Overview
- Could serve as a syllabus for second, third and fourth year undergraduate students in first rate universities
- Covers most of the material beyond usual linear algebra which is necessary for starting number theory, representation theory, algebraic geometry, and general algebra
- Not a standard presentation, lots of examples, subliminal introduction to categorical approach
- Offers a unique treatment of Dedekind Rings and modules over those
- Includes supplementary material: sn.pub/extras
Part of the book series: Mathematical Lectures from Peking University (MLPKU)
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Table of contents (3 chapters)
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Front Matter
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Back Matter
Keywords
About this book
During the springs of 2011 and 2012, the author was invited by Peking University to give an advanced undergraduate algebra course (once a week over two months each year). This book was written during and for that course. By no way does it claim to be too exhaustive. It was originally intended as a brief introduction to algebra for an extremely pleasant and passionate audience. It certainly reflects some of the author’s own tastes, and it was influenced by the feelings and the reactions of the students.
Nevertheless, the result covers some advanced undergraduate algebra (rings, ideals, basics of fields theory, algebraic integers, modules, hom and tensor functors, projective modules, etc.) illustrated by numerous examples, counterexamples and exercises. Following a worldwide tradition, the author had planned to conclude by lecturing on the structure of finitely generated modules over principal ideal domains. But during the course, after explaining that the notion of projective modules is more natural than the notion of free modules, it became clear that principal ideal domains needed to be replaced by Dedekind rings; this is much less traditional in the literature — but not more difficult.
Reviews
From the reviews:
“This textbook is an introduction and guide to advanced undergraduate algebra … and is based on two months author’s course at the Begijng International Centre for Mathematics Research. … It is self-contained, well written, understandable and enjoyable to read by undergraduate students. This textbook contains a lot of examples, counterexamples and numerous exercises.” (Marek Golasiński, zbMATH, Vol. 1287, 2014)Authors and Affiliations
Bibliographic Information
Book Title: Some Topics in Algebra
Book Subtitle: An Advanced Undergraduate Course at PKU
Authors: Michel Broué
Series Title: Mathematical Lectures from Peking University
DOI: https://doi.org/10.1007/978-3-642-41269-1
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2014
Hardcover ISBN: 978-3-642-41268-4Published: 13 November 2013
Softcover ISBN: 978-3-662-52505-0Published: 23 August 2016
eBook ISBN: 978-3-642-41269-1Published: 29 October 2013
Series ISSN: 2197-4209
Series E-ISSN: 2197-4217
Edition Number: 1
Number of Pages: XII, 201
Number of Illustrations: 4 b/w illustrations, 12 illustrations in colour
Topics: Algebra