Every study on modern mathematical sciences begins with Set Theory. The study of Discrete Mathematical Structures_ is no exception. In this chapter, we present an elementary and informal exposition of Set Theory from the point of Discrete Mathematics. It is presumed that the reader already has some familiarity with the concepts of sets and set operations.

Logic is the science dealing with the methods of reasoning. Reasoning plays a very important role in every area of knowledge, particularly mathematics. A symbolic language has been developed over the past two centuries to express the principles of logic in precise and unambiguous terms. Logic expressed in such a language has come to be called "Symbolic logic" or "Mathematical logic". Some basic no ......

In Section 3.4, we outlined some standard methods of proving and disproving mathematical statements. In this chapter, we consider one more method of proof called the Method of Mathematical Induction. Further, an alternative way of defining sequences and other mathematical concepts, which is closely related to the concept of induction, called Recursive Definition, is presented with appropriate illu ......

This chapter is a continuation of Chapter 1. In this chapter, the concept of relation is introduced and a special class of relations called functions are discussed in some depth. The emphasis is on set-theoretic properties of functions and their immediate consequences.

This chapter is a continuation of Chapter 5. In this chapter, the topic of relations is discussed further. Special types of relations called equivalence relations and partial orders are dealth-with in some detail. The matrix representation of relations and the pictorial representation of relations (known as digraphs) are used to illustrate the concepts and results.

In this chapter, we consider for discussion an important mathematical structure called a group. The student is already familiar with some of the material presented here.

In this Chapter, we present an elementary account of some basic ideas in Algebraic Coding Theory. Transmission of information in the form of strings (words) of zeros and ones that arises in digital communications is dealt-with.

This chapter is a continuation of Chapter 7 wherein we considered some basic aspects of the Group Theory. Here, we present an elementary treatment of the Ring Theory. The group theory and the ring theory form important parts of the subject of Abstract Algebra.

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