MATP33 Group and Ring Theory, Spring 2023

MATP33 Group and Ring Theory is a continuation of the course MATM31 Algebraic Structures.

Course description

This course is an elective course for second-cycle studies for a Degree of Master of Science (120 credits) in mathematics. The course treats:

  • Groups: Permutation groups. Burnside's lemma with application to Pólya arithmetic. Sylow's theorems. Symmetric and alternating groups. The structure of finitely generated Abelian groups.
  • Rings: Noetherian and Artinian rings and modules. Artin-Wedderburn's theorem. Finitely generated modules over a principal ideal domain with application to the Jordan normal form of matrices.
  • Linear algebra: Multilinear mappings. Tensor products.

Teaching

The teaching consists of lectures and some seminars. The lecturer is Gustavo Jasso. 

Assessment

The examination consists of a written examination (5 credits) followed by an oral examination (2.5 credits) at the end of the course. The oral examination may only be taken by those students who passed the written examination.

Course literature

The lecturer's notes will be uploaded to Canvas as the course progresses.

Below is a list of complementary textbooks (more might be added later). Some of them are available for download from within LU's network.

  • Dummit, David S. and Foote, Richard M, Abstract algebra. Third edition. John Wiley & Sons, Inc., Hoboken, NJ, 2004. xii+932 pp. ISBN: 0-471-43334-9.
  • Hungerford, Thomas W., Algebra.  Reprint of the 1974 original. Graduate Texts in Mathematics, 73. Springer-Verlag, New York-Berlin, 1980. xxiii+502.
  • Lang, Serge, Algebra. Revised third edition. Graduate Texts in Mathematics, 211. Springer-Verlag, New York, 2002. xvi+914 pp.
  • Leinster, Tom, Basic category theory. Cambridge Studies in Advanced Mathematics, 143. Cambridge University Press, Cambridge, 2014. viii+183 pp. 
  • Löh, Clara. Geometric group theory. An introduction. Universitext. Springer, Cham, 2017. xi+389 pp. ISBN: 978-3-319-72253-5; 978-3-319-72254-2.
  • Rotman, Joseph J. An introduction to the theory of groups. Fourth edition. Graduate Texts in Mathematics, 148. Springer-Verlag, New York, 1995. xvi+513 pp.
  • Rotman, Joseph J. A first course in abstract algebra. Prentice Hall, Inc., Upper Saddle River, NJ, 1996,
    pp. xiv+265.
  • Stanley, Richard P. Enumerative combinatorics. Vol. 1, Second edition. Cambridge Studies in Advanced Mathematics, 49. Cambridge University Press, Cambridge, 2012, xiv+626 pp.
  • Stanley, Richard P. Enumerative combinatorics. Vol. 2. With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin. Cambridge Studies in Advanced Mathematics, 62. Cambridge University Press, Cambridge, 1999. xii+581 pp. 

Schedule

The schedule is available in the TimeEdit schedule tool. The detailed course program will be published here at the start of course.

Official Course Description

Student Influence and Course Evaluation

General information about student influence can be found on the link below:

You should select a course representative in connection to one of the first lectures.

Results from last year's course evaluation