- 使用教室
- 火5-6(W832)
- 単位数
- 講義：2 演習：0 実験：0
- 講義コード
- 75051
- シラバス更新日
- 2014年3月20日
- 講義資料更新日
- 2014年3月31日
- アクセス指標
-
- 学期
- 前期
講義概要
This course is divided into three parts, each of which discusses
several basic concepts either in Algebra, Geometry or Analysis.
The materials covered in the course would be useful in the study
of Mathematical and Computing Sciences.
講義の目的
This course is intended to provide basic knowledges in Mathematics
necessary for advancing study in Mathematical and Computing Sciences.
講義計画
Part I : Algebra
Lecture 1: Review on Basic Algebra
Lecture 2: Field Extension
Lecture 3: Cyclotomic Field
Lecture 4: Geometric Construction
Lecture 5: Finite Field
Part II : Analysis
Lecture 6: Hyperbolic conservation laws
Lecture 7: Blow up and Weak solutions
Lecture 8: Riemann problem
Lecture 9: Viscous Conservation laws
Lecture 10: Time global solutions and Asymptotic behaviors
Part III : Geometry
Lecture 11: Euclidean Geometry and Parallel Lines
Lecture 12: Non-Euclidean Geometry
Lecture 13: More on Euclidean Geometry
Lecture 14: Projective Geometry
Lecture 15: From Classical Geometry to Modern Geometry
教科書・参考書等
Part I :
S. Lang,
Algebra (Chapter V) Revised third edition,
GTM Springer, 2002
Part II :
Renardy, Michael, Rogers, Robert C.
An Introduction to Partial Differential Equations,
Springer
Part III
S. Kobayashi, From Classical Geometry to Modern Geometry
(Japanese), Nihon-Hyoronsya 1990
ISBN4-535-78176-1
関連科目・履修の条件等
Audiences are expected to have basic knowledge in several fields of mathematics necessarily
for starting graduate study in Mathematical and Computing Sciences. These include calculus,
linear algebra, general topology, elementary algebra, complex analysis, differential equation,
combinatorics, etc.
成績評価
Grades will be based on homework in three parts evenly.
連絡先（メール、電話番号）
Email addresses of instructors
Part I : sadayosi＠is.titech.ac.jp
Part II : shinya＠is.titech.ac.jp
Part III : umehara＠is.titech.ac.jp
オフィスアワー
On appointment by email.
