Role Of Mathematics In Data Science

Introduction

While data scientists can work in almost every industry, one key thing that unites them all is an understanding of maths. Whether they are working on statistics, data analysis or machine learning, maths is at the heart of all of them.

The three main elements of mathematics in data science are:

• calculus
• linear algebra
• statistics and probability

Calculus

For most data scientists, it is only really important to understand the principles of calculus, and how those principles might affect their models. If we understand that the derivative of a function returns its rate of change, for example, then it will make sense that the rate of change trends toward zero as the graph of the function flattens out.

That, in turn, will allow us to understand how a gradient descent works by finding a local minima for a function. And it will also make it clear that a traditional gradient descent only works well for functions with a single minima. If we have multiple minima, a gradient descent might find a local minima without finding the global minima unless we start from multiple points. 

Linear Algebra

Computers use linear algebra for carrying out calculations efficiently and almost all models will require computations through linear algebra. At the same time, it is very unlikely that we are going to be hand writing code to apply transformations to matrices when applying existing models to our particular data set. So, again, understanding of the principles will be important, but we do not need to be a linear algebra guru to model most problems effectively.

Statistics and Probability

These fields are use to make a new data product lot of raw data can be analyzed using statistics and probability. It helps make data-driven decisions by providing different statistical tools.

More math (?)

There are lots of other types of math that may also help us when thinking about how to solve a data science problem. They include:

• discrete mathematics : Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.
• graph theory : Graph theory is a branch of mathematics concerned with networks of points connected by lines. The subject of graph theory had its beginnings in recreational math problems, but it has grown into a significant area of mathematical research
• information theory : Information theory is a mathematical approach to the study of coding of information along with the quantification, storage and communication of information.

References:

Critical Role of Mathematics in Data Science. Retrieved from https://blog.marwadiuniversity.ac.in/ccblog/critical-role-of-mathematics-in-data-science/

Discrete mathematics. Retrieved from https://en.wikipedia.org/wiki/Discrete_mathematics

Graph theory. Retrieved from https://www.britannica.com/topic/graph-theory

How Much Math Do You Need to Become a Data Scientist? Retrieved from https://flatironschool.com/blog/how-much-math-do-you-need-to-become-a-data-scientist

Information theory. Retrieved from https://www.tutorialspoint.com/principles_of_communication/principles_of_communication_information_theory.htm