Mathematical Foundations of Computer Science
eBook - ePub

Mathematical Foundations of Computer Science

  1. 236 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Mathematical Foundations of Computer Science

About this book

Mathematical Foundations of Computer Science introduces students to the discrete mathematics needed later in their Computer Science coursework with theory of computation topics interleaved throughout. Students learn about mathematical concepts just in time to apply them to theory of computation ideas. For instance, sets motivate the study of finite automata, direct proof is practised using closure properties, induction is used to prove the language of an automaton, and contradiction is used to apply the pumping lemma.

The main content of the book starts with primitive data types such as sets and strings and ends with showing the undecidability of the halting problem. There are also appendix chapters on combinatorics, probability, elementary number theory, asymptotic notation, graphs, loop invariants, and recurrences. The content is laid out concisely with a heavy reliance on worked examples, of which there are over 250 in the book. Each chapter has exercises, totalling 550.

This class-tested textbook is targeted to intermediate Computer Science majors, and it is primarily intended for a discrete math / proofs course in a Computer Science major. It is also suitable for introductory theory of computation courses.

The authors hope this book breeds curiosity into the subject and is designed to satisfy this to some extent by reading this book. The book will prepare readers for deeper study of game theory applications in many fields of study.

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Yes, you can access Mathematical Foundations of Computer Science by Ashwin Lall in PDF and/or ePUB format, as well as other popular books in Computer Science & Computer Science General. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover Page
  2. Half-Title Page
  3. Title Page
  4. Copyright Page
  5. Contents
  6. Preface
  7. Chapter 1 Mathematical Data Types
  8. Chapter 2 Deterministic Finite Automata
  9. Chapter 3 Logic
  10. Chapter 4 Nondeterministic Finite Automata
  11. Chapter 5 Regular Expressions
  12. Chapter 6 Equivalence of Regular Languages and Regular Expressions
  13. Chapter 7 Direct Proof and Closure Properties
  14. Chapter 8 Induction
  15. Chapter 9 Proving the Language of a DFA
  16. Chapter 10 Proof by Contradiction
  17. Chapter 11 Pumping Lemma for Regular Languages
  18. Chapter 12 Context-Free Grammars
  19. Chapter 13 Turing Machines
  20. Chapter 14 Computability
  21. A Counting
  22. B Probability
  23. C Elementary Number Theory
  24. D Asymptotic Notation
  25. E Graphs
  26. F Loop Invariants
  27. G Recurrence Relations
  28. Further Reading
  29. Bibliography
  30. Index