Mathematical Foundations of Machine Learning (Udemy.com)
Essential Linear Algebra and Calculus Hands-On in NumPy, TensorFlow, and PyTorch
Created by: Dr Jon Krohn
Last updated November 2024
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
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
Linear Algebra Data Structures
Tensor Operations
Matrix Properties
Eigenvectors and Eigenvalues
Matrix Operations for Machine Learning
Limits
Derivatives and Differentiation
Automatic Differentiation
Partial-Derivative Calculus
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.
Instructor Details
- 4.3 Rating
8,573 Reviews
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
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.
Quality Score
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Overall Score : 86 / 100






