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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 orga' 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.
Table des matières
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.
Résumé
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.
Texte suppl.
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)
Commentaire
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)
