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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

Kakeshi Tokuyama

Computational Complexity
Osamu Watanabe

Hiroshi Imai

Toshihide Ibaraki

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