The VNR Concise Encyclopedia of Mathematics

It is commonplace that in our time sc:iem:e 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. Front Matter....Pages 1-10 Introduction....Pages 11-16 Fundamental operations on rational numbers....Pages 17-47 Higher arithmetical operations....Pages 47-69 Development of the number system....Pages 69-80 Algebraic equations....Pages 80-106 Functions....Pages 107-139 Percentages, interest and annuities....Pages 139-145 Plane geometry....Pages 146-183 Solid geometry....Pages 184-203 Descriptive geometry....Pages 203-220 Trigonometry....Pages 220-240 Plane trigonometry....Pages 241-261 Spherical trigonometry....Pages 261-282 Analytic geometry of the plane....Pages 282-319 Set theory....Pages 320-332 The elements of mathematical logic....Pages 332-342 Groups and fields....Pages 343-356 Linear algebra....Pages 356-380 Sequences, series, limits....Pages 381-406 Differential calculus....Pages 406-443 Integral calculus....Pages 443-479 Series of functions....Pages 479-500 Ordinary differential equations....Pages 500-517 Complex analysis....Pages 517-529 Analytic geometry of space....Pages 530-547 Projective geometry....Pages 547-561 Differential geometry, convex bodies, integral geometry....Pages 561-575 Probability theory and statistics....Pages 575-607 Calculus of errors, adjustment of data, approximation theory....Pages 607-630 Numerical analysis....Pages 630-653 Mathematical optimization....Pages 653-668 Number theory....Pages 669-675 Algebraic geometry....Pages 675-677 Further algebraic structures....Pages 678-680 Topology....Pages 680-686 Measure theory....Pages 687-687 Graph theory....Pages 688-692 Potential theory and partial differential equations....Pages 693-698 Calculus of variations....Pages 698-702 Integral equations....Pages 703-705 Functional analysis....Pages 705-711 Foundations of geometry—Euclidean and non-Euclidean geometry....Pages 711-717 Foundations of mathematics....Pages 717-722 Game theory....Pages 723-730 Perturbation theory....Pages 731-732 The pocket calculator....Pages 732-745 Microcomputers....Pages 745-755 Back Matter....Pages 756-778 Explains the interrelationships between the various mathematical branches. Includes 950 diagrams, drawings, photographs, and plates