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Theory of Computer Science Unit 1 Sikkim Manipal University Page No.: 1 Unit 1 Mathematical Fundamentals for Computer Science Structure 1.1 Introduction Objectives 1.2 Sets and Properties 1.3 Functions and Relations 1.4 Equivalence Relations 1.5 Recursive Functions 1.6 Strings and Growth Functions 1.7 Summary 1.8 Terminal Questions 1.9 Answers 1.1 Introduction The idea of set is fundamental in the study of mathematical structures. All most all mathematical objects of can be defined in terms of sets and the language of set theory is used in every mathematical subject. Also the concept of relation and function arises when we consider a pair of objects and compare each other. In this unit we study the different relations on a set and the algebraic structures with single binary operation. In computer programming, recursion plays an important role. It is an important facility in many programming languages. We have discussed the concepts recursive functions and growth functions which are useful in analysis of algorithms and approximating the time complexity. The content of this unit provides a mathematical tool for the later units.

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