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Mathematical Foundations of Machine Learning (Udemy.com)

Essential Linear Algebra and Calculus Hands-On in NumPy, TensorFlow, and PyTorch

4.3
8,573 reviews

Created by: Dr Jon Krohn

Last updated November 2024

Our take

Based on the ratings of 8,573 students, a sample of their written reviews and the syllabus, as the course stood in November 2024. No course pays to be reviewed.

Dr. Jon Krohn's course teaches the linear algebra and calculus that sit under machine learning, and it does it in code. The syllabus runs from tensors, matrix properties and eigenvectors through limits, derivatives, automatic differentiation, partial derivatives and integrals. Every demo is in Python, switching between NumPy, TensorFlow and PyTorch. It is aimed at people who already train models with scikit-learn or Keras and want to know what happens underneath. About 147,000 students have enrolled, and it holds a 4.3 rating across roughly 8,500 reviews.

Reviewers praise the clear explanations and say the course builds intuition for how ML works. One working engineer with years of experience says they still picked up useful ideas for day-to-day work. The complaints are more specific. One reviewer found the lectures dry, with too few visuals and too few real-life examples. Another hit audio that jumps between loud and quiet and calls the depth thin, which sent them online for more. Links to the course code have also gone dead, though a GitHub copy turned up.

The biggest sore point is that the course feels unfinished. The description says statistics, optimization and more would follow, yet the last section is a short probability block of about 50 minutes, and several one and two star reviews are about exactly that. It was last updated in November 2024. At 16 hours, with one quiz and no coding exercises, it is a good fit if the core linear algebra and calculus is what you need. Treat the rest as a bonus that may never arrive.

Best forPython users of scikit-learn or Keras who want the linear algebra and calculus behind the models, coded in three libraries.
Skip it ifYou need the full math stack including statistics and optimization, or want visual, graph-heavy teaching.

Pros

  • Clear, easy explanations that reviewers say work even for people new to the maths
  • Same ideas coded in NumPy, TensorFlow and PyTorch, so the demos transfer to real work
  • Covers eigenvectors, SVD, PCA, gradients and the chain rule as ML actually uses them
  • About 90% of the 8,573 ratings are four or five stars

Cons

  • Promised statistics and optimization content never appeared, only a short probability section
  • Few visuals and few real-world ML examples, so some topics feel dry, one reviewer says
  • Audio volume jumps around, and some links to the course code no longer work
Clear and easy explanations. Good e amples. Straightforward overall!
GIUSEPPE PAOLO ABATE, a student

Listed for all levels. It asks for secondary school maths and some Python; one reviewer says it suits those with past university maths.

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What you will learn

  • Understand the fundamentals of linear algebra and calculus, critical mathematical subjects underlying all of machine learning and data science
  • Manipulate tensors using all three of the most important Python tensor libraries: NumPy, TensorFlow, and PyTorch
  • How to apply all of the essential vector and matrix operations for machine learning and data science
  • Reduce the dimensionality of complex data to the most informative elements with eigenvectors, SVD, and PCA
  • Solve for unknowns with both simple techniques (e.g., elimination) and advanced techniques (e.g., pseudoinversion)
  • Appreciate how calculus works, from first principles, via interactive code demos in Python
  • Intimately understand advanced differentiation rules like the chain rule
  • Compute the partial derivatives of machine-learning cost functions by hand as well as with TensorFlow and PyTorch
  • Grasp exactly what gradients are and appreciate why they are essential for enabling ML via gradient descent
  • Use integral calculus to determine the area under any given curve
  • Be able to more intimately grasp the details of cutting-edge machine learning papers
  • Develop an understanding of what’s going on beneath the hood of machine learning algorithms, including those used for deep learning

Course content

11 sections · 114 lectures · 16 hours of video 1 quiz, 2 articles

  1. 1Data Structures for Linear Algebra 1 free preview13 lectures · 1.7 hours
  2. 2Tensor Operations9 lectures · 55 min
  3. 3Matrix Properties 1 free preview9 lectures · 1.4 hours
  4. 4Eigenvectors and Eigenvalues10 lectures · 2.2 hours
  5. 5Matrix Operations for Machine Learning 1 free preview8 lectures · 1.3 hours
  6. 6Limits8 lectures · 1.1 hours
  7. 7Derivatives and Differentiation14 lectures · 1.4 hours
  8. 8Automatic Differentiation6 lectures · 1.3 hours
  9. 9Partial Derivative Calculus 1 free preview16 lectures · 3.2 hours
  10. 10Integral Calculus 1 free preview13 lectures · 1.1 hours

Who it is for

The instructor says it suits

  • You use high-level software libraries (e.g., scikit-learn, Keras, TensorFlow) to train or deploy machine learning algorithms, and would now like to understand the fundamentals underlying the abstractions, enabling you to expand your capabilities
  • You’re a software developer who would like to develop a firm foundation for the deployment of machine learning algorithms into production systems
  • You’re a data scientist who would like to reinforce your understanding of the subjects at the core of your professional discipline
  • You’re a data analyst or A.I. enthusiast who would like to become a data scientist or data/ML engineer, and so you’re keen to deeply understand the field you’re entering from the ground up (very wise of you!)

What you need before you start

  • All code demos will be in Python so experience with it or another object-oriented programming language would be helpful for following along with the hands-on examples.
  • Familiarity with secondary school-level mathematics will make the class easier to follow along with. If you are comfortable dealing with quantitative information — such as understanding charts and rearranging simple equations — then you should be well-prepared to follow along with all of the mathematics.

How it compares

Against the other 127 rated Udemy courses in Math on CourseDuck:

  • Rating4.3 out of 5higher than 7% of them
  • Reviews8,573#4 of 128 by number of reviews
  • Length16.4 hourslonger than 66% of them
  • Last updatedNovember 2024earlier than 53% of them

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Course Description

Mathematics forms the core of data science and machine learning. Thus, to be the best data scientist you can be, you must have a working understanding of the most relevant math.

Getting started in data science is easy thanks to high-level libraries like Scikit-learn and Keras. But understanding the math behind the algorithms in these libraries opens an infinite number of possibilities up to you. From identifying modeling issues to inventing new and more powerful solutions, understanding the math behind it all can dramatically increase the impact you can make over the course of your career.

Led by deep learning guru Dr. Jon Krohn, this course provides a firm grasp of the mathematics — namely linear algebra and calculus — that underlies machine learning algorithms and data science models.


Course Sections

  1. Linear Algebra Data Structures

  2. Tensor Operations

  3. Matrix Properties

  4. Eigenvectors and Eigenvalues

  5. Matrix Operations for Machine Learning

  6. Limits

  7. Derivatives and Differentiation

  8. Automatic Differentiation

  9. Partial-Derivative Calculus

  10. Integral Calculus

Throughout each of the sections, you'll find plenty of hands-on assignments, Python code demos, and practical exercises to get your math game in top form!

This Mathematical Foundations of Machine Learning course is complete, but in the future, we intend on adding extra content from related subjects beyond math, namely: probability, statistics, data structures, algorithms, and optimization. Enrollment now includes free, unlimited access to all of this future course content — over 25 hours in total.


Are you ready to become an outstanding data scientist? See you in the classroom.
Read More All Levels All Levels product length iconTime: 16.4h

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Instructor Details

Dr Jon Krohn

Jon Krohn is Chief Data Scientist at the machine learning company untapt. He authored the book Deep Learning Illustrated, an instant #1 bestseller that was translated into six languages.

Jon is renowned for his compelling lectures, which he offers in-person at Columbia University and New York University, as well as online via O'Reilly and the SuperDataScience podcast.

He holds a PhD from Oxford and has been publishing on machine learning in leading academic journals since 2010; his papers have been cited over a thousand times.

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Reviews

4.3

8,573 ratings on Udemy

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By Hasan Ebrahim on 7/30/2026

I would rate this course a solid 4.5 stars. The good news is that the instructor explains concepts very clearly, provides helpful examples, and presents the material in a well-structured way. It’s also very beginner-friendly, making it easy to follow even for people who are new to the topic. The only downside is that the instructor mentioned adding a statistics, optimization section, but it seems those part was missed. If that section is added, this course would definitely deserve a full 5-star rating.

By Davi Miranda on 7/3/2026

Very good! Even though I am a engineer with years of experience, I still learned a lot of useful information that I could use in my day to day at work to solve complex problems in new and more elegant e efficient ways.

By Shatanik Chatterjee on 5/12/2026

The course covers the basics well enough for you to code through the concepts. While the course is still incomplete the concepts it does cover were easy to comprehend. If you are wondering whether it's worth it or not, consider this course if you want to understand the foundational concepts from scratch and code it in Python.

By Dániel Sándor Kovács on 5/3/2026

The curriculum is good overall, but the lectures could be better organized. I would have appreciated more visualizations, as some topics were difficult to follow and felt quite dry without visual support. Furthermore, it would be great to see practical, real-life examples to illustrate the usecase of the mathematics taught here.

By Donald Stinchfield on 5/1/2026

I'm in module 1, not super interested in the history. Sped through it, always an option :-). A single slide showing the history and the names would be enough for me along with how the use and understanding of linear algebra changed over time.

By Alex Chen on 3/23/2026

Amazing class, none of the other classes goes into these basic details which is fundermental to gaining an accurate intuition to deep learning

By Devendran Sylajan on 1/22/2026

Overall Ok, but some of the pytorch code not working any more has to be updated in the code. eg: regression(x_min, my_m, my_b).detach().item() line no longer working , I had to be fixed it. Also it would be better if he could have used standard terminology for eg: loss function he is using the term as cost function , this would be confusing initially.

By Brian on 1/17/2026

I returned to school to get my Master's degree in Data Science and I needed a review of the topics in calculus, linear algebra and statistics. This course was perfect because it was targeted to machine learning. I tried a couple of other courses that I thought would be good but Jon did a much better job of explaining topics in a clear and understandable way. Very helpful. Thanks Jon!

By Dwayne Martin on 12/20/2025

First the course is absolutely magnificent. John is a great instructor and makes complicated topics clear. My only regret is that the course is not complete yet, and I have had the course for an extended period of time. I would love to see the rest of the course published on this platform.

By Andrew Tonks on 12/13/2025

When I purchased the course, there were some interesting subjects at the end, like statistics and basic ML. As I worked through the content I started to get to the parts I had most interest, and it was removed. Bit of deception, as I wanted to see the end of the film.

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Overall Score : 86 / 100

Mathematical Foundations of Machine Learning
$17.99Original price $124.9986% off
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  • Video Duration: icon 16.4h
  • Price: $17.99
  • Provider: icon Udemy
  • Updated: icon November 2024
  • Level: All Levels All Levels
  • Language: icon English
  • Certificate: icon Yes
  • Lectures:114 in 11 sections
  • Practice:1 quiz
  • Students:147,100
  • Subtitles:27 languages
  • Udemy badge:Bestseller
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