The Discrete Math Workbook

1. Front Matter

   Pages i-xvii

   PDF

2. Fundamentals of Mathematical Logic

   • Sergei Kurgalin, Sergei Borzunov

   Pages 1-62

3. Set Theory

   • Sergei Kurgalin, Sergei Borzunov

   Pages 63-101

4. Relations and Functions

   • Sergei Kurgalin, Sergei Borzunov

   Pages 103-148

5. Combinatorics

   • Sergei Kurgalin, Sergei Borzunov

   Pages 149-178

6. Graphs

   • Sergei Kurgalin, Sergei Borzunov

   Pages 179-216

7. Boolean Algebra

   • Sergei Kurgalin, Sergei Borzunov

   Pages 217-249

8. Complex Numbers

   • Sergei Kurgalin, Sergei Borzunov

   Pages 251-280

9. Recurrence Relations

   • Sergei Kurgalin, Sergei Borzunov

   Pages 281-331

10. Concept of an Algorithm. Correctness of Algorithms

    • Sergei Kurgalin, Sergei Borzunov

    Pages 333-342

11. Turing Machine

    • Sergei Kurgalin, Sergei Borzunov

    Pages 343-355

12. Asymptotic Analysis

    • Sergei Kurgalin, Sergei Borzunov

    Pages 357-375

13. Basic Algorithms

    • Sergei Kurgalin, Sergei Borzunov

    Pages 377-433

14. Parallel Algorithms

    • Sergei Kurgalin, Sergei Borzunov

    Pages 435-477

15. Back Matter

    Pages 479-500

    PDF

This practically-focused study guide introduces the fundamentals of discrete mathematics through an extensive set of classroom-tested problems. Each chapter presents a concise introduction to the relevant theory, followed by a detailed account of common challenges and methods for overcoming these. The reader is then encouraged to practice solving such problems for themselves, by tackling a varied selection of questions and assignments of different levels of complexity.

This updated second edition now covers the design and analysis of algorithms using Python, and features more than 50 new problems, complete with solutions.

Topics and features: provides a substantial collection of problems and examples of varying levels of difficulty, suitable for both laboratory practical training and self-study; offers detailed solutions to each problem, applying commonly-used methods and computational schemes; introduces the fundamentals of mathematical logic, the theory of algorithms, Boolean algebra, graph theory, sets, relations, functions, and combinatorics; presents more advanced material on the design and analysis of algorithms, including Turing machines, asymptotic analysis, and parallel algorithms; includes reference lists of trigonometric and finite summation formulae in an appendix, together with basic rules for differential and integral calculus.

This hands-on workbook is an invaluable resource for undergraduate students of computer science, informatics, and electronic engineering. Suitable for use in a one- or two-semester course on discrete mathematics, the text emphasizes the skills required to develop and implement an algorithm in a specific programming language.

• Discrete mathematics
• Algorithm analysis
• Problem complexity
• Boolean algebra
• Set theory
• algorithm analysis and problem complexity

“The content is pretty comprehensive. … The writing is well-done and the text is nicely edited. … it could be very effectively used for self-study. The discovery aspect of problems and solutions can be much more engaging than straight forward reading of text. The reader is also able to build up their knowledge, starting with the problems with short answers and moving to those that are more involved with proofs or longer solutions.” (Tricia Muldoon Brown, MAA Reviews, September 20, 2021)

• Voronezh State University, Voronezh, Russia

  Sergei Kurgalin, Sergei Borzunov

​Dr. Sergei Kurgalin is a Professor and Head of the Department of Digital Technologies at Voronezh State University, Russia.

Dr. Sergei Borzunov is an Associate Professor at the same institution.

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