Master the Mathematics Behind AI and Unlock Your Potential

Mathematics for Machine Learning and Data Science is a beginner-friendly specialization where you’ll master the fundamental mathematics toolkit of machine learning: calculus, linear algebra, statistics, and probability.

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What you’ll get from this course

A deep understanding of what makes algorithms work, and how to tune them for custom implementation.
Statistical techniques that empower you to get more out of your data analysis.
Skills that employers desire, helping you ace machine learning interview questions and land your dream job.

About this course

Newly updated for 2024! Mathematics for Machine Learning and Data Science is a foundational online program created by DeepLearning.AI and taught by Luis Serrano. In machine learning, you apply math concepts through programming. And so, in this specialization, you’ll apply the math concepts you learn using Python programming in hands-on lab exercises. As a learner in this program, you'll need basic to intermediate Python programming skills to be successful.

Many machine learning engineers and data scientists need help with mathematics, and even experienced practitioners can feel held back by a lack of math skills. This Specialization uses innovative pedagogy in mathematics to help you learn quickly and intuitively, with courses that use easy-to-follow visualizations to help you see how the math behind machine learning actually works.

We recommend you have a high school level of mathematics (functions, basic algebra) and familiarity with programming (data structures, loops, functions, conditional statements, debugging). Assignments and labs are written in Python but the course introduces all the machine learning libraries you’ll use.

Instructors

Luis Serrano

Instructor

Serrano Academy

Who should join?

This is a beginner-friendly course for anyone who wants to develop their mathematical fundamentals for a career in machine learning and data science. A high school level of mathematics (functions, basic algebra), a beginner’s understanding of machine learning concepts, and basic familiarity with a programming language, ideally Python (loops, functions, if/else statements, lists/dictionaries, importing libraries) will help you get the most out of this specialization.

Enroll now and take your career to the next level!

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Concepts you will learn

Data Analysis
Calculus
Bayesian Statistics
Linear Regression
Machine Learning
Probability
Mathematics

Syllabus

Linear Algebra for Machine Learning and Data Science:

2024 updates!

All three graded assignments rewritten for clarity and to add exciting new topics
Entire new section of video lectures in Week 4 going deeper into eigenvectors and showing their application to Principal Component Analysis (PCA)
All quizzes reviewed and updated for clarity
Week 1 lectures consolidated to provide a streamlined experience with introductory linear algebra topics
Formal definitions of mathematical topics added throughout the course to supplement the more intuitive approach in previous versions

Week 1: Systems of Linear Equations

Lesson 1: Systems of Linear equations: two variables

Machine learning motivation
Systems of sentences
Systems of equations
Systems of equations as lines
A geometric notion of singularity
Singular vs nonsingular matrices
Linear dependence and independence
The determinant

Lesson 2: Systems of Linear Equations: three variables

Systems of equations (3×3)
Singular vs non-singular (3×3)
Systems of equations as planes (3×3)
Linear dependence and independence (3×3)
The determinant (3×3)

Week 2: Solving systems of Linear Equations

Lesson 1: Solving systems of Linear Equations: Elimination

Machine learning motivation
Solving non-singular systems of linear equations
Solving singular systems of linear equations
Solving systems of equations with more variables
Matrix row-reduction
Row operations that preserve singularity
Gaussian elimination

Lesson 2: Solving systems of Linear Equations: Row Echelon Form and Rank

The rank of a matrix
The rank of a matrix in general
Row echelon form
Row echelon form in general
Reduced row echelon form

Week 3: Vectors and Linear Transformations

Lesson 1: Vectors

Norm of a vector
Sum and difference of vectors
Distance between vectors
Multiplying a vector by a scalar
The dot product
Geometric Dot Product
Multiplying a matrix by a vector
Lab: Vector Operations: Scalar Multiplication, Sum and Dot Product of Vectors

Lesson 2: Linear transformations

Matrices as linear transformations
Linear transformations as matrices
Matrix multiplication
The identity matrix
Matrix inverse
Which matrices have an inverse?
Neural networks and matrices

Week 4: Determinants and Eigenvectors

Lesson 1: Determinants In-depth

Machine Learning Motivation
Singularity and rank of linear transformation
Determinant as an area
Determinant of a product
Determinants of inverses

Lesson 2: Eigenvalues and Eigenvectors

Bases in Linear Algebra
Span in Linear Algebra
Interactive visualization: Linear Span
Eigenbases
Eigenvalues and eigenvectors
Principal Component Analysis (PCA)

Probability & Statistics for Machine Learning & Data Science:

2024 updates!

A sequence of 5 ungraded labs teaching Exploratory Data Analysis in Python was added to the course, highlighting the Pandas library and showing real world applications of statistical concepts
Assignment 1 was re-written to improve clarity and emphasize the most important and interesting applications of the “Naive Bayes” algorithm
All quizzes reviewed and updated for clarity
Several videos in Weeks 2, 3, and 4 were re-recorded to improve explanations of concepts including Bayesian Statistics, Expected Value, Variance, Sample Variance, and Confidence Intervals

Week 1: Introduction to probability and random variables

Lesson 1: Introduction to probability

Concept of probability: repeated random trials
Conditional probability and independence
Discriminative learning and conditional probability
Bayes theorem

Lesson 2: Random variables

Random variables
Cumulative distribution function
Discrete random variables: Bernoulli distribution
Discrete random variables: Binomial distribution
Probability mass function
Continuous random variables: Uniform distribution
Continuous random variables: Gaussian distribution
Continuous random variables: Chi squared distribution
Probability distribution function

Week 2: Describing distributions and random vectors

Lesson 1: Describing distributions

Measures of central tendency: mean, median, mode
Expected values
Quantiles and box-plots
Measures of dispersion: variance, standard deviation

Lesson 2: Random vectors

Joint distributions
Marginal and conditional distributions
Independence
Measures of relatedness: covariance
Multivariate normal distribution

Week 3: Introduction to statistics

Lesson 1: Sampling and point estimates

Population vs. sample
Describing samples: sample proportion and sample mean
Distribution of sample mean and proportion: Central Limit Theorem
Point estimates
Biased vs Unbiased estimates

Lesson 2: Maximum likelihood estimation

ML motivation example: Linear Discriminant Analysis
Likelihood
Intuition behind maximum likelihood estimation
MLE: How to get the maximum using calculus

Lesson 3: Bayesian statistics

ML motivation example: Naive Bayes
Frequentist vs. Bayesian statistics
A priori/ a posteriori distributions
Bayesian estimators: posterior mean, posterior median, MAP

Week 4: Interval statistics and Hypothesis testing

Lesson 1: Confidence intervals

Margin of error
Interval estimation
Confidence Interval for mean of population
CI for parameters in linear regression
Prediction Interval

Lesson 2: Hypothesis testing

ML Motivation: AB Testing
Criminal trial
Two types of errors
Test for proportion and means
Two sample inference for difference between groups
ANOVA
Power of a test

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Course Slides

Download the course slides for the Mathematics For Machine Learning & Data Science Specialization. A specialization that teaches you the fundamental mathematics toolkit of machine learning: calculus, linear algebra, statistics, and probability.

*Note: The slides might not reflect the latest course video slides. Please refer to the lecture videos for the most up-to-date information. We encourage you to make your own notes.

What Learners From Previous Courses Say About DeepLearning.AI

“Within a few minutes and a couple slides, I had the feeling that I could learn any concept. I felt like a superhero after this course. I didn’t know much about deep learning before, but I felt like I gained a strong foothold afterward.”

Jan Zawadzki
Data Scientist at Carmeq

“The whole specialization was like a one-stop-shop for me to decode neural networks and understand the math and logic behind every variation of it. I can say neural networks are less of a black box for a lot of us after taking the course.”

Kritika Jalan
Data Scientist at Corecompete Pvt. Ltd.

“During my Amazon interview, I was able to describe, in detail, how a prediction model works, how to select the data, how to train the model, and the use cases in which this model could add value to the customer.”

Chris Morrow
Sr. Product Manager at Amazon

“As a Behavioral Scientist, I was able to adopt methods to understand my customers better, overcome the traditional ‘one-size-fits-all’ approach, and design interventions which account for personality and individual differences.”

Luo Yuzheng
Assistant Director, Monetary Authority of Singapore

“I gained confidence in my knowledge of machine learning. Since then, I’ve become a machine learning mentor, got a research paper published in IEEE, decided to pursue my Masters in Machine Learning, and was able to land a job at JP Morgan Chase.”

Chirag Godawat
Data Engineer, Vista

“The Machine Learning course became a guiding light. Andrew Ng explains concepts with simple visualizations and plots. I learned how to evaluate my training results and explain the outcomes to my colleagues, boss, and even the vice president of our company.”

Hsin-Wen Chang
Sr. C++ Developer, Zealogics

Master the Mathematics Behind AI and Unlock Your Potential

What you’ll get from this course

About this course

Instructors

Luis Serrano

Who should join?

Concepts you will learn

Syllabus

Week 2: Solving systems of Linear Equations

Week 3: Vectors and Linear Transformations

Week 4: Determinants and Eigenvectors

Week 1: Functions of one variable: Derivative and optimization

Week 2: Functions of two or more variables: Gradients and gradient descent

Week 3: Optimization in Neural Networks and Newton’s method

Week 1: Introduction to probability and random variables

Week 2: Describing distributions and random vectors

Week 3: Introduction to statistics

Week 4: Interval statistics and Hypothesis testing

Course 1: Linear Algebra for Machine Learning and Data Science

Course 2: Calculus for Machine Learning and Data Science

Course 3: Probability & Statistics for Machine Learning & Data Science

Course Slides

What Learners From Previous Courses Say About DeepLearning.AI

Frequently Asked Questions