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

- Basic Vector Operations
- Unit Vector
- Dot Product and Orthogonal Vectors
- Linear Independence
- Vector Projections
- Basic Matrix Operations
- Matrix Multiplication
- Transformation Matrix
- Determinant of a Matrix
- Gauss Jordan Elimination
- Diagonal Matrix
- Identity Matrix and Inverse Matrix
- Transpose Matrix
- Orthogonal Matrix
- Change of Basis Matrix
- Gram Schmidt Process
- Eigenvectors
- Eigenvalue Decomposition
- Singular Value Decomposition

## Calculus

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

## Statistics and Probability

**Basic Statistics and Probability**

- Introduction to Probability and Random Variables
- Probability Mass Function and Probability Density Function
- Conditional Probability and Independence
- The Law of Total Probability and Bayesian Inference
- Variance and the Expected Value
- Covariance and Correlation
- Bernoulli Random Variables and the Binomial Distribution
- Normal Distribution and Gaussian Random Variables
- Maximum Likelihood Estimation
- Multivariate Gaussian Distribution
- Maximum Likelihood Estimation for Gaussian Distributions
- The Law of Large Numbers
- The Central Limit Theorem
- Confidence Intervals and Z Score

**Probability Distributions**

- Factorization Theorem and the Exponential Family
- Poisson Distribution
- Exponential Distribution
- Gamma Distribution
- Beta Distribution
- Conjugate Priors
- Geometric Distribution
- Chi-Square Distribution and Degrees of Freedom
- Student’s T-Distribution

**Statistical Testing**

**Critical Value Tables**

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

## 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.