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Mathematics is the bedrock of any contemporary discipline of science. Almost all the techniques of modern data science, including machine learning, have a deep mathematical underpinning.

It goes without saying that you will absolutely need all the other pearls of knowledge—programming ability, some amount of business acumen, and your unique analytical and inquisitive mindset—about the data to function as a top data scientist.

But it always pays to know the machinery under the hood, rather than just being the person behind the wheel with no knowledge about the car. Therefore, a solid understanding of the mathematical machinery behind the cool algorithms will give you an edge among your peers.

The knowledge of this essential math is particularly important for newcomers arriving at data science from other professions: hardware engineering, retail, the chemical process industry, medicine and health care, business management, etc. Although such fields may require experience with spreadsheets, numerical calculations, and projections, the math skills required in data science can be significantly different.

The importance of having a solid grasp over essential concepts of statistics and probability cannot be overstated. Many practitioners in the field actually consider classical (non-neural network) machine learning to be nothing but statistical learning. The subject is vast, and focused planning is critical to cover the most essential concepts:

- Data summaries and descriptive statistics, central tendency, variance, covariance, correlation
- Basic probability: basic idea, expectation, probability calculus, Bayes’ theorem, conditional probability
- Probability distribution functions: uniform, normal, binomial, chi-square, Student’s t-distribution, central limit theorem
- Sampling, measurement, error, random number generation
- Hypothesis testing, A/B testing, confidence intervals, p-values
- ANOVA, t-test
- Linear regression, regularization

This is an essential branch of mathematics for understanding how machine-learning algorithms work on a stream of data to create insight. Everything from friend suggestions on Facebook, to song recommendations on Spotify, to transferring your selfie to a Salvador Dali-style portrait using deep transfer learning involves matrices and matrix algebra. Here are the essential topics you will learn:

- Basic properties of matrix and vectors: scalar multiplication, linear transformation, transpose, conjugate, rank, determinant
- Inner and outer products, matrix multiplication rule and various algorithms, matrix inverse
- Special matrices: square matrix, identity matrix, triangular matrix, idea about sparse and dense matrix, unit vectors, symmetric matrix, Hermitian, skew-Hermitian and unitary matrices
- Matrix factorization concept/LU decomposition, Gaussian/Gauss-Jordan elimination, solving Ax=b linear system of equation
- Vector space, basis, span, orthogonality, orthonormality, linear least square
- Eigenvalues, eigenvectors, diagonalization, singular value decomposition

Whether you loved or hated it in college, calculus pops up in numerous places in data science and machine learning. It lurks behind the simple-looking analytical solution of an ordinary least squares problem in linear regression or embedded in every back-propagation your neural network makes to learn a new pattern. It is an extremely valuable skill to add to your repertoire. Here are the topics yo will learn:

- Functions of a single variable, limit, continuity, differentiability
- Mean value theorems, indeterminate forms, L’Hospital’s rule
- Maxima and minima
- Product and chain rule
- Taylor’s series, infinite series summation/integration concepts
- Fundamental and mean value-theorems of integral calculus, evaluation of definite and improper integrals
- Beta and gamma functions
- Functions of multiple variables, limit, continuity, partial derivatives
- Basics of ordinary and partial differential equations

This area is not discussed as often in data science, but all modern data science is done with the help of computational systems, and discrete math is at the heart of such systems. A refresher in discrete math will include concepts critical to daily use of algorithms and data structures in analytics project:

- Sets, subsets, power sets
- Counting functions, combinatorics, countability
- Basic proof techniques: induction, proof by contradiction
- Basics of inductive, deductive, and propositional logic
- Basic data structures: stacks, queues, graphs, arrays, hash tables, trees
- Graph properties: connected components, degree, maximum flow/minimum cut concepts, graph coloring
- Recurrence relations and equations
- Growth of functions and
*O(n)*notation concept

Please don’t feel overwhelmed. Though there are a lot of things to learn, we are here to help you to achieve this. After a refresher on these topics (which you probably studied as an undergrad) and learning new concepts, you will be empowered to hear the hidden music in your daily data analysis and machine-learning projects. And that’s a big leap toward becoming an amazing data scientist.