Mathematics for Data Scientist

The beauty and the powerful of math, is represent ‘intuitive’ thinking to equations. Each equation is usually short, but it can capture all variance of variables. Understanding equations, we can knows what the universe works.

This post is a collection of courses about mathematics for data scientist.

Foundations of Data Science, John Hopcroft, Ravindran Kannan

concepts: High-Dimensional Space, Best-Fit Subspaces and Singular Value Decomposition (SVD), Random Graphs, Random Walks and Markov Chains, Learning and VC-dimension, Algorithms for Massive Data Problems, Clustering, Topic Models, Hidden Markov Process, Graphical Models, and Belief Propagation, Other Topics

Multivariate Calculus

concepts: dot product, determinants, matrices, square systems, parametric equations, Kepler’s second law, partial derivatives, max-min and least squares, chain rule, gradient, Lagrange multipliers, non-independent variables, partial differential equations, double integrals, polar coordinates, change of variables, vector fields, path independence, gradient fields, Green’s theorem, flux, simply connected regions, triple integrals, spherical coordinates, vector fields in 3D, divergence theorem, line integrals, Stokes theorem, Maxwell’s equations

Multivariable Calculus, MIT 18.02

materials: video

This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space.

Linear Algebra

Linear Algebra, MIT 18.06

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Linear Algebra, MIT 18.06sc

materials: video

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering.

Probability

concept: probability models and axioms, expectation, Bayes’ rule, the Poisson distribution, discrete vs continuous, the uniform, normal distribution, location, scale and LOTUS, exponential distribution, moment generating functions, join, conditional and marginal distributions, Markov chains

Statistics 110: Probability, MIT

Statistics 110 (Probability) has been taught at Harvard University by Joe Blitzstein (Professor of the Practice in Statistics, Harvard University) each year since 2006. The on-campus Stat 110 course has grown from 80 students to over 300 students per year in that time. Lecture videos, review materials, and over 250 practice problems with detailed solutions are provided. This course is an introduction to probability as a language and set of tools for understanding statistics, science, risk, and randomness. The ideas and methods are useful in statistics, science, engineering, economics, finance, and everyday life.

Probabilistic Systems Analysis and Applied Probability, MIT 6.041

materials: video

a subject on the modeling and analysis of random phenomena and processes, including the basics of statistical inference. Nowadays, there is broad consensus that the ability to think probabilistically is a fundamental component of scientific literacy. The aim of this class is to introduce the relevant models, skills, and tools, by combining mathematics with conceptual understanding and intuition.

Statistics

Intro to Statistics: Making Decisions Based on Data, udacity

Statistics is about extracting meaning from data. In this class, we will introduce techniques for visualizing relationships in data and systematic techniques for understanding the relationships using mathematics.

References

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