How Discrete Mathematics and Computer Science are closely related

Mathematics is an exciting growth area of research in the modern information age.Computer science and Mathematics are closely related, each providing support and suggesting new problems to the other.

Today, Discrete Mathematics is an exciting and rapidly developing area, with roots in Pure Mathematics, most particularly Combinatorics, and a wide range of applications in the modern world.

Discrete mathematics

 
Discrete math is concerned with structures, often finite, that take on discrete values. It is an interdisciplinary field with roots in pure mathematics, and a wide range of applications in networks, algorithms, etc. Its also a tool of choice in a host of applications, from computers to telephone call routing.

For those preparing for GATE- Mathematics is a section in which you can score 100% and raise your total score in GATE exam.In GATE exam Engineering Mathematics / Discrete Mathematics has weightage 15 % and this is consistent over the years.  This section does not require extra efforts even the topics which you learn during graduation are sufficient to clear it. You just need proper study material, books and guidance. 

Do programmers need to learn discrete math. The choice is up to you. You can choose fields that don’t need math like web programming or math heavy like machine learning.

 
Here is a lecture series by Prof. Tom Leighton on Discrete mathematics . He is co-founder of Akamai – a reputed company that works on content delivery networks. Akamai’s foundations are built on applying advanced mathematics to real world problems. https://www.youtube.com/watch?v=L3LMbpZIKhQ

The concept you really need to know about discrete mathematics for computer science are these – followed by some good reference books

Mathematical Induction

It is a technique which proves a statement, a formula or a theorem is true for every natural number.

Here i have listed some resources to refer for mathematical induction.

  1. Prof.Leighton at MIT (founder of Akamai ) explains the basics of mathematics – Induction, Number theory, Modular arithmetic
  2. Khan academey videos
  3. Check your real understanding by trying these advanced exercises 
Pigeon Hole Principle

As defined in Wikipedia,the pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item.

Pigeon hole principle looks very simple again, but has applications in surprising places

What is the relationship between  Hashtables, Pigeonholes, and Birthdays

Probability

Probability is a measure or estimate of how likely a certain event is to happen.

Probability theory is the branch of mathematics concerned with these measurements and estimations. It’s gaining a lot of importance in recent years, with applications in medical sciences, computer sciences, artificial intelligence, big data and so on.

Refer links to study materials of probability here

Mathematical Logic

http://careerhunt.net/topic/303/mathematical-logic

Graph Theory

http://careerhunt.net/topic/304/graph-theory

Set Theory and Algebra

http://careerhunt.net/topic/305/set-theory-and-algebra

Combinatorics

http://careerhunt.net/topic/306/combinatories

(Optional exploration) but only after exhausting recommended materials: Mathematics: https://github.com/rossant/awesome-math