Computation

When I talk to people around me about Mathematics as a subject, I get to hear about their love-hate relationship with numbers, they being good or bad with mental calculations and..and that’s it. Hardly anybody goes beyond primary arithmetic. When I tried to press the subject  with anyone and explain the various areas in Mathematics like ‘number theory’ or ‘combinatorics’, I always heard “well that should be interesting to study but ultimately all that you could do after studying Mathematics  is teach Mathematics.” So the article is for those who love Math as much as I do but do not know where they can apply their mathematical knowledge apart from teaching it as a subject to their nephews.

Lets divide mathematics into the following broad topics:

-Pure mathematics

-Applied mathematics

Pure mathematics is a discipline where one studies entirely abstract concepts without much considering their applications in the real world.

Applied mathematics is a branch of mathematics which deals with real life problems and their mathematical modeling. This branch of mathematics applies the tools developed in pure mathematics to the domains of life sciences, finance, computers, analytics and engineering.

Algebra

We study algebra in high school and most of us will describe it as the subject of ‘the unknown x’. It can also be thought of as a branch of mathematics that joins almost all the other branches together.  Starting from linear equations, polynomials to vectors and matrices, we all learn algebra and use it in our day to day lives without realizing it. Do you love animations and video games? Every animation is a rendition of linear algebra. The animated characters move in a vector space, their motion being a mathematical equation.

Calculus

It’s a branch of mathematics which studies continuous change in a quantity. Broadly speaking, we study rate of change in differential calculus whereas in integral calculus lets us add up infinitely many infinitesimal quantities. From pharmaceutical science to aerospace engineering, applications of calculus are extensive. In quantitative finance, stochastic calculus, differential equations, and Taylor series are used regularly. Along with linear algebra, animators need some knowledge of multi-variable calculus. Creating realistic looking design, rendering common 3-D effects is done using the tools which use the power of calculus. Even certain algorithms to solve discrete problems use calculus by considering the original problem as a continuous analog and later discretizing the solution.

Geometry

Computational geometry is a branch of geometry emerged to study algorithms which assume geometric nature. Disciplines where computational geometry is applied are Computational graphics, robotics, computer aided design and manufacturing and IC design.

Statistics

Applications of Statistics include fields like machine learning, data science which in turn are used in virtually all fields.

Number Theory

Number theory is a branch of mathematics dealing with numbers, their properties and their relation with one another. Traditionally, number theory was thought to be used only in mathematical puzzles, having no real applications. But it plays a pivotal role in modern cryptography. RSA algorithm is a classic example of usage of this branch of mathematics in advancement of cryptology.