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2018　Advanced Applied Mathematics for Physicists

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Academic unit or major
Physics
Instructor(s)
-
Class Format
Lecture / Exercise     
Media-enhanced courses
Day/Period(Room No.)
Mon1-4(H116)  Thr5-8(H116)  
Group
-
Course number
ZUB.M330
Credits
4
Academic year
2018
Offered quarter
1Q
Syllabus updated
2018/4/13
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

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.

Student learning outcomes

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.

Keywords

group theory, topological space, topology, differential geometry, Lie groups, Lie algbera

Competencies that will be developed

✔ Specialist skills Intercultural skills Communication skills Critical thinking skills ✔ Practical and/or problem-solving skills

Class flow

Lectures and exercises

Course schedule/Required learning

  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

Textbook(s)

none required

Reference books, course materials, etc.

Ichiro Yokota, Groups and Topology, Shokabo (Japanese)

Assessment criteria and methods

excercise (70 per cent) and final exam (30 per cent)

Related courses

  • ZUB.M201 ： Applied Mathematics for Physicists and Scientists I
  • ZUB.M213 ： Applied Mathematics for Physicists and Scientists II

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Calculus and Linear algbera are required to be completed.

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