Mathematics: Concepts and Foundations

Edited by : Huzihiro Araki,

Research Institute of Mathematical Sciences, Kyoto University, Japan

1. General Background

Jean Pierre Bourguignon, Institut des Hautes Etudes Scientifiques, France

2. Geometry

Toshikazu Sunada

3. Algebra

Toshikazu Sunada

4. Mathematical Analysis

Huzihiro Araki, Research Institute of Mathematical Sciences, Kyoto University, Japan

Differential and Integral Calculus

Yoshio Togawa, Department of Information Sciences, Faculty of Science & Technology, Tokyo University of Science, Japan

Complex Analysis

Sin Hitotumatu, Kyoto University, Japan

Measure and Probability

Hisoa Watanabe, Kyushu University, Japan

Functional Analysis and Function Spaces

Mikihiro Hayashi, Department of Mathematics, Hokkaido University, Japan

Numerical Analysis and Computation

Yasuhiko Ikebe, Information Science Research Center, Meisei University, Japan

Asymptotic and Perturbative Methods

Christopher J. Howls

Fourier Analysis and Integral Transforms

Satoru Igari, Tohoku University, Japan

Operator Theory and Operator Algebra

Hideki Kosaki, Graduate School of Mathematics, Kyushu University, Japan

Unitary Representation of Lie Groups

Bertrami Kostant, MIT, USA

5. Formal Logic

Yiannis N. Moschovakis, University of California, Los Angeles (UCLA), USA

Model Theory

H. Jerome Keisler

Proof Theory and Constructive Mathematics

Anne S. Troelstra

Complexity, Computability and Undecidability

Martin Davis

Set Theory

John Steel

Logic and Computer Science

Phokion G. Kolaitis

Logic, Language and Philosophy

Kit Fine

6. Differential Equations of Mathematicals Physics

Huzihiro Araki, Research Institute of Mathematical Sciences, Kyoto University, Japan

General Setting and Historical Background

Hikosaburo Komatsu, University of Tokyo, Japan

A Basic Example of Non Linear Equation: The Navier-Stokes Equations

Claude Bardos

Variational Problems

Fabrice Bethuel

Linear Differential Equations

Louis Boutet de Monvel

Differential Equations and Symplectic Geometry

Hans DuisDuistermaat

Microlocal Analysis

Louis Boutet de Monvel

Dynamic Systems

Carls Simo, Barcelona University, Spain

7. Discrete Mathematics

Kazuo Murota

Graph Theory

Hikoe Enomoto

Combinatorics

Kakeshi Tokuyama

Computational Complexity

Osamu Watanabe

Algorithms

Hiroshi Imai

Optimization

Toshihide Ibaraki