Introduction to representation theory
Bachelor's degree
In Maynard (USA)
Description
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Type
Bachelor's degree
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Location
Maynard (USA)
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Start date
Different dates available
The goal of this course is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.
Facilities
Location
Start date
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Reviews
Subjects
- GCSE Mathematics
- Algebra
- Mathematics
Course programme
Lectures: 2 sessions / week, 1.5 hours / session
The goal of this course is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.
The prerequisites for the course are the standard algebra sequences Algebra I and II (18.701, 18.702) or Linear Algebra and Modern Algebra (18.700, 18.703). This means that to understand this course, it is necessary and sufficient to have a strong background in linear algebra and a decent understanding of basic algebraic structures, such as groups, rings, and fields. We will prove some general results, but a lot of the attention will be paid to examples, and there will be many hands-on exercises illustrating the course.
Besides the lecture notes, we will also use the beginning part of the books:
Fulton, William, and Joe Harris. Representation Theory: A First Course. Graduate texts in mathematics. Vol. 129. New York, NY: Springer, 1991. ISBN: 9780387974958.
Serre, Jean Pierre. Linear Representations of Finite Groups. Graduate texts in mathematics. Vol. 42. New York, NY: Springer-Verlag, 1977. ISBN: 9780387901909.
To pass the course, it will be required to solve homework assignments which will be assigned every Thursday and due the following Thursday. The homeworks are 75% of the grade. It is ok to collaborate on homework if you creatively participate in solving it and understand what you write. Also there will be a take-home final assignment at the end of the term, which will weigh 25% of the grade.
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Introduction to representation theory