Mathematics for Data Science

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Mathematics is the bedrock of any contemporary control of science. Practically all the procedures of current information science, including AI, have profound Scientific support. 

It’s a given that you will totally require the various pearls of Mathematics and Programming capacity, some measure of business accuracy, and your one of a kind Expository and Curious attitude about the information to work as a top Data Scientist. Be that as it may, it generally pays to know the apparatus in the engine, instead of simply being the individual in the driver’s seat with no information about the vehicle. In this way, a strong comprehension of the Scientific apparatus behind the cool calculations will give you an edge among your companions. 

The information on this fundamental Math is especially significant for newcomers showing up at information science from different callings: equipment designing, retail, the compound procedure industry, medication, and medicinal services, business executives, and so on. 

Data and such fields may require involvement in spreadsheets, numerical estimations, and projections, the math abilities required in information science can be fundamentally unique.

Think about a web designer or business analyst. They might be managing a great deal of information and data regularly, however, there may not be an accentuation on thorough demonstrating of that information. Frequently, the accentuation is on utilizing the information for a quick need and proceeding onward, instead of on profound logical investigation. Data science, then again, ought to consistently be about science (not information). Following that string, certain instruments and strategies become fundamental. Most are the signs of the sound logical procedure:

  • Modeling a process (physical or informational) by probing the underlying dynamics
  • Constructing hypotheses
  • Rigorously estimating the quality of the data source
  • Quantifying the uncertainty around the data and predictions
  • Identifying the hidden pattern from the stream of information
  • Understanding the limitation of a model
  • Understanding mathematical proof and the abstract logic behind it

Data science, by its very nature, isn’t attached to a specific branch of knowledge. This delivers the chance of a confounding cluster of n-dimensional scientific articles, measurable appropriations, advancement target capacities, and so forth. 

Here are my recommendations for the points to concentrate to be at the head of the game in data science.

Functions, Variables, Equations, and Graphs

This area of math covers the basics, from the equation of a line to the binomial theorem and everything in between:

  • Logarithm, exponential, polynomial functions, rational numbers
  • Basic geometry and theorems, trigonometric identities
  • Real and complex numbers, basic properties
  • Series, sums, inequalities
  • Graphing and plotting, Cartesian and polar coordinates, conic sections

Where You Might Use It-

If you want to understand how a search runs faster on a million-item database after you’ve sorted it, you will come across the concept of “binary search.” To understand the dynamics of it, you need to understand logarithms and recurrence equations. Or, if you want to analyze a time series, you may come across concepts like “periodic functions” and “exponential decay.”

Where You Can Learn It

Coursera: Data Science Math Skills-

edX: Introduction to Algebra

Khan Academy: Algebra I

Statistics and Probability

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

Where You Might Use It-

In interviews. If you can show you’ve mastered these concepts, you will impress the other side of the table fast. And you will use them nearly every day as a data scientist.

Where You Can Learn It

Coursera: Statistics with R specialization

Coursera: Business statistics and analysis specialization

edX: Statistics and probability in data science using Python

Linear Algebra

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 to 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, an 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

Where You Might Use It-

If you have used the dimensionality reduction technique principal component analysis, then you have likely used the singular value decomposition to achieve a compact dimension representation of your data set with fewer parameters. All neural network algorithms use linear algebra techniques to represent and process network structures and learning operations.

Where You Can Learn It

edX: Linear algebra: foundations to frontiers

Coursera: Mathematics for machine learning: linear algebra

Calculus

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 to 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

Where You Might Use It-

Ever wondered how exactly a logistic regression algorithm is implemented? There is a high chance it uses a method called “gradient descent” to find the minimum loss function. To understand how this works, you need to use concepts from calculus: gradient, derivatives, limits, and chain rule.

Where You Can Learn It

edX: Pre-university calculus

Khan Academy: Calculus I

Coursera: Mathematics for machine learning: multivariable calculus

Discrete Math

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 the 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

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Where You Might Use It-

In any social network analysis, you need to know the properties of a graph and fast algorithm to search and traverse the network. In any choice of algorithm, you need to understand the time and space complexity—i.e., how the running time and space requirement grows with input data size, by using O(n) (Big-Oh) notation.

Where You Can Learn It

Coursera: Introduction to discrete mathematics for computer science specialization

Coursera: Introduction to mathematical thinking

Udemy: Master discrete mathematics: sets, math logic, and more

Operation Research

These topics are most relevant in specialized fields like theoretical computer science, control theory, or Operation Research. But a basic understanding of these powerful techniques can also be fruitful in the practice of machine learning. Virtually every machine-learning algorithm aims to minimize some kind of estimation error subject to various constraints—which is an optimization problem. 

Here are the topics to learn:

  • Basics of optimization, how to formulate the problem
  • Maxima, minima, convex function, global solution
  • Linear programming, the simplex algorithm
  • Integer programming
  • Constraint programming, knapsack problem
  • Randomized optimization techniques: hill-climbing, simulated annealing, genetic algorithms

Where You Might Use It-

Simple linear regression problems using the least-square loss function often have an exact analytical solution, but logistic regression problems don’t. To understand the reason, you need to be familiar with the concept of “convexity” in optimization. This line of investigation will also illuminate why we must remain satisfied with “approximate” solutions in most machine-learning problems. 

Where You Can Learn It

edX: Optimization methods in business analytics

Coursera: Discrete optimization

edX: Deterministic optimization

Conclusion

Please don’t feel overwhelmed. Though there are a lot of things to learn, there are excellent resources online. 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.

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