Fundamentals of Mathematical and Computing Sciences:Mathematics

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Umehara Masaaki  Kojima Sadayoshi  Nishibata Shinya 
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Lecture notes updated
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Spring Semester

Outline of lecture

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.

Purpose of lecture

This course is intended to provide basic knowledges in Mathematics
necessary for advancing study in Mathematical and Computing Sciences.

Plan of lecture

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

Textbook and reference

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,

Part III
S. Kobayashi, From Classical Geometry to Modern Geometry
(Japanese), Nihon-Hyoronsya 1990

Related and/or prerequisite courses

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.

Contact Information

Email addresses of instructors
Part I : sadayosiツシ
Part II : shinyaツシ
Part III : umeharaツシ

Office Hours

On appointment by email.

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