Mathematics: Concepts and Foundations

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Editor(s):
Huzihiro Araki
Volume(s):
3
Published:
2009
Format:
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Book Contents

Mathematics: Concepts and Foundations is a component of Encyclopedia of Mathematical Sciences in which is part of the global Encyclopedia of Life Support Systems (EOLSS), an integrated compendium of twenty one Encyclopedias.

The Theme is organized into several topics which represent the main scientific areas of the theme: The first topic provides a brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations. The succeeding topics are Algebra; Geometry; Mathematical Analysis; Formal Logic; Differential Equations; Discrete Mathematics, which are then expanded into multiple subtopics, each as a chapter.

These three volumes are aimed at the following five major target audiences: University and College students Educators, Professional practitioners and Research personnel.

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

Table of Contents (40 Chapters)
  • 1. A View of Mathematics

    Alain CONNES
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    Volume : 1
  • 2. Mathematics through Millenia

    V.L. Hansen
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    Volume : 1
  • 3. Mathematics Alive and in Action

    V.L. Hansen
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    Volume : 1
  • 4. Algebra

    Tadao ODA
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    Volume : 1
  • 5. Matrices, Vectors, Determinant and Linear Algebra

    Tadao ODA
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    Volume : 1
  • 6. Groups and Applications

    Tadao ODA
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    Volume : 1
  • 7. Rings and Modules

    Tadao ODA
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    Volume : 1
  • 8. Fields and Algebraic Equations

    Tadao ODA
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    Volume : 1
  • 9. Number Theory and Applications

    Katsuya MIYAKE
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    Volume : 1
  • 10. Algebraic Geometry and Applications

    Tadao ODA
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    Volume : 1
  • 11. Basic Notions of Geometry and Euclidean Geometry

    Tetsuya Ozawa
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    Volume : 1
  • 12. Affine Geometry, Projective Geometry, and Non-Euclidean Geometry

    V.L. Hansen
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    Volume : 1
  • 13. Differential Geometry

    Takashi Sakai
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    Volume : 1
  • 14. Topology

    Takashi Tsuboi
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    Volume : 1
  • 15. Complex Analytic Geometry

    Tatsuo SUWA
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    Volume : 1
  • 16. Differential and Integral Calculus

    Yoshio Togawa
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    Volume : 2
  • 17. Complex Analysis

    Sin HITOTUMATU
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    Volume : 2
  • 18. Measure and Probability

    H. Watanabe
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    Volume : 2
  • 19. Functional Analysis and Function Spaces

    Mikihiro HAYASHI
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    Volume : 2
  • 20. Numerical Analysis and Computation

    Yasuhiko Ikebe
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    Volume : 2
  • 21. Infinite Analysis

    Tetsuji Miwa
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    Volume : 2
  • 22. Fourier Analysis and Integral Transforms

    Satoru Igari
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    Volume : 2
  • 23. Operator Theory and Operator Algebra

    H. Kosaki
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    Volume : 2
  • 24. Formal Logic

    Yiannis N. Moschovakis
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    Volume : 2
  • 25. Model Theory

    H. Jerome Keisler
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    Volume : 2
  • 26. Proof Theory and Constructive Mathematics

    Anne S. Troelstra
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    Volume : 2
  • 27. Computability and Complexity

    Martin Davis
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    Volume : 2
  • 28. Set Theory

    John R. Steel
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    Volume : 3
  • 29. Logic and Computer Science

    Phokion G. Kolaitis
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    Volume : 3
  • 30. Modal Logic and Its Applications

    Kit Fine
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    Volume : 3
  • 31. A Basic Example of NonLinear Equations: The Navier-Stokes Equations

    Claude Bardos
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    Volume : 3
  • 32. Calculus of Variations, Partial Differential Equations, and Geometry

    Fabrice Bethuel
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    Volume : 3
  • 33. Linear Differential Equations

    L. Boutet de Monvel
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    Volume : 3
  • 34. Differential Equations and Symplectic Geometry

    J.J. Duistermaat
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    Volume : 3
  • 35. From the Atomic Hypothesis To Microlocal Analysis

    Claude Bardos,Louis Boutet De Monvel
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    Volume : 3
  • 36. Discrete Mathematics

    Kazuo Murota
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    Volume : 3
  • 37. Graph Theory

    Hikoe Enomoto
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    Volume : 3
  • 38. Combinatorics

    Takeshi Tokuyama
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    Volume : 3
  • 39. Computational Complexity

    Osamu Watanabe
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    Volume : 3
  • 40. Optimization

    Toshihide Ibaraki
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    Volume : 3
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