Back to Mathematics for Machine Learning: Multivariate Calculus

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5,562 ratings

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....

JT

Nov 12, 2018

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.

SS

Aug 3, 2019

Very Well Explained. Good content and great explanation of content. Complex topics are also covered in very easy way. Very Helpful for learning much more complex topics for Machine Learning in future.

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By Tyler W

•Jun 18, 2022

Some interactive components were interesting to work through and the videos themselves were well polished and fairly engaging. However, much of the in-depth working throughs (particularly in later weeks as things get more difficult) are omitted in favor of having nicely packaged 5-10 minute videos. As a result, assignments can have Qs that are exceedingly easy or impossibly difficult (without needing to consult external resources, which you will have to do to fully grasp these concepts).

Much of the "programming" is also just implementing the pure math in Python; the actual programming you'd need to implement these concepts is pre-written, so you don't get any experience with this. I realize this isn't a programming course, but I don't think it's unreasonable for a course specifically targetting people looking to do ML can write their own functions / practice implementation.

By Rina F

•Nov 14, 2020

This is a very useful course for brushing up on college multivariate calculus as well as learning many new skills and concepts necessary for understanding machine learning. I especially enjoyed the fact that the lecturers focus on understanding concepts rather than rote formulas (although there is certainly a fair amount of hand solving equations to make sure you understand the mechanics and concepts). I gained an understanding of the Taylor Series and its significance that was lost to me in college courses (years ago). The lectures, visual aids, and especially the interactive graphics were very well done. Thanks to Imperial College for offering this course and to the lecturers for all their care in producing it.

By ash g

•Mar 18, 2019

I am enjoying this course massively. I am on week 5 and the lecturer has been great so far. Some of the programming assignments are a bit easy as in some cases the blanks to fill in are rather self-explanatory.

The exercise questions progress in difficulty nicely and are sized well. References to tackle more questions to solidify the understanding could be good, however I recognise that the aim is to teach the intuition and then move on and apply it in Machine Learning examples, rather than being a mathematics course alone.

By Luiz G R C ( G

•Mar 13, 2021

This course is very important for a deep understanding of the main optimization algorithms used in several machine learning techniques, such as gradient descent with practical examples of fit linear and non-linear functions, in the course is shown also Lagrange multipliers for optimization with constraints and Raphson-Newton numerical method for to find the approximation of the roots of any math function. Recommended for people with or without a Calculus background.

By Nelson F A

•Mar 22, 2019

Very intense course. However, now that I have moved on to Andrew Ng's ML course, I am so glad I finished it. Understanding the math behind ML makes learning it so much more enjoyable. Before it was like shooting in the dark. My python code wouldn't and ML-concepts would take a lot of time and effort to sink in. Sometimes not at all... This course armed me with the tools to succeed in a career in ML and AI. Looking forward to finishing the specialization!

By 周玮晨

•Jun 6, 2018

his course really meet expetation.It really help understand a lot multivariate Calculusand build me intuitions.Now i'm confident in learning ml.

The content is abundant,i really love the visualization and programming work.The programming work is fascinating,elabrated-designed,fully explained,i want more and harder programming work.

Sam is very passionate, creating a excitied study atmosphere, i really like his stress when speaking.

By Kwame A G

•Jul 28, 2019

I'll call this course, Multivariable calculus made easy!!! Like the first course in this specialization, the lecturers tried to appeal to my intuition. Avoiding the very precise technical presentation in the traditional multivariable calculus course. Another impressive feature is how the applications were introduced. No need for any memorization as usually required everywhere else. Thank you coursera!!!

By Juan P M C

•Aug 31, 2020

Wonderful course! The teachers explain everything in such a clear way that if you pay enough attention and take notes throughout the videos you won't have many problems understanding the subjects. Also the assignments and tests help a lot in reinforcing what you just learned with all the clear instructions that guide you step-by-step through the several methods and algorithms of the course.

By Arnab C

•Sep 3, 2018

I found this one to be probably one the best courses on neural network if someone is keen to learn the underlying mathematics of it. The content of the course is very concise, enough to cover the most important parts that are required to learn machine learning and just enough depth. The quizzes and assignments are of excellent qualities. Overall, I will highly recommended this course.

By J A M

•Mar 11, 2019

Excellent class! Understanding the math "under the hood" of the Python, Matlab, and R libraries is indeed the missing link holding back many data scientists from truly achieving competence and excellence. This course addresses such lacunae squarely by tackling a robust menu of relevant mathematical methods. Well done and kudos to Imperial College for taking the initiative.

By Frank N

•Feb 10, 2021

This is excellent ! The instructors are awesome. You could tell they are ready to help us learn. I did not have a technical background and had no prior knowledge. Just have your basic math skills intact and you would have a great experience with mathematics.

Note: I have already moved on to other higher level courses in data science and have come back to testify.

By Aravind T E

•Nov 15, 2020

If you are beginner or came here to know about how math is applied in Machine Learning, this course is for you. The instructors are technically sound and the video quality is great. The assessments are intriguing and literally I fell in love with math after this course. Thank you Imperial College London and Coursera for providing this course.

By Nur M H

•Mar 23, 2023

Excellent course. Both the content and the explanation are excellent. Also handled in a very simple manner are complex subjects. In the future, studying much more complicated topics for machine learning will be very helpful.

By John F

•May 1, 2020

Great course. In my view students need to supplement their learning with material from the Kahn Academy and 3Blue1Brown youtube channel - as recommended in the resources section of the course. Thanks to David and Sam.

By Preetam S

•Jul 17, 2021

Samuel J. Cooper is one of the best teachers I've been taught by till date. His ability to build an intuition about concepts and more than that his desire to do so really helps to get a strong grasp over the concept.

By Lorenzo

•Oct 23, 2019

Very clear and concise course material. The inputs given during the videos and the subsequent practice quiz almost force the student to carry out extra/research studies which is ideal when learning.

By Ashish S

•Apr 15, 2018

Excellent course!

I studied multivariate calculus during engineering. I hardly understood the concepts at that time, this course helped me understand and visualize what is going behind formulas.

By João S

•Apr 17, 2019

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 Cesar E B G

•Apr 29, 2022

The course was ok. Specially the first four weeks. However, on week 5 and week 6, there is a change of instructor. He talks very fast, and do not stop to explain with greater detail the concepts, nor he visualise with examples. He just declares what's happening. with now emphasis on the underlaying concept, which makes the subject, already complicated, more challenging. Conversely, the first instructur has a gift for teaching. He really knows how to portray calculus in an easier way to visualise.

By Sergio A G

•Oct 21, 2020

It starts brilliantly, but the last 2 weeks are quite bad. It has nothing to do with the new teacher taking over that part, I think he is as good as the other one. It's a matter of goals and focus. It seems like everything you learn in those weeks are just random things and little 'magic tricks', it's hard to see why they're relevant to the subject and everything seems disconnected.

Still, I really enjoyed the first 4 weeks. Awesome content, they made me realize I love calculus.

By Benjamin F

•Nov 1, 2019

Relevant content. Great instructions. Likable instructors. Very bad coding assignments.

By Maprang S

•Jul 1, 2020

I'd have loved to give a 5 or at least a 4-star but really the explanations on each topic have gaps, which make it super hard to know what really was going on. One could have never completed this entire specialization with only the materials in the course. A lot of further research is required to understand the concepts and to complete the assignments. The 2 stars I gave are mainly for the assignments which help to reinforce the learning and the help that other students provide in the forum. However, I don't regret having taken this course. I'm just little disappointed because I thought I'd have gotten more out of this course than I actually did.

By Ong J R

•Jul 23, 2018

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.

By Oliverio J S J

•May 26, 2020

This mathematics for machine learning course is not a mathematics course. It starts well, explaining mathematical concepts and, suddenly: neural networks, python programming, numpy, scikit... The speed at which the concepts are explained makes it impossible to assimilate anything unless you already know the concepts beforehand, which means this course only serves as a refresher course.

By Abhishek B

•Apr 15, 2020

Instructions were very poor in many cases , Khan Academey is much better source for explanation of concepts

Instrructions on PCA are so Awful , that I decided to drop from the course