Mathematical Foundation of Computer Science ( Free PDF )


  • Preface
  • Why
  • Book function
  • Thanksgiving
  • Different concepts, relationships and applications
  • Distinguish between numeric functions and generating functions
  • Regression relationships and constant coefficients
  • Algebraic structure
  • Comments accepted
  • Lattice theory
  • Introduction to languages ​​and finite automata
  • Balancing NFA and DFA
  • Normal conversation
  • Regular and irregular languages
  • Irregular grammar
  • Introduction to mechanical engineering
  • Appendix – Boolean Algebra


To understand the fundamentals of computer science, it is important that we start with the study of mathematics from different fields, automation and formal languages. It is time to realize the importance of special mathematics as it finds various applications in the field of computer science. However, it requires meticulous research and its potential in the fields of science and natural sciences has long been known. To understand both the principles of computer science and the mathematics of computer science, this book offers a range of topics from specific mathematics and the concepts of automation and formal languages. The reason I chose this topic was that I wanted to start with as much of the basic terminology used in basic computer science courses as possible. Based on research needs, standard mathematics course covers set theory, algebraic systems, combinatorics, Boolean algebra, logical propositions, and other related problems. As cognitive behavior, it represents computational methods, computational models, language concepts, and implementation of language concepts, which are part of the definition of functional languages ​​and formal languages. These topics will also help in understanding the concepts and philosophies used in the early stages of computing, such as computation and computation, artificial intelligence, logic manipulation and design, software design such as fast compilers, advanced word processors and programming languages, assembly and programming. recovery information.

The text of this book is intended primarily for use by undergraduate and graduate students in the fields of ‘Mathematical Foundations of Computer Science’, ‘Discrete Mathematics’ and ‘Automata Theory and Formal Language’. Although the topics discussed in this book focus primarily on the technical aspects of computer science, it is also suitable for technical professionals.

The outline presented in this book is the result of experiences gained over the past decade in teaching courses such as Discrete Mathematics, Automatic Mathematics and Computer Science in the Department of Computer Science and Engineering at IET, UP Technical University, Lucknow and elsewhere. I hope that the presentation of this document reflects the plan of the investigation. I have always tried to stay away from complex numbers and concepts full of formalism and present them in a clear and interesting way. I also believe that when teaching, students not only learn the subject as a powerful tool for mathematics, but also increase their skills, understanding, reasoning and testing of mathematics problems, and the application of teaching in computer science. Numerous and helpful comments from my students motivated me to prepare this article. In conclusion, I hope this article will increase your knowledge about computer science and the explosion in computers, computer science, engineering and information technology.

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