Product details:
| ISBN13: | 9781009001922 |
| ISBN10: | 1009001922 |
| Binding: | Paperback |
| No. of pages: | 250 pages |
| Size: | 228x151x13 mm |
| Weight: | 360 g |
| Language: | English |
| 845 |
Category:
Algebraic Number Theory for Beginners
Following a Path From Euclid to Noether
Publisher: Cambridge University Press
Date of Publication: 11 August 2022
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GBP 29.99
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Short description:
A concise and well-motivated introduction to algebraic number theory, following the evolution of unique prime factorization through history.
Long description:
This book introduces algebraic number theory through the problem of generalizing 'unique prime factorization' from ordinary integers to more general domains. Solving polynomial equations in integers leads naturally to these domains, but unique prime factorization may be lost in the process. To restore it, we need Dedekind's concept of ideals. However, one still needs the supporting concepts of algebraic number field and algebraic integer, and the supporting theory of rings, vector spaces, and modules. It was left to Emmy Noether to encapsulate the properties of rings that make unique prime factorization possible, in what we now call Dedekind rings. The book develops the theory of these concepts, following their history, motivating each conceptual step by pointing to its origins, and focusing on the goal of unique prime factorization with a minimum of distraction or prerequisites. This makes a self-contained easy-to-read book, short enough for a one-semester course.
'In Algebraic Number Theory for Beginners, John Stillwell once again displays his remarkable talent for using the history of mathematics to motivate and explore even the most abstract mathematical concepts at an accessible, undergraduate level. This book is another gem of the genre Stillwell has done so much to enhance.' Karen Hunger Parshall, University of Virginia
'In Algebraic Number Theory for Beginners, John Stillwell once again displays his remarkable talent for using the history of mathematics to motivate and explore even the most abstract mathematical concepts at an accessible, undergraduate level. This book is another gem of the genre Stillwell has done so much to enhance.' Karen Hunger Parshall, University of Virginia
Table of Contents:
Preface; 1. Euclidean arithmetic; 2. Diophantine arithmetic; 3. Quadratic forms; 4. Rings and fields; 5. Ideals; 6. Vector spaces; 7. Determinant theory; 8. Modules; 9. Ideals and prime factorization; References; Index.
