Comprehensive Mathematics for Computer Scientists 1: Sets and Numbers, Graphs and Algebra, Logic and Machines, Linear Geometry (Universitext) (v. 1) [Paperback]

Guerino Mazzola (Author), Gérard Milmeister (Author), Jody Weissmann (Author)

Book Description

Publication Date: November 13, 2006 | ISBN-10: 3540368736 | ISBN-13: 978-3540368731 | Edition: 2nd

Contains all the mathematics that computer scientists need to know in one place.

Editorial Reviews

Review

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)

From the Back Cover

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.

Product Details

• Paperback: 402 pages
• Publisher: Springer; 2nd edition (November 13, 2006)
• Language: English
• ISBN-10: 3540368736
• ISBN-13: 978-3540368731
• Product Dimensions: 9.3 x 6.2 x 0.9 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 3.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,487,230 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

4 of 4 people found the following review helpful:

2.0 out of 5 stars Not suitable for use as an introductory textbook, February 4, 2009

By 

I-lun Tseng (Taipei, Taiwan) - See all my reviews
(REAL NAME)   

This review is from: Comprehensive Mathematics for Computer Scientists 1: Sets and Numbers, Graphs and Algebra, Logic and Machines, Linear Geometry (Universitext) (v. 1) (Paperback)

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. The topics covered include sets, numbers, graphs, logic, grammars, automata, algebra, and geometry. Many of those topics can be found in books on discrete mathematics and linear algebra.

This book is part of a larger e-learning project, which also includes a companion Web site [...] The Web site contains slides, errata, and modular courses, as well as other information about the e-learning project. Although the book contains a broad range of topics in 26 chapters, it is relatively compact compared to other mathematics textbooks designed for computer science students.

The book has the following shortcomings. First, many important concepts are not clearly explained. Most of the definitions and theorems are listed without detailed explanations. Second, many figures in the book are not referred to in the text; they just appear close to some definitions, theorems, or examples. Third, the book does not contain enough examples for students to practice after definitions and theorems are stated, nor does it contain a collection of exercises at the end of each chapter. Teachers who use this as a textbook may need to find other complementary materials or come up with their own exercises in order for students to practice the techniques described in the book. Generally speaking, this book looks like a collection of handouts since it lacks detailed information throughout.

The book is also weak in terms of the depth of its coverage. For example, it discusses graph theory, but does not mention the graph coloring problem or the shortest path problem. It covers trees, but does not include Huffman trees or sorting. Many of topics covered have a close relationship to data structures and algorithms, but the book does not discuss them clearly.

In my opinion, the book is not suitable 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.

9 of 20 people found the following review helpful:

5.0 out of 5 stars Set high standards, August 17, 2004

By 

E. Gutknecht - See all my reviews
(REAL NAME)   

This review is from: Comprehensive Mathematics for Computer Scientists 1 (Paperback)

This book is very exciting and motivating, as it sets high standards both with respect to the contents and the style.

It contains the main topics of modern math from the beginning, with applications to Computer Science: Sets, Relations, Logic, Numbers, Groups, Rings, Modules, Linear Algebra, Geometry, Quaternions.

The style is extremely compact, precise and readable, with a professional notation. The book is optimal designed (modularized)
which results in a moderate size (360 p.)

The objective of his approach is to provide a better formal competence for computer scientists by a sound mathematical education:

"Improved formal competence is urged by the object-oriented paradigm which progressively requires a programming style and a design strategy of high abstraction level in conceptual engineering."

The accompanying online course contains illustrations and animations, which at the moment don't go far beyond the book's contents.
Nevertheless, the online part has a great potential for further applications, e.g. programming projects (Moebius-Strip, Raytracing, 3D Stereo, ...)

We hope, this book will establish itself as a standard for ambitious schools and students.