Mathematics for Machine Learning: Multivariate Calculus

For a lot of higher level courses in Machine Learning and Data Science, you find you need to freshen up on the basics in mathematics - stuff you may have studied before in school or university, but which was taught in another context, or not very intuitively, such that you struggle to relate it to how it's used in Computer Science. This specialization aims to bridge that gap, getting you up to speed in the underlying mathematics, building an intuitive understanding, and relating it to Machine Learning and Data Science.In the first course on Linear Algebra we look at what linear algebra is and

Created by: Samuel J. Cooper

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Overall Score : 94 / 100

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Course Description

This course offers a brief introduction to the multivariate calculus required to build many common machine learning techniques. We start at the very beginning with a refresher on the "rise over run" formulation of a slope, before converting this to the formal definition of the gradient of a function. We then start to build up a set of tools for making calculus easier and faster. Next, we learn how to calculate vectors that point up hill on multidimensional surfaces and even put this into action using an interactive game. We take a look at how we can use calculus to build approximations to functions, as well as helping us to quantify how accurate we should expect those approximations to be. We also spend some time talking about where calculus comes up in the training of neural networks, before finally showing you how it is applied in linear regression models. This course is intended to offer an intuitive understanding of calculus, as well as the language necessary to look concepts up yourselves when you get stuck. Hopefully, without going into too much detail, you'll still come away with the confidence to dive into some more focused machine learning courses in future.

Instructor Details

Samuel J. Cooper

Dr Sam Cooper is a Lecturer of energy science and materials design in the Dyson School of Design Engineering at Imperial College London. His PhD was on the characterisation and optimisation of battery and fuel cell electrodes through 3D imaging and simulation. His research group is primarily focused on developing next generation energy storage technologies.



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By Tanuj J on 19-Jan-19

Topics need to be covered more in depth. Too much information packed into this course. Instructor's explanations are also not clear most of the time. It will be hard to follow this course if you don't have some background with calculus.

By Valeria B on 17-Jun-19

The first part of the course is fine. Towards the end, lots of interesting concepts explained too quickly. I'd rather have more detailed explanations, especially about linear and non-linear regression. The examples are quite good.

By Marc P on 28-Apr-19

The course is led by two instructor and my ratings is an average of the two performances. The videos in week 1 to 4 are absolutely outstanding and a pleasure to follow. The ones in week 5 and 6 are ok but not great. The use of quizzes and coding assignments throughout the course is very engaging and of great use for retention and application of the learned subjects.

By Nushaine F on 18-Jul-19

This is my first time learning calculus (I'm a 16 y/o high-school sophomore), and I'm satisfied with this course. The instructors were great, and the assignments are awesome.If I would suggest one improvement, it would be to give more examples in the lectures. Some lectures were packed with examples, and some had none at all. I had to often refer to Khan Academy and YouTube to learn the concepts which the instructors did not provide an example for. (Especially in Week 4). Sometimes this would frustrate me because it would take me hours to grasp a concept. Having said this, this course is for you if: (1) - you want a refresher on fundamental calculus concepts that relate to machine learning, or (2) - if you want to learn calculus for the first time, and you have a strong desire to learn these concepts. But no matter what, DON'T GIVE UP and don't stop until you've completed the course.I hoped this has helped and good luck on your ML journey!

By Yan on 31-Mar-19

Some errors confused many students. And they are remained unfixed.

By Andrii S on 20-Jan-19


By James L T on 13-Nov-18

Excellent course. I completed this course with no prior knowledge of multivariate calculus and was successful nonetheless. It was challenging and extremely interesting, informative, and well designed.

By Oleg B on 12-Dec-18

Excellent summaries of important points.

By Jo�o C L S on 17-Apr-19

I liked the course specially because I finally understood Backpropagation, an old frustration from Andrew Ng's Machine Learning course. It covers the main topics for Mathematics for Machine Learning as promised. Two weak points: (1) the Newton-Raphson convergence problems, superficially covered in the lectures, but has a challenging test, no forum support, no other source indicated for helping us. (2) The forum is abandoned. I've set two problems, one of them about an error in a lecture and the second about the problem with Newton-Raphson lecture. No responses from the lecturers or mentors.

By Jonathan C on 24-Oct-19

I don't want to be too hard on this course since I reallyliked some parts of it. Especially, the instructor in Week 1 - 4 did a good jobexplaining the concepts and overall one can clearly see that a lot of effortwas put into the creation of this course. However, I found that a lot of topicscould be handled a lot more in-depth. The assessment at the end of a week was notreally challenging and does not require a deep understanding of the concepts.Some of the quizzes were more challenging but in the assessments it was oftenonly required to answer questions based on graphs or other images offunctions. Most of the programming assignments only required the studentto fill in some easier blanks.I still do not know what the TaylorSeries Chapter was about. I guess this is an important concept but I wasnot sure how this relates to machine learning. If you call a course Mathfor Machine Learning, I would expect that you relate the concepts to MachineLearning.Maybe, itis just me but I would have been glad if this course had offered more depth andtook at least double the amount of time to complete. This would have been morerewarding, as I do not feel that I learned as much as I hoped for when Istarted this course.

By Carsten H on 31-Mar-18

Too many derivatives of pointless functions.

By Ong J R on 23-Jul-18

Course videos and quizzes are good and content is clearly explained. However, too many concepts are covered with too little depth. For example least squares and non-linear least squares involve fundamental concepts that should be covered and alone, would at least 2 weeks to teach. Lagrange multipliers and Taylor series are barely introduced with very little mathematical derivation involved. I had the impression that I would learn more mathematical theory than machine learning in this course, it didn't turn out to be so.