Skip to main content
SpringerLink
Log in
Book cover

Comprehensive Mathematics for Computer Scientists 1

Sets and Numbers, Graphs and Algebra, Logic and Machines, Linear Geometry

  • Textbook
  • © 2006

Overview

Authors:
  1. Guerino Mazzola

    1. Department of Informatics, University Zurich, 8057, Zurich, Switzerland

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Gérard Milmeister

    1. Department of Informatics, University Zurich, 8057, Zurich, Switzerland

    View author publications

    You can also search for this author in PubMed   Google Scholar

  3. Jody Weissmann

    1. Department of Informatics, University Zurich, 8057, Zurich, Switzerland

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Universitext (UTX)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 64.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 84.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (26 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Sets, Numbers, and Graphs

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Fundamentals–Concepts and Logic

      Pages 3-14

    3. Axiomatic Set Theory

      Pages 15-23

    4. Boolean Set Algebra

      Pages 25-28

    5. Functions and Relations

      Pages 29-44

    6. Ordinal and Natural Numbers

      Pages 45-54

    7. Recursion Theorem and Universal Properties

      Pages 55-71

    8. Natural Arithmetic

      Pages 73-78

    9. Infinities

      Pages 79-80

    10. The Classical Number Domains Z, Q, R, and C

      Pages 81-105

    11. Categories of Graphs

      Pages 107-128

    12. Construction of Graphs

      Pages 129-135

    13. Some Special Graphs

      Pages 137-142

    14. Planarity

      Pages 143-148

    15. First Advanced Topic

      Pages 149-156

  3. Algebra, Formal Logic, and Linear Geometry

    1. Front Matter

      Pages 157-157
      Download chapter PDF

    2. Monoids, Groups, Rings, and Fields

      Pages 159-179

    3. Primes

      Pages 181-189

    4. Formal Propositional Logic

      Pages 191-207
Back to top

Keywords

About this book

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.

Reviews

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)

Authors and Affiliations

  • Department of Informatics, University Zurich, 8057, Zurich, Switzerland

    Guerino Mazzola, Gérard Milmeister, Jody Weissmann

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation