Back to Mathematics for Machine Learning: Multivariate Calculus

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5,574 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 Alfian A H

•Mar 22, 2021

Very good

By hemant k

•Dec 17, 2018

Its good.

By henry c

•Jan 19, 2020

It is ok

By R. D B D

•Mar 7, 2021

so hard

By MUTHUKUMAR P

•Sep 26, 2021

Good

By Prof(Dr) S R

•Aug 24, 2019

nice

By Monhanmod K

•Oct 10, 2018

g

By Tony J

•Aug 19, 2020

Pretty good in terms of material covered. This course does a much better job of balancing what you should know vs pace than the linear algebra course (which breezed through or skipped a couple concepts that made it difficult to complete assignments or subsequent lessons).

Both courses so far would really benefit from another couple turns at the wheel in terms of polish, making sure that concepts are covered adequately and nothing is lost in the gaps. Also there is room for more and better 'further reading' pointers for those who are interested.

The biggest issue in both courses so far is the discontinuity when the lecturers (for whatever reason) switch in the last 2 weeks of the respective courses. Things seem to get lost or forgotten.

For example, in this course there's no mention in week 5 of how the previous week's topic relates to the material being covered, even though in the assignment there is a very interesting application of the topics in week 4 being presented, but it's completely hidden. And, judging from the forum posts from that week, the vast majority of students missed that insight.

I'm not sure why this course hasn't received any updates since it launched over 2 years ago. It's rough in more than a couple spots, but it could polish up really nicely.

By Maksim U

•Jan 3, 2019

I did learn quite a lot throughout the course. The problem is that most of my knowledge came from elsewhere while the explanations by the course instructors were quite unclear till I referred to extra resources. At the same time, some other explanations were on the obvious side, so I'd say the instructions are kind of inconsistent in their difficulty. The real-life examples were relly good though. The same concerns the quizzes, some are absolutely great and intuitive, while the others just leave you puzzled about what you are even expected to do with no extra info offered when failed.

The course is kind of sloppier than the first one and the reviews say the third one is even worse, so I won't be doing it.

Finally, I cannot even complete the last graded assignment and get my certificate as well as some other learners because the thing just throws an error all the time. There is zero reaction from the crew that is supposed to be moderating the forums.

All in all, a fine "guideline" course. But do not expect to be presented much inside the course itself.

By Pritam D

•Sep 13, 2020

While the topics covered in the course are good, the depth and clarity with which each topic deserves to be explained, remains unfulfilled. The lectures are easy to understand, but sometimes you'll have to jump to other resources to get a better understanding of the topics covered. The difficulty of assignments is relatively very high, compared to their respective lectures.

Moreover, I feel that categorizing this course as a "beginner" course is somewhat questionable, as a complete beginner will face a lot of hurdles, given the number of new topics introduced in each lecture, the succeeding (often difficult) assignment, and the brevity of explanation. This course is more of an intermediate level, and some prior experience of Multivariate Calculus is required. I personally had glazed over Multivarious Calculus during my undergraduate, and even with that background, the difficulty seemed frustrating. For me, other resources, such as 3blue1brown youtube videos and Grant's KhanAcademy videos were necessary to complete the course.

By Leandro C F

•Mar 22, 2021

I've took the first course about linear algebra and it was brilliant. Unfortunately I did not have the same impression on this course.

The contents of the course is very important, but some topics were covered very quickly and superficially.

I also noticed that many people liked the first instructor, but for me the fact that he emphasizes one in every four words annoyed my learning experience. I spent more time paying attention in the emphasis than in the contents.

By Harsh D

•Jun 14, 2020

After the first course of the series, I expected more out of this. Certainly, the course covers basics but there's a gap in between the weeks. May be it was done to ensure the course could be restricted to 6 weeks, but then again course 3 is just 4 weeks. Not sure what happened there, this one certainly requires restructuring.

For Imperial College: If you would like to know what I am talking about, please go through the discussion forums.

By Paul F

•May 10, 2020

Towards the end, you see that the lecturers and the Team lost their motivation for a bit. Explanations are done very quickly and the exercises lack proper programming. The last one for example can't be passed if you write the functions in two different cells (as it is displayed in the workbook when you start), you need to copy them to one cell. This is really badly designed.

By Oliver K

•Feb 1, 2020

The first few weeks were a great introduction to derivatives, but the further it got the more the content seemed rushed and the exercises lazy. I will now go back and read secondary literature to really understand those parts, and not just calculate derivatives over and over. Samuel was a fantastic instructor though, kudos!

By Marcin

•Aug 12, 2018

It's one of the toughest things that I've done in my life. The content is really interesting and applicable, but at times you might get stuck with quizzes or assignments because there is not enough guidance given. All in all, I'd recommend this course to everyone working in analytics.

By Sam C

•Apr 17, 2018

A quick short introduction to multivariate calculus and few machine learning techniques, but without much detail mathematical proofs for some ideas. It's a maybe good introductory course for beginners of calculus. Not recommended for learns who seek for details of ideas.

By Kirill N

•Aug 16, 2020

Weeks 1-3 (4) were pretty nice; weeks 5 and 6 were terrible. The harder the topics, the less explanation was given, the pacing by the end was atrocious and course delves into statistical topics while it probably could've dedicated these weeks to other relevant topics.

By Khang “ P

•Sep 22, 2021

The last 2 modules have very promising content, yet the instructor did not do well enough. I found myself totally lost in the confusing explanation of David, although I've already have experience in Multivar Calc and take this course just as a refresher.

By Joshua V R

•Aug 26, 2022

Weeks 5 and 6 could be greatly improved in terms of clarity and quality of the explanations. More solved examples would be very helpful and appreciated. On the other hand, weeks 1 to 4 met the expectations and were very ilustrating.

By Yi Z

•Aug 3, 2018

Such a easy course, if you totally a novice in multi-variables calculus, you could take this course, Whereas, if you are familiar with calculus, it will be quite easy for you.

I hope more programming assignment about Machine Learning

By ZHANSHAOXUN

•Nov 9, 2021

the connection seemed poor between weekly targets. it was super easy at first and became very difficult at last, honestly i do not think this is designed for students with no relavant foundations in math or machine learning.

By Rob E

•Aug 11, 2020

The instructor for this course actually tried to explain the concepts, unlike the other two courses in this specialization. However, no one is available to answer questions.

By Shivam K

•Jun 30, 2020

I feel that the course was too fast paced. I had to constantly refer to many other website like khan academy and 3b1b. The course skipped many details and lacked intuition.

By pranshu s

•Oct 17, 2020

You will get some intuition of mathematics used in Machine Learning as well as there will be less fear in doing ML courses if you would complete this course.