Guerino Mazzola, Gérard Milmeister, Jody Weissmann

Comprehensive Mathematics for Computer Scientists 1 (eBook, PDF)

Sets and Numbers, Graphs and Algebra, Logic and Machines, Linear Geometry

• Format: PDF

Produktbeschreibung

This two-volume textbook Comprehensive Mathematics for Computer Scientists is a self-contained comprehensive presentation of mathematics including sets, numbers, graphs, algebra, logic, grammars, machines, linear geometry, calculus, ODEs, and special themes such as neural networks, Fourier theory, wavelets, numerical issues, statistics, categories, and manifolds. The concept framework is streamlined but defining and proving virtually everything. The style implicitly follows the spirit of recent topos-oriented theoretical computer science. Despite the theoretical soundness, the material stresses a large number of core computer science subjects, such as, for example, a discussion of floating point arithmetic, Backus-Naur normal forms, L-systems, Chomsky hierarchies, algorithms for data encoding, e.g., the Reed-Solomon code. The numerous course examples are motivated by computer science and bear a generic scientific meaning.

For the second edition the entire text has been carefully reread, and many examples have been added, as well as illustrations and explications to statements and proofs which were exposed in a too shorthand style. This makes the book more comfortable for instructors as well as for students to handle.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 388
• Erscheinungstermin: 5. Oktober 2006
• Englisch
• ISBN-13: 9783540368748
• Artikelnr.: 44128318

Autorenporträt

Guerino Mazzola, University of Zurich, Switzerland / Gérard Milmeister, University of Zurich, Switzerland / Jody Weissmann, University of Zurich, Switzerland

Inhaltsangabe

Sets, Numbers, and Graphs.- Fundamentals-Concepts and Logic.- Axiomatic Set Theory.- Boolean Set Algebra.- Functions and Relations.- Ordinal and Natural Numbers.- Recursion Theorem and Universal Properties.- Natural Arithmetic.- Infinities.- The Classical Number Domains Z, Q, R, and C.- Categories of Graphs.- Construction of Graphs.- Some Special Graphs.- Planarity.- First Advanced Topic.- Algebra, Formal Logic, and Linear Geometry.- Monoids, Groups, Rings, and Fields.- Primes.- Formal Propositional Logic.- Formal Predicate Logic.- Languages, Grammars, and Automata.- Categories of Matrixes.- Modules and Vector Spaces.- Linear Dependence, Bases, and Dimension.- Algorithms in Linear Algebra.- Linear Geometry.- Eigenvalues, the Vector Product, and Quaternions.- Second Advanced Topic.

Rezensionen

From the reviews:

"The solution proposed by the authors of this book consists essentially of a course on the foundations of mathematics and computer science. ... As one can see ... the book covers a lot of material. ... One of the good things about the book is that it covers a lot of ground in an extremely systematic way. ... the book is written with conviction, and one can see that the authors made a great effort to make it interesting to their readers." (S. C. Coutinho, The Mathematical Gazette, Vol. 90 (517), 2006)

"This book meets the needs of a sound mathematical education of computer scientists improving formal competence and flexibility. It very well sets forth (and proves) the essential core theory and theorist or executive on all levels of Computer Science and IT industry will appreciate. ... Having passed through all ... the student will have a broad and sufficiently deep mathematical knowledge." (H. Mitsch, Monatshefte für Mathematik, Vol. 145 (2), 2005)

From the reviews of the second edition:

"As the title of this book suggests, it covers a broad range of topics in mathematics; it is intended for use as an introductory textbook for computer science undergraduates. ... It may be suitable for people who are already familiar with the subject and need a reference to quickly check definitions and theorems." (I-Lun Tseng, ACM Computing Reviews, Vol. 49 (4), April, 2008)