- School of Science
- School of Engineering
- Group 2
- Group 3
- Group 4
- Group 5
- Group 6
- Metallurgical Engineering
- Organic and Polymeric Materials
- Inorganic Materials
- Chemical Engineering Course
- Chemical Engineering Course(Chemical Engineering)
- Applied Chemistry Course(Chemical Engineering)
- Polymer Chemistry
- Mechanical Engineering and Science
- Mechanical and Intelligent Systems Engineering
- Mechano-Aerospace Engineering
- International Development Engineering
- Control and Systems Engineering
- Industrial and Systems Engineering
- Electrical and Electronic Engineering
- Computer Science
- Civil Engineering
- Architecture and Building Engineering
- Social Engineering
- International Development Engineering
- International Development Engineering
- International Development Engineering
- International Development Engineering
- International Development Engineering
- International Development Engineering
- Common Cource of Engineering

- School of Bioscience and Biotechnology
- Common Course of Undergraduate School

- Graduate School of Science and Engineering
- Mathematics
- Physics(Particle- Nuclear- and Astro-Physics)
- Physics(Condensed Matter Physics)
- Chemistry
- Earth and Planetary Sciences
- Chemistry and Materials Science
- Metallurgy and Ceramics Science
- Organic and Polymeric Materials
- Applied Chemistry
- Chemical Engineering
- Common Course of Mechanical Engineering
- Mechanical Sciences and Engineering
- Mechanical and Control Engineering
- Mechanical and Aerospace Engineering
- Common Course of Electronic Engineering
- Electrical and Electronic Engineering
- Physical Electronics
- Communications and Integrated Systems
- Communications and Computer Engineering
- Civil Engineering
- Architecture and Building Engineering
- International Development Engineering
- Nuclear Engineering

- Graduate School of Bioscience and Biotechnology
- Interdisciplinary Graduate School of Science and Engineering
- Built Environment
- Energy Sciences
- Computational Intelligence and Systems Science
- Electronic Chemistry
- Materials Science and Engineering
- Innovative and Engineered Materials
- Environmental Chemistry and Engineering
- Environmental Science and Technology
- Mechano-Micro Engineering
- Information Processing
- Electronics and Applied Physics

- Graduate School of Information Science and Engineering
- Graduate School of Decision Science and Technology
- Graduate School of Innovation Management
- Common Course of Graduate School
- Program for Leading Graduate Schools

- Place
- Tue5-6(W832)

- Credits
- Lecture2 Exercise0 Experiment0

- Code
- 75051

- Syllabus updated
- 2014/3/20

- Lecture notes updated
- 2014/3/31

- Access Index

- Semester
- Spring Semester

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.

This course is intended to provide basic knowledges in Mathematics

necessary for advancing study in Mathematical and Computing Sciences.

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

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

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.

Grades will be based on homework in three parts evenly.

Email addresses of instructors

Part I : sadayosiﾂｼis.titech.ac.jp

Part II : shinyaﾂｼis.titech.ac.jp

Part III : umeharaﾂｼis.titech.ac.jp

On appointment by email.