Discrete Mathematics

Introduction to discrete mathematics pdf:

Discrete mathematics is part of 3 main topics

Mathematics Logic
Boolean Algebra
Graph Theory

discrete mathematics pdf-Mathematics Logic

The find of logic which is used in mathematics is called deductive logic. Mathematical arguments must be strictly deductive in nature. In other words, the truth of the statements to be proved must be established assuming the truth of some other statements.

For example, in geometry we deduce the statement the statement that he sum of the three angles of a triangle is 180 degrees from the statement that an external angle of a triangle is equal to the sum of the other (i.e., opposite) two angles of the triangles of the triangle.

The kind of logic which we shall use here is bi-valued i.e. every statement will have only two possibilities, either True’ or ‘False’ but not both.

Definition:- The symbols, which are used to represent statements, are called statement letters or sentence variables.

To represent statements usually the letters P, Q, R, …, p, q, r, … etc., are used

discrete mathematics pdf-Boolean algebra

Boolean algebra was firstly introduced by British Mathematician George Boole (1813 – 1865).the original purpose of this algebra was to simplify logical statements and solve logic problems. In case of Boolean algebra, there are mainly three operations (i) and (ii) or and (iii) not which are denoted by ‘^^’ ,’vv’ and (~) respectively. In this chapter, we will use +, . , ‘ in place of above operations respectively.

Definition:-Let B be a non-empty set with two binary operations + and ., a unary operation ‘ and two distinct elements 0 and 1. Then B , +, . ,’ is called Boolean algebra, if the following axioms are satisfied.

discrete mathematics pdf-Graph theory

Graphs appear in many areas of mathematics, physical, social, computer sciences and in many other areas. Graph theory can be applied to solve any practical problem in electrical network analysis, in circuit layout, in operations research etc.

By a graph, we always mean a linear graph because there is no such thing as a non-linear graph. Thus in our discussion we shall drop the adjective ‘linear’, and will say simply a ‘graph’

Definition:- A graph G = (V, E) consists of a set of objects V = (v1, v2, …), whose elements are called vertices (or points or nodes) and an another set E = {e1, e2, ….} whose elements are called edges (or lines or branches) such that each ek is identified with an unordered pair (vi, vj) of vertices. The vertices vi and vj associated with the edge ekare said to be the end vertices of ek

Comprehend more on about What are Significant Figures? and its Circumstances. Between, if you have problem on these topics Weight Conversions Please share your views here by commenting.


The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World
Algorithms increasingly run our lives. They find books, movies, jobs, and dates for us, manage our investments, and discover new d…

The Princeton Companion to Mathematics
This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the …

Mathematics for the Nonmathematician (Dover Books on Mathematics)
Practical, scientific, philosophical, and artistic problems have caused men to investigate mathematics. But there is one other mot…

The Seven Pillars of Statistical Wisdom
What gives statistics its unity as a science? Stephen Stigler sets forth the seven foundational ideas of statistics—a scientific…

The Moscow Puzzles: 359 Mathematical Recreations (Dover Recreational Math)
This is, quite simply, the best and most popular puzzle book ever published in the Soviet Union. Since its first appearance in 195…



Related Articles:

Published at: Science News Articleshttp://sciencenewsarticles.org

Article Source