Mathematical Lectures from Peking University

Some Topics in Algebra

An Advanced Undergraduate Course at PKU

Authors: Broué, Michel

  • 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
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eBook $84.99
price for USA (gross)
  • ISBN 978-3-642-41269-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-642-41268-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-3-662-52505-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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)

Table of contents (3 chapters)

Buy this book

eBook $84.99
price for USA (gross)
  • ISBN 978-3-642-41269-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-642-41268-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-3-662-52505-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Some Topics in Algebra
Book Subtitle
An Advanced Undergraduate Course at PKU
Authors
Series Title
Mathematical Lectures from Peking University
Copyright
2014
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-41269-1
DOI
10.1007/978-3-642-41269-1
Hardcover ISBN
978-3-642-41268-4
Softcover ISBN
978-3-662-52505-0
Series ISSN
2197-4209
Edition Number
1
Number of Pages
XII, 201
Number of Illustrations and Tables
4 b/w illustrations, 12 illustrations in colour
Topics