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  6. MX5502: Algebra 2

MX5502: ALGEBRA 2 (2014-2015)

Last modified: 28 Jun 2018 10:27


Course Overview

This course is dispensed by the Scottish Mathematical Sciences Training Centre, with different teachers taking turns broadcasting their lectures from and to universities around Scotland.

 

It builds on MX5002 Algebra 1 to further extend the algebraic knowledge of students.

 

The first part continues the study of rings and modules begun in MX5002. Starting with free and projective modules, it culminates with the Artin-Wedderburn Theorem on the structure of modules.

The second part is an introduction to representation theory of groups, starting with finite groups, representations and characters, Maschke’s Theorem and the Orthogonality Relations, and ending with compact groups.





Course Details

Study Type Postgraduate Level 5
Term Second Term Credit Points 20 credits (10 ECTS credits)
Campus None. Sustained Study No
Co-ordinators
  • Dr Jean-Baptiste Gramain

What courses & programmes must have been taken before this course?

None.

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

No

Course Description

Modules and Rings: finitely generated modules over a PID; Jordan canonical form of a matrix; the Artin-Wedderburn theorem; modules over semisimple Artinian rings. Ordinary representations theory of finite groups: Maschke's theorem; characters and character tables; tensor products; applications to groups such as Burnside's theorem.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

More Information about Week Numbers


Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

One 3-hour written examination (80%); one in-course assessment (20%).

Formative Assessment

There are no assessments for this course.

Feedback

None.

Course Learning Outcomes

None.
 

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