Description

About the Book:

This book is meant to be more than just a text in discrete mathematics. It is a forerunner of another book ‘Applied Discrete Structures’ by the same author. The ultimate goal of the two books is to make a strong case for the inclusion of discrete mathematics in the undergraduate curricula of mathematics by creating a sequence of courses in discrete mathematics parallel to the traditional sequence of calculus-based courses. The present book covers the foundations of discrete mathematics in seven chapters. It lays a heavy emphasis on motivation and attempts clarity without sacrificing rigour. A list of typical problems is given in the first Chapter. These problems are used throughout the book to motivate various concepts. A review of logic is included to gear the reader into a proper frame of mind. The basic counting techniques are covered in Chapters 2 and 7. Those in Chapter 2 are elementary, but they are, intentionally Covred in a formal manner so as to acquaint the reader with the traditional ‘definition-theoremproof’ pattern of mathematics. Chapter 3 introduces abstraction and shows how the focal point of today’s mathematics is not numbers but sets carrying suitable structures. Chapter 4 deals with Boolean algebras and their applications. Chapters 5 and 6 deal with more traditional topics in algebra, viz., groups, rings, fields, vector spaces and matrices.

The presentation is elementary and pre-supposes no mathematical maturity on the part of the reader. Instead, comments are inserted liberally to increase his maturity. Each chapter has four sections. Each section is followed by exercises (of various degrees of difficulty) and by ‘Notes and Guide to Literature’. Answers to the exercises are provided at the end of the book.

Contents:

Introduction and Preliminaries

Elementary Counting Techniques

Sets with Additional Structures

Boolean Algebras

Group Theory

Rings, Fields and Vector Spaces

Advanced Counting Techniques

With all these features, this is an invaluable book for undergraduate/postgraduate students and faculties of Mathematics and Statistics.

Contents:

Statistics

Classification, Tabulation and Frequency Distribution

Diagramatic and Graphical Representation

Measures of Central Tendency

Measures of Dispersion, Skewness and Kurtosis

Elementary Probability

Random Variable, Mathematical Expectation and Probability Distributions

Bivariate Random Variable and Distributions

Sampling Methods

Theory of Estimation

Testing Parametric Hypotheses

Nonparametric Statistical Methods

Regression and Correlation Methods

Measures of Association of Attributes

Interpolation and Extrapolation

Time Series Analysisa

Index Numbers

Business Forecasting

Statistical Techniques in Quality Control

Vital and Population Statistic

Basic Experimental Designs

Multivariate Statistical Methods