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Cover: 9783540368731 | Comprehensive Mathematics for Computer Scientists 1 | Mazzola (u. a.)
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Comprehensive Mathematics for Computer Scientists 1
Sets and Numbers, Graphs and Algebra, Logic and Machines, Linear Geometry
Buch von Guerino Mazzola (u. a.)
Sprache: Englisch

85,25 €*

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Beschreibung
A second edition of a book is a success and an obligation at the same time. We are satis ed that a number of university courses have been orgä nized on the basis of the rst volume of Comprehensive Mathematics for Computer Scientists. The instructors recognized that the self¿contained presentation of a broad specturm of mathematical core topics is a rm point of departure for a sustainable formal education in computer sci¿ ence. We feel obliged to meet the valuable feedback of the responsible in¿ structors of such courses, in particular of Joel Young (Computer Science Department, Brown University) who has provided us with numerous re¿ marks on misprints, errors, or obscurities. We would like to express our gratitude for these collaborative contributions. We have reread the entire text and not only eliminated identi ed errors, but also given some addi¿ tional examples and explications to statements and proofs which were exposed in a too shorthand style. A second edition of the second volume will be published as soon as the errata, the suggestions for improvements, and the publisher¿s strategy are in harmony.
A second edition of a book is a success and an obligation at the same time. We are satis ed that a number of university courses have been orgä nized on the basis of the rst volume of Comprehensive Mathematics for Computer Scientists. The instructors recognized that the self¿contained presentation of a broad specturm of mathematical core topics is a rm point of departure for a sustainable formal education in computer sci¿ ence. We feel obliged to meet the valuable feedback of the responsible in¿ structors of such courses, in particular of Joel Young (Computer Science Department, Brown University) who has provided us with numerous re¿ marks on misprints, errors, or obscurities. We would like to express our gratitude for these collaborative contributions. We have reread the entire text and not only eliminated identi ed errors, but also given some addi¿ tional examples and explications to statements and proofs which were exposed in a too shorthand style. A second edition of the second volume will be published as soon as the errata, the suggestions for improvements, and the publisher¿s strategy are in harmony.
Zusammenfassung

This two-volume textbook, of which this is the first volume, is a self-contained comprehensive presentation of mathematics for computer scientists. It includes coverage of sets, numbers, graphs, algebra, logic, grammars and machines. It also deals with linear geometry, calculus, ODEs, and special themes such as neural networks, Fourier theory, wavelets, numerical issues, statistics, categories, and manifolds. This text is complemented by an online university course which covers the same theoretical content in a totally different presentation. The student or working scientist who gets involved with this text may at any time consult the online interface which contains applets and other interactive tools. For the second edition the entire text has been carefully re-written, and many examples have been added, as well as illustrations and explications to statements and proofs which were exposed in a too short a style. This makes the book easier for both instructors and students.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2006
Genre: Informatik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Universitext
Inhalt: xiv
388 S.
ISBN-13: 9783540368731
ISBN-10: 3540368736
Sprache: Englisch
Herstellernummer: 11803911
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Mazzola, Guerino
Weissmann, Jody
Milmeister, Gérard
Auflage: 2nd ed. 2006
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Universitext
Maße: 241 x 160 x 27 mm
Von/Mit: Guerino Mazzola (u. a.)
Erscheinungsdatum: 20.09.2006
Gewicht: 0,77 kg
Artikel-ID: 102171451
Zusammenfassung

This two-volume textbook, of which this is the first volume, is a self-contained comprehensive presentation of mathematics for computer scientists. It includes coverage of sets, numbers, graphs, algebra, logic, grammars and machines. It also deals with linear geometry, calculus, ODEs, and special themes such as neural networks, Fourier theory, wavelets, numerical issues, statistics, categories, and manifolds. This text is complemented by an online university course which covers the same theoretical content in a totally different presentation. The student or working scientist who gets involved with this text may at any time consult the online interface which contains applets and other interactive tools. For the second edition the entire text has been carefully re-written, and many examples have been added, as well as illustrations and explications to statements and proofs which were exposed in a too short a style. This makes the book easier for both instructors and students.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2006
Genre: Informatik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Universitext
Inhalt: xiv
388 S.
ISBN-13: 9783540368731
ISBN-10: 3540368736
Sprache: Englisch
Herstellernummer: 11803911
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Mazzola, Guerino
Weissmann, Jody
Milmeister, Gérard
Auflage: 2nd ed. 2006
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Universitext
Maße: 241 x 160 x 27 mm
Von/Mit: Guerino Mazzola (u. a.)
Erscheinungsdatum: 20.09.2006
Gewicht: 0,77 kg
Artikel-ID: 102171451
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