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Imperial College London

Mathematics for Machine Learning: Multivariate Calculus

Imperial College London via Coursera


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.

Taught by

Samuel J. Cooper, David Dye and A. Freddie Page


4.9 rating, based on 9 Class Central reviews

Start your review of Mathematics for Machine Learning: Multivariate Calculus

  • Profile image for Shivani Sharma
    Shivani Sharma

    Shivani Sharma completed this course, spending 3 hours a week on it and found the course difficulty to be medium.

    The course is a great introduction to how one can translate pre-learned mathematical concepts into machine learning. I think it just makes you appreciate complicated mathematical equations as they are tied into neat computational applications.
    For those who want an introduction to the math first, the course has plenty of explanatory videos as well. But as someone who did know the math, it just made me realize that my college math can actually be used to do something useful.
  • Giuliano Lemes completed this course, spending 3 hours a week on it and found the course difficulty to be hard.

    This is the best course I have done so far, the practical part of the course is wonderful, you get to program a neural network just using numpy as a help, learn to differentiate, jacobians, hessians, newton ramphson, it is a very difficult course but it compensates when you can finish it.
  • Anonymous

    Anonymous completed this course.

    The teaching is clear and concise with an impressive breadth of material covered during the 6 weeks. There is an emphasis on developing intuition, and content is made highly engaging through visual descriptions of calculus techniques. Having completed the course, the understanding you are left with feels profound and rigorous.
  • Anonymous

    Anonymous completed this course.

    Clear explanations, cool animations, informative interactive activities and challenging assignments.
    I especially enjoyed understanding back propagation from first principals and had also never seen multivariate Taylor series before!
  • Anonymous

    Anonymous is taking this course right now.

    The part taught by Dr. Samuel J. Cooper is the best course I have ever seen in Calculus. It is very important to illustrate the essence of the topic with the methods used to solve the problems.
  • Profile image for Sajil C K
    Sajil C K

    Sajil C K is taking this course right now.

    This course is an excellent one. It helped me grasp many complex concepts in an easy way. I hope every explanation/book/video follow this style. I strongly recommend this course to anyone.
  • Anonymous

    Anonymous completed this course.

    The concepts taught in the 3 courses are very relevant to Machine Learning. Professors Dye, Cooper and Deisenroth are excellent at teaching and making the material easy to understand. They make the best use of audiovisual technology I have seen in all online classes that I have taken.
    I have continued to pursue machine learning education, with the mathematical foundation from these courses, it is much easier to understand how machines learn, and how to improve the performance of existing Machine Learning frameworks by proper choice of architecture and hyper-parameter tuning.

    I strongly recommend starting your Machine Learning education by completing this certification.
  • Sagar Ladhwani

    Sagar Ladhwani completed this course and found the course difficulty to be medium.

    Of all the three courses in the mathematics for ML specialization, this one was the best course since it covered all the fundamentals of Machine Learning Cost minimization algorithms and even the assignments notebooks were pretty well designed. I'd recommend this to anyone who wants to understand the math behind ML. For the course topics and applications details, go through this post - I've included all the major points:
  • Benjamin Lau completed this course, spending 5 hours a week on it and found the course difficulty to be medium.

    Decent exposure to the topic and introduce some common technique used in data science. Learning curve is steep if you do not have any prior knowledge in calculus

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