Discrete Mathematics

Introduction to Discrete Mathematics

Target Audience

  • Students who are preparing competitive exams like GATE, NET, SET, TRB
  • Students pursue a degree in any field of computer science and mathematics
  • School and college going students who have Discrete Mathematics in their syllabus (B.Sc., BCA, M.Sc., MCA, BE,)
  • Some Researchers who want to learn Discrete Mathematics as a whole or may be a small subset of their research works

 Why Study Discrete Mathematics

  • Improves your problem solving ability
  • Develop your mathematical thinking ability
  • Many real time problem can be solved using Discrete Mathematics
  • If you are a computer science student, then no need to go anywhere else because Discrete Mathematics is for you
  • Discrete Mathematics is important to survive in subjects like: compiler design, databases, operating system, automata theory, computer security and etc.,

 What is Discrete Mathematics?

  • Discrete Mathematics is the study of Discrete Structures
  • Discrete means: “distinct or not connected”
  • It is the branch of Mathematics dealing with objects– that they are discrete and not continuous
  • Example of structures that are discrete are propositional logic, graphs, groups, combinations and etc.,
  • It is not a branch of Mathematics. It is rather a description of set of branches that have one common property - that they are discrete and not continuous 

Discrete Vs Continuous

The whole world of Mathematics is divided into two categories

Discrete Objects

Continuous Objects

Natural numbers are discrete

ie between any two points, there are a countable number of points.

 For example: 1, 2, 3, 4, 5… .. 

Real numbers are continuous

ie between any two numbers, there are almost always an infinite set of numbers.

 For example: between 0 and 1

0.001, 0.10010, 0.00110,… .. and so on

Digital clock is “discrete” in nature

There is no continuous time

Transition from one time to another is sharp

         10:25:57 -> 10:25:58

Analog clock is continuous in nature.

In analog clock - hour, minute and  second hands move smoothly over time

 

 

Topics in Discrete Mathematics

Propositional Logic

https://deepanotes.blogspot.com/2020/08/propositional-logic.html

 

Set Theory

https://deepanotes.blogspot.com/2020/08/discrete-mathematics.html

 

Relations

https://deepanotes.blogspot.com/2020/08/relations-introduction-relation-can-be.html

 

Functions

https://deepanotes.blogspot.com/2020/08/functions-discrete-mathematics.html

 

Tree

https://deepanotes.blogspot.com/2020/09/tree-discrete-structures.html

 

Graph Theory

https://deepanotes.blogspot.com/2020/09/graph-theory.html

 

Group Theory

https://deepanotes.blogspot.com/2020/09/group-theory-discrete-structures.html

 

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