Back to Mathematics for Machine Learning: Multivariate Calculus

4.7

stars

4,260 ratings

•

762 reviews

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....

DP

Nov 25, 2018

Great course to develop some understanding and intuition about the basic concepts used in optimization. Last 2 weeks were a bit on a lower level of quality then the rest in my opinion but still great.

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.

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By Donna D C

•Apr 25, 2020

Nice balance between rigor and developing intuition (again as in the previous linear algebra course in this series). I would’ve liked some “homework” reading about backpropagation for training the simple neural to prepare for the future courses. Also, more references for additional reading on least squares minimization techniques to tie more into the statistics underlying the techniques. I love the stuff, thank you!!

By Dan L

•Mar 30, 2019

The course accomplishes its goal of connecting concepts in calculus to machine learning, and is appropriately paced for students who have covered calculus in the past and are seeking a refresher or deeper understanding of its applications to real-world problems. For those who don't already have a certain minimum familiarity with the mathematics, however, the course will probably move at too fast a pace.

By Matt P

•Jul 19, 2018

Great class - very informative and eye opening - even with quite a bit of linear algebra background. Really liked the eigenvector and eigenvalue section - great descriptions. I wish the neural network discussion went on a bit further. I found some of the programming assignments' instructions a bit vague and confusing - what should have taken a few minutes ends up taking a half hour.

By Aneev D

•Oct 19, 2018

This course is great in the sheer efficiency with which it goes through the content required to prepare you for machine learning. It builds an intuition for what's going on, which is amazing. Some parts are confusing, and I recommend looking at Khan Academy for the lectures on Jacobians and steepest ascent, and 3Blue1Brown for feedforward neural networks.

By Wenyuan Z

•Jan 10, 2019

Well the course is generally good, the only problem is that David sometimes may just skip the process and lack more explanation when performing the calculation, it's easy to lose track of what he is calculating if not reviewing the video over and over again, but anyway, the whole class is worth recommendation, thank you for your teaching, professors

By Anton K

•Sep 18, 2020

It was exciting at some points. However, I left the course with the feeling that some subjects were not covered properly. The technical aspect of the course (e.g. video quality, visualizations, practice with python) were really great, lots of interesting and new teaching methods (at least for me). I wish this course was longer and more detailed.

By Mihai R F

•Nov 1, 2019

Very valuable training course from the insight/intuition point of view. This is more of an overview of the calculus for machine learning giving the student a good direction of what to study and where to start from. I think that actually mastering the subject will require extensive additional exercises from other sources

By Dmytro B

•Feb 11, 2019

Very helpful to review and get introduced to mathematical concepts behind machine learning. There is a fair bit of practical exercises as well. The only thing I am less happy about this cousre was a lack of additional suporting materials and references to other resources to help gain more knowledge on the subject.

By Gerard G I R

•May 11, 2020

I had no previous experience with multivariate calculus. This was a nice introduction to the topic, but in my opinion it does not allow me to say that "I know" multivariate calculus. Nevertheless, I think it is work taking as an introduction before going to more complete courses in multivariate calculus.

By Luis M V F

•Mar 16, 2019

I think Samuel Cooper is an amazing instructor. However, the last two weeks taught by David Dye were very difficult to follow. I think David should improve his explanations because I did not enjoy too much his course on linear algebra, and this course was great until he started with the last two weeks.

By Abhirup B

•Aug 30, 2020

exercise and programming assignments are good ....and i can grow a sound concepts after completeing them.lectures are also good ...but some lecatures are too quick and a little elaboratiion in some places would have been helpful(particularly those in the last couple of lectures)

By Kevin E

•Jun 15, 2020

Excellent course. It covers so much without making me feel overwhelmed. I would like to see more hands-on demonstration on linear and non-linear regression, but I was able to complete the quizzes and assignments. This without any previous multivariate calculus instruction.

By Divyang S

•Aug 8, 2020

Overall a good course to give us a better idea of what sort of math is used in ML. But I feel they went too fast in this course, so I personally lagged a bit in understanding certain crucial concepts. Also, it'd be much help if the instructors could mention reference books.

By Michelle W

•Nov 17, 2019

I would say this entire series is better advertised as a quick *review* of the pertinent concepts. Otherwise, someone with no background in the topics covered may struggle (unless they are particularly talented with quickly learning new mathematical concepts).

By Glendronach 3

•Mar 22, 2020

This felt like time well spent. A really good course which I should have taken before doing the Machine Learning Course by Andrew Ng. That would have made life easier.

Beware, the 'gradient of the learning curve' at any point during this course is steep.

By 胡震远

•Aug 30, 2020

Generally, it is a good course. Many new tools and fancy representation method, but for mathematical idea and explanation, it is just too simple. Maybe the biggest contribution to me is that It lets me know the Kahn Academy and 3b1b courses.

By Aditya J

•Apr 13, 2020

Could have explained in a way that the audience requires a slower and better and little more in-depth explanation. Some places felt a little rushed, so had to spend more time in forums and other resources to get more idea. Overall was great.

By Saikumar S

•Jan 13, 2020

Need a bit more clarity in terms of integrating the calculus in the last week sessions.

I agree they are very good but would be great if there is some more additional clarity. And also some project using the whole course would be helpful.

By Ankit C

•Mar 28, 2020

It gives you a good head-start to the math required in Machine learning. Some major concepts are touched just on the surface level but the mathematics involved in those concepts is explained quite well. Overall, it's good experience

By SUJITH V

•Sep 16, 2018

Very good course to start of with mutivariable calculus basics. Helps to refresh your memory if already familiar with concepts, additionally helps in getting fresher perspective because of geometrical intuition presented very well.

By Switt K

•Jul 27, 2020

Good details, great at building intuitions. Instructors are pleasant to listen to :)

As expected, it's enough to get you going in the right direction, that if you want to know more, you'd have enough knowledge to build on from.

By George K

•Sep 21, 2018

Lack of support from the staff. Some parts/lectures are not clearly explained (for example, constrained optimization) and some quiz questions are not directly related to the course content. Otherwise, it's a very good course.

By Jacqueline B

•Apr 6, 2020

up to week 5 , it was masterpiece.

week6 (although it should be the most important one) was a mess and disappointing.. as it was not explainable, i couldn't link what is happening with previous weeks.. require to be enhanced

By Izzan D

•Mar 29, 2020

The first 3 weeks is really good, the fourth week is okay but the last 2 weeks is kinda confusing. The explanation is quite clear but it is quite hard to grasp the intuition and relationship between each material.

By Peiyuan C

•Sep 29, 2018

Along with the advanced and popular technique, this course gives me impressive insight over how machine learning works. But it would be much better if the concept in linear algebra combines more with this course.

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