学部・大学院区分
Undergraduate / Graduate

多・博前

時間割コード
Registration Code

3211002

科目区分
Course Category

Ａ類Ⅰ（基礎科目）
Category A-1

科目名　【日本語】
Course Title

数理科学展望Ⅱ

科目名　【英語】
Course Title

Perspectives in Mathematical Science II

コースナンバリングコード
Course Numbering Code

担当教員　【日本語】
Instructor

杉本充 ○ LE GALL Francois Pierre M 永尾太郎

担当教員　【英語】
Instructor

SUGIMOTO Mitsuru ○ LE GALL Francois Pierre Marcel NAGAO Taro

単位数
Credits

開講期・開講時間帯
Term / Day / Period

秋火曜日３時限
Fall Tue 3

授業形態
Course style

学科・専攻
Department / Program

多元数理科学研究科

必修・選択
Required / Selected

選択

授業の目的　【日本語】
Goals of the Course(JPN)

この講義は講師三人によるオムニバス形式の英語講義である.
内容は英文を参照すること.
See English text.

授業の目的　【英語】
Goals of the Course

The purpose of this course is to introduce and explain various concepts and methods in mathematical sciences.
This year, the course is provided by three instructors.
Part I (SUGIMOTO Mitsuru) Fourier analysis and its applications
Part II (LE GALL Francois) Algebraic complexity theory and matrix multiplication
Part III (NAGAO Taro) Introduction to the theory of random matrices

到達目標　【日本語】
Objectives of the Course(JPN))

各講師ごとに与えられたテーマに則した問題について考察し, レポートを作成, 提出することによってテーマの理解を深める. 各テーマの内容は英文を参照すること.
See English text.

到達目標　【英語】
Objectives of the Course

Part I (SUGIMOTO Mitsuru) Students should understand how Fourier analysis is applied to various problems of mathematics.

Part II (LE GALL Francois) Students should become familiar with the basis of algebraic complexity theory.

Part III (NAGAO Taro) Students should become familiar with the basic theory of random matrices, and ready to apply it to scientific problems.

授業の内容や構成
Course Content / Plan

Part I (SUGIMOTO Mitsuru) In this part of the lecture, the basic theory of Fourier analysis is introduced.

Part II (LE GALL Francois) Algebraic complexity theory is the study of computation and algorithms using algebraic models. This part of the course will give an overview of this field and in particular describe several powerful techniques to analyze the complexity of important computational problems from linear algebra. The presentation of these techniques will follow the history of progress on constructing fast algorithms for matrix multiplication, and also include some of its recent developments.

Part III (NAGAO Taro) In this part of the lecture, the basic theory of random matrices is introduced.

履修条件
Course Prerequisites

Part I (SUGIMOTO Mitsuru) Undergraduate calculus
Part II (LE GALL Francois) Undergraduate linear algebra
Part III (NAGAO Taro) Undergraduate linear algebra, calculus and complex analysis