The VNR concise encyclopedia of mathematics

書誌事項

The VNR concise encyclopedia of mathematics

W. Gellert ... [et al.], editors ; K. A. Hirsch, H. Reichardt, scientific advisors

Van Nostrand Reinhold Co., 1977, c1975

1st American ed

  • pbk

統一タイトル

Mathematik

この図書・雑誌をさがす
注記

Translation of: Mathematik

Previously published under title: Mathematics at a glance

Includes indexes

内容説明・目次

内容説明

It is commonplace that in our time science and technology cannot be mastered without the tools of mathematics; but the same applies to an ever growing extent to many domains of everyday life, not least owing to the spread of cybernetic methods and arguments. As a consequence, there is a wide demand for a survey of the results of mathematics, for an unconventional approach that would also make it possible to fill gaps in one's knowledge. We do not think that a mere juxtaposition of theorems or a collection of formulae would be suitable for this purpose, because this would over- emphasize the symbolic language of signs and letters rather than the mathematical idea, the only thing that really matters. Our task was to describe mathematical interrelations as briefly and precisely as possible. In view of the overwhelming amount of material it goes without saying that we did not just compile details from the numerous text-books for individual branches: what we were aiming at is to smooth out the access to the specialist literature for as many readers as possible. Since well over 700000 copies of the German edition of this book have been sold, we hope to have achieved our difficult goal. Colours are used extensively to help the reader. Important definitions and groups of formulae are on a yellow background, examples on blue, and theorems on red.

目次

I. Elementary mathematics.- 1. Fundamental operations on rational numbers.- 2. Higher arithmetical operations.- 3. Development of the number system.- 4. Algebraic equations.- 5. Functions.- 6. Percentages, interest and annuities.- 7. Plane geometry.- 8. Solid geometry.- 9. Descriptive geometry.- 10. Trigonometry.- 11. Plane trigonometry.- 12. Spherical trigonometry.- 13. Analytic geometry of the plane.- II. Steps towards higher mathematics.- 14. Set theory.- 15. The elements of mathematical logic.- 16. Groups and fields.- 17. Linear algebra.- 18. Sequences, series, limits.- 19. Differential calculus.- 20. Integral calculus.- 21. Series of functions.- 22. Ordinary differential equations.- 23. Complex analysis.- 24. Analytic geometry of space.- 25. Projective geometry.- 26. Differential geometry, convex bodies, integral geometry.- 27. Probability theory and statistics.- 28. Calculus of errors, adjustment of data, approximation theory.- 29. Numerical analysis.- 30. Mathematical optimization.- III. Brief reports on selected topics.- 31. Number theory.- 32. Algebraic geometry.- 33. Further algebraic structures.- 34. Topology.- 35. Measure theory.- 36. Graph theory.- 37. Potential theory and partial differential equations.- 38. Calculus of variations.- 39. Integral equations.- 40. Functional analysis.- 41. Foundation of geometry - Euclidean and non-Euclidean geometry.- 42. Foundations of mathematics.- Tables.

「Nielsen BookData」 より

詳細情報
  • NII書誌ID(NCID)
    BA20226203
  • ISBN
    • 0442226462
    • 0442226470
  • LCCN
    76014575
  • 出版国コード
    us
  • タイトル言語コード
    eng
  • 本文言語コード
    engger
  • 出版地
    New York
  • ページ数/冊数
    760 p., [28] leaves of plates
  • 大きさ
    24 cm
  • 分類
  • 件名
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