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 Links to an external site.. Cambridge Studies in Advanced Mathematics, 143. Cambridge University Press, Cambridge, 2014. viii+183 pp.
- Löh, Clara. Geometric group theory Links to an external site.. 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, Links to an external site. Second edition. Cambridge Studies in Advanced Mathematics, 49. Cambridge University Press, Cambridge, 2012, xiv+626 pp.
- Stanley, Richard P. Enumerative combinatorics. Vol. 2. Links to an external site. 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 Links to an external site. 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:
- Information for students on student influence, work environment, complaints and study support at the Faculty of Science.pdf Download Information for students on student influence, work environment, complaints and study support at the Faculty of Science.pdf
You should select a course representative in connection to one of the first lectures.
- Checklist – what does a course representative do.pdf Download Checklist – what does a course representative do.pdf
Results from last year's course evaluation