Essential Mathematics for Data Science

Introduction

“Data Scientist is a professional who uses scientific methods and algorithms and create a meaning from raw data.”

Data Science is much interesting to learn and also most booming field but why people fails in Data Science and they “QUIT”? Ever wondered. One of the most common reasons for quitting Data Science because of lack of knowledge of “FUNDAMENTALS”.

It’s a clear that if you want to excel in certain field one needs have quite knowledge of basics. Programming is one of the important basics of Data Science. But the most vital subject is Math. We can say that Math is the back-end for Data Science and Machine Learning. Because if you don’t know the math behind the algorithm or the way the prediction values you are getting then how you will convey your reports. So Math is one of the most important fundamental of the data science and Machine Learning.

Math in Data Science mainly comprises of Statistics, Probability, Linear Algebra and Differential Calculus. Almost all the techniques of modern data science have some deep mathematical concepts because as I usually say Math is the back-end of the Machine Learning Algorithms. So this is one of the important article in which we are going to study the essential math topics to excel Data Science concepts.

Importance of Mathematics

Always remember applying for the position of Data Scientist doesn’t just require you to know the Tensor flow or some other machine learning frame work, what you require is to know the math behind an algorithm. You required to know how a cost function of a linear regression model is optimized, or what does the decision function for a linear SVM classifier do? and even many more the list will go on…

Different Mathematics topic distribution

When you see the above representation you can clearly see the distribution of Math’s topics needed for Data Science. Linear Algebra and Statistics + Probability is most important branch covering 35% and 25%. And other branches you need is calculus and Algorithmic Complexity.

Statistics

Statistics in the must to know concept if you want to become a Data Scientist. Because Statistics is the fuel of Data Science process. Many people call Machine Learning as Statistical Learning because of scope of Statistics in the area. Statistics is vast but if done properly you can find it much easy.

Some topics you should know are:

• Descriptive Statistics, measures of central tendency, variance, standard deviation, covariance, correlation.
• Basic idea of probability, Conditional probability, Bayes Theorem.
• Probability Distribution function which includes: Uniform, Normal, Binomial, t-distribution, central limit theorem, etc.
• Hypothesis testing
• A/B testing, p values error measurement
• ANOVA, t-test
• Least square methods and regression.

You should know the above concepts because you are going to use in your day to day data science activities. During interviews you can
even impress your interviewer easily if you know the concepts of Statistics.

Linear Algebra

Have you every thought how recommendation system works it works through Deep learning concept and Linear Algebra. What is there in Linear Algebra? Basically, Linear Algebra consist of Matrix Algebra. This is one of the important branch of Mathematics which will help you to understand how Machine Learning and Deep Learning algorithms work.

Some topics you should know are:

• Basic matrix operation: Scalar Multiplication, Transpose, determinant, etc.
• Matrix multiplication and Inverse of Matrix
• Different types of Matrix.
• Linear system of equation
• Gauss-Jordan elimination Gaussian elimination
• Vector operations
• Eigen values, Eigen vectors
• Diagonalization
• Projection onto line and plane
• Singular Value Decomposition (SVD)

SVD concept is used in Dimension reduction and Principal Component Analysis (PCA). Most of the Deep Learning and Neural Network concepts use Linear Algebra in their algorithms.

Calculus

“Ladies and Gentlemen Calculus the rebel of Mathematics here in the house.” Calculus is the topic most of the people face difficulties and the only reason why people hate Math.

But the truth is Calculus is used in various fields of Machine Learning and this is the reason you should learn Calculus. There are many online resources which we will discuss at the end of the blog.

So some of the essential topics are:

• Limit and Continuity
• Mean value theorems
• L’Hospital Rule
• Maxima and Minima
• Product chain rule
• Differential Equations
• Beta Gama functions
• Partial Derivatives
• Gradient, etc

Have you wondered how logistic regression works. How Gradient Descent finds Minimum Loss function. To understand this concept of calculus is important. Also there are many algorithms who use calculus.

Discrete Mathematics

One of the easiest and coolest branch of Mathematics. Modern Data Science and computational systems has Discrete Math at its core. Many a times Discrete Math is also used in analytics project.

So lets discuss some of the important topics for Discrete Math

• Set theory: Power set, super sets, Subsets , etc.
• Venn diagrams
• Counting functions
• Positional Logic
• Basic proofs: Induction and Contradiction
• Graph Theory
• Basic Data Structures
• Recurrence Complexity concepts and many more

When you study any algorithm then you need to understand the time space complexities for this purpose Discrete Math is used also there are many applications where you can find Discrete Math.

Some other topics

Also there are some other topics which you should know because you can encounter them many times. They are—

• Logarithm and Exponential Functions
• Rational Numbers
• Basic geometric theorems
• Trigonometric identities
• Real and Complex numbers
• Sequence and Series
• Graphing Plotting
• Cartesian and Polar Co-ordinate System
• Conic Sections
• Linear and Integer programming

Conclusion

So here we have discussed the essential topics to excel in Data Science and Machine Learning. There are many topics but this are some of the
important topics that you should know.

But I must say one thing to my readers that do not feel scared or worried by reading this topics. Please!  But one thing is sure if you want to be successful in Data Science you need have that will power and dedication to learn new things. You should have excitement of learning. Data science is indeed tough and vast but if you show your interest here you can do wonders.

Consistency and handwork will make you successful. But I can guarantee you that studying this topics you Data Science understanding level will change. The learning and application of Math will take time and is lengthy process but this will provide you with long term results. And that is the big step towards becoming a successful Data Scientist….