Comprehensive Mathematics for Computer Scientists 2: Calculus and ODEs, Splines, Probability, Fourier and Wavelet Theory, Fractals and Neural Networks, ... and Lambda Calculus (Universitext) (v. 2) (Paperback)

~ Guerino B. Mazzola (Author), (Author), (Author) "Throughout this section we work with the n-dimensional real vector space Rn..." (more)
Key Phrases: affine simplex, applicative order, diagram scheme, Proof Let, Fast Fourier Transform, Proof Clearly (more...)

Editorial Reviews

Review

From the reviews:

"This book is the second volume of … . each chapter summarizes rich and flourishing theories … . The authors are honest, and provide extensive references for the interested reader. … will find several exercises as well. … My overall opinion of this book is very positive. It provides a good and well-founded starting point for the study of several different areas of mathematics. I recommend it for students and scientists, especially in computer science … ." (A. Pethö, Computing Reviews, April, 2005)

"This two-volume textbook Comprehensive Mathematics for Computer Scientists is a self-contained comprehensive presentation of mathematics … . The concept framework is streamlined but defining and proving virtually everything. The style implicitly follows the spirit of recent topos-oriented theoretical computer science. … The numerous course examples are motivated by computer science and bear a generic scientific meaning." (Zentralblatt für Didaktik der Mathematik, August, 2005)

"The second volume of this comprehensive tour through mathematical subjects for computer scientists deals with topology, differential- and integral-calculus in one and several variables, and ordinary differential equations. … if she (he) masters these … the result will be an excellent computer scientist. With the aim to achieve this it would be quite motivating for the reader to see more concrete applications of the abstract mathematical theory." (H. Mitsch, Monatshefte für Mathematik, Vol. 147 (2), 2006)

"This is the second volume of a self-contained comprehensive presentation of mathematics for the working computer scientists. … The presentation of the book uses in an appropriate way the unifying language of category theory. This gives a new and more elegant view of the content … . The text is complemented by a large number of examples, illustrations, and applications and ends with the guide for future reading on the different topics." (Yves Félix, Bulletin of the Belgian Mathematical Society, Vol. 12 (2), 2005)

Product Description

 

This two-volume textbook Comprehensive Mathematics for the Working Computer Scientist 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. This text is complemented by an online university course which covers the same theoretical content, however, in a totally different presentation. The student or working scientist who once gets involved in this text may at any time consult the online interface which comprises applets and other interactive tools.

Product Details

• Paperback: 355 pages
• Publisher: Springer; 1 edition (November 23, 2004)
• Language: English
• ISBN-10: 3540208615
• ISBN-13: 978-3540208617
• Product Dimensions: 9.2 x 6.1 x 0.9 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 3.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon.com Sales Rank: #1,640,833 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

2 of 2 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.