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Zbl 1177.00012
Drmota, Michael; Gittenberger, Bernhard; Karigl, Günther; Panholzer, Alois
Mathematics for computer science. (Mathematik für Informatik.) (English)
[B] Berliner Studienreihe zur Mathematik 17. Lemgo: Heldermann Verlag. viii, 438~p. EUR~36.00 (2007). ISBN 978-3-88538-117-4/pbk

This volume comprises all the standard material for basic lectures of mathematics, starting in chapter 1 with Peano's axioms of the natural numbers, propositional logic and naive set theory. Chapter 2 introduces into elementary combinatorics and graph theory, then quickly moves on to algebraic structures (groups, rings, fields, boolean algebra). Chapter 3 is devoted to linear algebra, using vector spaces over arbitrary fields, includung eigenvalues and positive definite matrices. The rest of the book (chapters 4 to 8) contains a rather complete survey of calculus, including improper and multiple integrals, ordinary and partial differential equations, discrete and continuous Fourier transform, Fourier series and Laplace transform, difference equations of first and second order, followed by a last chapter on numerical methods: approximation, interpolation, numerical integration, finite elements methods. Complex numbers are used whenever they are necessary and appropriate. \par The material is intended for about three courses. The exposition sets value on complete and rigorous proofs, although sometimes they are left as an exercise. Occasionally there are terse samples of applications to computer science, but the bulk of material is more appropriate for computer engineering. Self-study is supported by lots of exercises, regrettably without solutions.
[Dieter Riebesehl (Lüneburg)]

MSC 2000:: *00A06 Mathematics for non-mathematicians
03-01 Textbooks (mathematical logic)
05-01 Textbooks (combinatorics)
26-01 Textbooks (real functions)
34-01 Textbooks (ordinary differential equations)
35-01 Textbooks (partial differential equations)
39-01 Textbooks (functional equations)
40-01 Textbooks (sequences, etc.)
42-01 Textbooks (Fourier analysis)
65-01 Textbooks (numerical analysis)

Keywords: general mathematics; Combinatorics; linear Algebra; calculus; numerical analysis

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	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.
	Elementary number theory. Primes, congruences, and secrets.

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