The book has been designed to serve as a useful textbook for the undergraduate students of Mathematics. IN this book, there are eight units and nine chapters.
In Section IA (Logic and SEts), there are two units. Unit I introduces logic, rules of inference and quantifiers. Unit II covers set operations, laws of set theory, probability, axioms of probability, conditional probability and discrete random vriables.
In Section IB (Theory of Equations), there are two units. Unit I introduces the methods of solving polynmial equations. In Unit II,relations between roots and coefficients, cube roots of unity and symmeric functions of roots were discussed.
In Section IC (Real Analysis), there are four units. The topics, sequences, limit of a sequence and Cauchy sequences are discussed in Unit I. Unit II covers sub-sequences, alternating series and integral tests. In Unit III, power series and uniform convergence are introduced. In Unit IV, Riemann integration is introduced.
Section-1A:Locic and Sets
1. Logical Connectives
2. Sets and Subsets
3. Probability-Discrete Random Variables
Section-1B:Theory of Equations
4. Theory of Equations- Preliminaries
5. Relation Between the Roots and Coefficients
7. Subsequences and Infinite Series
8. Sequences and Series of Functions
9. riemann Integration