former professor at the "University of Illinois at Urbana–Champaign", known for his work in "number theory" and algebra. He is especially respected for creating clear, well-structured lecture notes that help students understand advanced mathematical concepts step by step. His work, "A Course in Algebraic Number Theory", introduces key ideas such as "algebraic number fields", "Dedekind domains", and ideal factorization.
Read or Downloadable A Course in Algebraic Number Theory
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