The VNR Concise Encyclopedia of Mathematics

Buch | Softcover

760 Seiten

2013 | 1975 ed.
Springer-Verlag New York Inc.
9781468482393 (ISBN)

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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.

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.

Zusatzinfo	760 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Schulbuch / Wörterbuch
	Geisteswissenschaften
	Mathematik / Informatik ► Mathematik
	Naturwissenschaften
	Sozialwissenschaften
ISBN-13	9781468482393 / 9781468482393
Zustand	Neuware