Any modern scientific discipline is built on mathematics. Machine learning is one of the many modern data science techniques that has a strong mathematical foundation.

It goes without saying that in order to be a top data scientist, you will unquestionably need all the other pearls of knowledge, including programming skills, a certain level of business savvy, and your own analytical and inquisitive perspective regarding the data. But knowing the workings of the engine is always preferable than simply being the driver and having no knowledge of the vehicle. Therefore, you will have an advantage over your competitors if you have a firm grasp of the mathematical framework that underlies the smart algorithms.

Most are indicators of a reliable scientific method:

• Examining the underlying dynamics while modeling a process (physical or informational).
• Developing hypotheses
• Exactly calculating the data source's quality
• calculating the degree of uncertainty in the data and projections
• Finding the hidden pattern in the information stream
• recognising a model's limitations
• understanding the abstract reasoning behind mathematical proof
• Equations, graphs, variables, and functions

From the equation of a line through the binomial theorem and all in between, this branch of mathematics covers the fundamentals:

• Exponents, polynomial functions, rational numbers, and logarithms
• trigonometric identities, fundamental geometric theorems,
• Standard characteristics of real and complex numbers
• Series, totals, and inequality
• Conic sections, polar and cartesian coordinates, graphing, and plotting

Where It Might Be Used

The term 'binary search' will be used to explain how a search on a million-item database operates more quickly after it has been sorted. You need to grasp logarithms and recurrence equations in order to comprehend its dynamics. Or you can run into terms like 'exponential decay' and 'periodic functions' if you wish to study a time series.

Where to Learn About It

Coursera: Data science Math competencies edX: Algebra I

 Algebra I at Khan Academy

Statistics

It is crucial to have a firm understanding of the fundamental ideas behind probability and statistics. In fact, many experts in the area believe that traditional (non-neural network) machine learning is nothing more than statistical learning. The subject is extensive, thus careful planning is vital to covering the most important ideas:

• Descriptive statistics, central tendency, variance, covariance, and correlation are all used to summarize data.
• Basic concepts in probability include the Bayes' theorem, expectation, probability calculus, and conditional probability.
• Uniform, normal, binomial, chi-square, Student's t-distribution, and central limit theorem are examples of probability distribution functions.
• sampling, measurement, inaccuracy, and production of random numbers
• ANOVA, p-values, confidence intervals, t-tests, and hypothesis testing
• Both regularization and linear regression

Where It May Be Used Interviews. You will quickly win over the opposing side of the table if you can demonstrate that you have mastered these ideas. And as a data scientist, you'll use them almost daily.

Where to Learn About It

Coursera offers statistics with a focus on R.

edX: Statistics and probability in data science using Python; Coursera: Business statistics and analysis specialization.

Algebra I: Linear

Understanding how machine-learning algorithms operate on a stream of data to generate insight is dependent on this area of mathematics. Matrix algebra is used in anything from Facebook friend suggestions to Spotify music recommendations to deep transfer learning techniques that turn your selfie into a Salvador Dali-inspired painting. The following are the key subjects to learn:

Scalar multiplication, linear transformation, transpose, conjugate, rank, determinant inner and outer products, matrix multiplication rule and various algorithms, matrix inverse are among the fundamental matrix and vector properties.

Square, identity, triangular, notion of sparse and dense matrix, unit vectors, symmetric matrix, Hermitian, skew-Hermitian, and unitary matrices are examples of special matrices.

Concept of matrix factorization, LU decomposition, Gaussian/Gauss-Jordan elimination, and solution of the linear system Ax=b

basis, span, orthogonality, orthonormality, and least squares in a vector

Singular value decomposition, diagonalization, eigenvalues, and eigenvectors

Where It Might Be Used

In order to obtain a compact dimension representation of your data set with fewer parameters, you probably utilized the singular value decomposition if you used the dimensionality reduction technique principal component analysis. All neural network algorithms represent and process network architecture and learning processes using concepts from linear algebra.

Where to Learn About It

edX: Foundations and frontiers of linear algebra

Coursera: Linear algebra as a tool for machine learning

Calculus

Calculus appears frequently in data science and machine learning, whether you liked it or loathed it in college. In every back-propagation your neural network performs to learn a new pattern, it hides behind the apparent simplicity of the analytical solution to a standard least squares issue in linear regression. Adding it to your skill set will be very beneficial. These are the subjects to research:

single-variable functions, limit, continuity, and differentiability

L'Hospital's rule, indeterminate forms, and mean value theorems

Minimum and maximum

Chain and product rules

Concepts of infinite series summation/integration and Taylor's series

Integral calculus fundamental and mean value theorems, evaluation of definite and improper integrals

The gamma and beta functions

Multiple variable functions, limit, continuity, and partial derivatives

Where It Might Be Used

Have you ever wondered how a logistic regression algorithm is put into practise? It is likely to utilize a technique known as 'gradient descent' to identify the smallest loss function. You need to apply calculus principles like gradient, derivatives, limits, and chain rule to comprehend how this works.

Where to Learn About It

Pre-university calculus on edX

Calculus I at Khan Academy

Coursera: Multivariable Calculus for Machine Learning

Calculus Discrete

Discrete mathematics is at the core of all computer systems used in existing data science, despite the fact that this area is less frequently studied in data science. Concepts essential to routine use of algorithms and data structures in analytics projects will be reviewed in discrete math:

Power sets, subsets, and sets

Combinatorics, countability, and counting functions

Fundamental proving techniques include induction and non sequitur demonstration.

Propositional, deductive, and inductive logic foundations

Basic data structures include stack, queues, graphs, arrays, hash tables, and trees.

Examples of network features include connected components, degree, optimum flow/minimum cut principles, and graph coloring.

recurrent relationships and equations

Function expansion as well as the concept of O(n) notation

Where It Might Be Used

In order to search and traverse the network in any social network study, you need to be acquainted with a map's attributes and a quick algorithm. You must comprehend the time and space complexity of any algorithm you choose, i.e., how the running time and space need increases with the volume of input data, by using the O(n) (Big-Oh) notation.

Where to Learn About It

Coursera: Discrete Mathematics for Computer Science Specialization Introduction

Introduction to mathematical reasoning on Coursera

Learn discrete mathematics with Udemy's courses on sets, logic, and more.

Research Topics in Optimization and Operation

These topics are particularly relevant in specialized areas like theoretical computer science control theory, or control theory. However, machine learning can also benefit from having a fundamental understanding of these effective methods. A common goal of machine learning algorithms is to minimize an estimation error under a set of constraints, which is known as an optimization problem. These are the subjects to research:

Fundamentals of optimization and problem formulation

Convex function, global solution, maxima, minima

Algorithms for linear programming and simplex

Arithmetic programming

The knapsack problem and constraint programming

Techniques for randomized optimization include genetic algorithms, simulated annealing, and hill climbing.

Where It Might Be Used

Simple linear regression issues employing the least-square gradient descent, in contrast to logistic regression issues, typically have a precise solution. You must be familiar with the idea of 'convexity' in optimization to get the explanation. This line of inquiry will also shed light on the necessity of accepting 'approximate' answers to the majority of machine-learning issues.

Where to Learn About It

edX: Business analytics optimization methodologies

Discrete optimization on Coursera

Deterministic optimization on edX

A Few Final Words

Please try not to feel stressed. Despite the fact that there is a lot to learn, the internet has some great resources. You will be equipped to hear the hidden melodies in your daily data analysis and machine learning tasks after reviewing these topics (which you undoubtedly studied as an undergrad) and learning new ideas. And that's a huge step in the direction of being a fantastic data scientist.