This course is intended to explain some topics in mathematics to learn modern physics. The subjects includes the set theory, the group theory, topological spaces, manifolds, differential geometry and Lie algebra and groups.
In order to understand modern physics, it becomes increasingly necessary to learn methods of algebra and geometry.
This course is intended to learn basic ideas and techniques in these areas through lectures and exercises.
You will be able to understand the basics of set theory, group theory, and theory of topological space.
You will also have an ability to prove some mathematical theorems by yourselves. Through experiences of explaining your calculations during exercises, you will be able to learn a way of deductive reasoning and learn mathematical techniques and methods.
group theory, topological space, topology, differential geometry, Lie groups, Lie algbera
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Lectures and exercises
Course schedule | Required learning | |
---|---|---|
Class 1 | group theory | Understand definition of groups and thier examples |
Class 2 | cyclic group, homomorphism theorem | Understand cyclic group and homomorphism theorem |
Class 3 | irreducible resideu class group | Understand irreducible resideu class group |
Class 4 | topological space I, metric space, continuity, neighbourhood system | Understand metric space, continuity and neighbourhood system in topological space |
Class 5 | topological space II, compactness, conectivity | Understand compactness and conectivity |
Class 6 | manifold I differentiable manifold | Understand differentiable manifold |
Class 7 | manifold II, tangent space and differential forms | Understand tangent space and differential forms |
Class 8 | topology I homology and cohomology of manifolds | Understand homology and cohomology of manifolds |
Class 9 | topology II de Rham's theorem | Understand de Rham's theorem and its applications |
Class 10 | representation of real Clifford algebra | Understand representation of real Clifford algebra |
Class 11 | vector field on sphere | Understand vector field on sphere |
Class 12 | representation of complex Clifford algebra | Understand representation of complex Clifford algebra |
Class 13 | Dirac spinor and charge conjugation | Understand Dirac spinor and charge conjugation |
Class 14 | representation of rotation annd the Lorentz group | Understand representation of rotation annd the Lorentz group |
Class 15 | representation of Lie algebra | Understand representation of Lie algebra |
none required
Ichiro Yokota, Groups and Topology, Shokabo (Japanese)
excercise (70 per cent) and final exam (30 per cent)
Calculus and Linear algbera are required to be completed.