Geometry I

Numbering Code U-SCI00 33142 LJ55 Year/Term 2021 ・ First semester
Number of Credits 4 Course Type Lecture
Target Year 3rd year students or above Target Student
Language Japanese Day/Period Wed.2・3
Instructor name KATOU TSUYOSHI (Graduate School of Science Professor)
Outline and Purpose of the Course This is a basic course on smooth manifolds.
A manifold is one of the fundamental concepts in modern geometry,
and many mathematical problems are formulated with manifolds.
Course Goals The students are expected to understand basic concepts related to a manifold -- smooth maps between manifolds and their derivatives, vector fields, and differential forms and to apply them to geometric problems.
Schedule and Contents Two or three weeks are devoted to each topics in the following:

1. the definition of a manifold and examples of manifolds.
2. sub manifolds.
3. tangent space, smooth maps and their derivatives.
4. vector fields and their integral curves.
5. differential forms.
6. integration on manifolds, Stokes' theorem.
7. some advanced topics.
Course Requirements The students are expected to have basic knowledge on calculus, linear algebra, and topological spaces.
Study outside of Class (preparation and review) We ask the students to review the lecture by theirselves.