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Welcome to the “Mathematics for Machine Learning and Data Science” blog post series. The information contained in these posts will give you the necessary mathematical grounding in linear algebra, calculus, and statistics for a successful career in data science or machine learning. This guide is intended to be a roadmap for learning the math, and as a reference to quickly lookup and acquire mathematical background knowledge for solving concrete problems. For an in-depth guide to the math you need to succeed in machine learning, check out my post on what math is required for machine learning.

I hope it will make the math for becoming a data scientist less intimidating.

Linear Algebra

  1. Basic Vector Operations
  2. Unit Vector
  3. Dot Product and Orthogonal Vectors
  4. Linear Independence
  5. Vector Projections
  6. Basic Matrix Operations
  7. Matrix Multiplication
  8. Transformation Matrix
  9. Determinant of a Matrix
  10. Gauss Jordan Elimination
  11. Diagonal Matrix
  12. Identity Matrix and Inverse Matrix
  13. Transpose Matrix
  14. Orthogonal Matrix
  15. Change of Basis Matrix
  16. Gram Schmidt Process
  17. Eigenvectors
  18. Eigenvalue Decomposition
  19. Singular Value Decomposition


  1. Rise Over Run: Understand the Definition of a Derivative
  2. Differential Calculus: How to Find the Derivative of a Function
  3. Products, Quotients, and Chains: Simple Rules for Calculus
  4. How to Take Partial Derivatives
  5. The Jacobian Matrix: Introducing Vector Calculus
  6. The Hessian Matrix: Finding Minima and Maxima
  7. The Multivariable Chain Rule
  8. Power Series: Understand the Taylor and MacLaurin Series
  9. Linearization of Differential Equations for Approximation
  10. Understanding The Gradient Descent Algorithm
  11. Lagrange Multipliers: An Introduction to Constrained Optimization
  12. The Fundamental Theorem of Calculus and Integration

Statistics and Probability

Basic Statistics and Probability

  1. Introduction to Probability and Random Variables
  2. Probability Mass Function and Probability Density Function
  3. Conditional Probability and Independence
  4. The Law of Total Probability and Bayesian Inference
  5. Variance and the Expected Value
  6. Covariance and Correlation
  7. Bernoulli Random Variables and the Binomial Distribution
  8. Normal Distribution and Gaussian Random Variables
  9. Maximum Likelihood Estimation
  10. Multivariate Gaussian Distribution
  11. Maximum Likelihood Estimation for Gaussian Distributions
  12. The Law of Large Numbers
  13. The Central Limit Theorem
  14. Confidence Intervals and Z Score

Probability Distributions

  1. Factorization Theorem and the Exponential Family
  2. Poisson Distribution
  3. Exponential Distribution
  4. Gamma Distribution
  5. Beta Distribution
  6. Conjugate Priors
  7. Geometric Distribution
  8. Chi-Square Distribution and Degrees of Freedom
  9. Student’s T-Distribution

Statistical Testing

  1. Hypothesis Testing and P-Values
  2. T-Tests
  3. Chi-Square Test for Independence and Goodness of Fit

Critical Value Tables

For your convenience, here are the most important tables for looking up critical values.

  1. Z-Table
  2. T-Table
  3. Chi-Square Table

Further Resources

For writing these posts I’ve primarily relied on the following books:

Introduction to Linear Algebra by Gilbert Strang
Calculus Made Easy by Silvanus Thompson
Introduction to Mathematical Statistics by Hogg, McKean, and Craig
Mathematics for Machine Learning by Deisenroth, Faisal and Ong
Pattern Recognition and Machine Learning by Christopher Bishop
The Elements of Statistical Learning by Trevor Hastie, Robert Tibshirani, et al.
Deep Learning by Ian Goodfellow, Yoshua Bengio, et al.
Machine Learning: A Probabilistic Perspective by Kevin Murphy

as well as the Khan Academy Youtube Channel.

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