Customer Reviews

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

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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.

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.