Discrete Mathematics is the study of discrete mathematical structures such as, Integers, Graphs and logical statements.  In other words, it is a branch of mathematics which deals countable (discrete or distinct) sets.  As we count 1,2,3,… all sets having an 1-1 relationship with the set of natural numbers {1,2,3,..} are termed as countable sets.  We will discuss these countable sets and 1-1 relationships in later sections.  

Why is Discrete Mathematics? 

Computer algorithms, Programming Languages, Cryptography,  Automated theorem proving, Computer networking and software development are some of the areas where discrete mathematical structures and concepts are widely being used. 

The concept of Spanning trees are used in computer networking to find the optimal length of wires used.  Theory of Numbers is being used in Cryptography, where encryption and decryption done are simply the behaviors of numbers.  Finding best and shortest route using Google Map while driving is nothing but the shortest route in Graphs.

Scheduling problems –  Using of 1 mathematics teacher to 3 or 4 classes in a day,  Using of one computer to 3 persons in a day with 3 shifts, Using of 1 canteen in cinema theaters to many screens by giving different break timings are all comes under the category of scheduling problems.  These problems are being solved using the mathematical concepts of graph coloring or combinatorial optimization.  

Simply saying, any real life problem which needs solution could be answered with mathematics.  These need to all mathematical concepts, all together named as Discrete Mathematics.  Let us discuss them one after the other.