Back to Mathematics for Machine Learning: Multivariate Calculus

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5,573 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.

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.

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By Tuan Q N

•Feb 5, 2021

The highest level of math I took was Algebra 2 almost ten years ago. The professors are pretty good, but many times their examples would not be very clear in terms of what needs to be done. I had to go watch some extra YouTube videos to understand derivatives and only then was I able to come back to the course and work my way through the assignments. My recommendation is when walking students through problems, please provide more details on the steps you're taking. Otherwise, I'm quite happy with this course and I'm learning forward to the PCA module.

By Ryan B

•Nov 24, 2020

A background in Mathematics is highly recommended before beginning this course. I learned these concepts 20+ years ago while completing my Engineering degree. They are presented so quickly here I needed to do a lot of research to truly understand the concepts they are presenting. A great external resource for mathematics is the 3Bule1Brown channel on YouTube where these concepts are brilliantly presented in a layman's format. Overall I thought this course was a good way to link the concepts of Linear Algebra and Calculus to Machine Learning.

By Salem A

•Jun 20, 2020

If you do not have a background in programming, some of the assignments will be intimidating and hard to do but if you go over it sequentially you will get the hang of it but it will take you time to do so. The lectures are too short and I feel that some concepts were not clarified enough because of how fast the lecturers go over them. The course, in general, is good for having an overview of the material so do not expect to cover these topics deeply. The presentation and the way some concepts were tough were enjoyable and enriching.

By Fang Z

•Jul 11, 2019

I really love Samuel's teaching style. He strived to make people understood by showing a lot of graph and I can easily follow him step by step. However, David's teaching I couldn't follow up his mind much maybe because less explanations given during the lecture.

In addition, I found some quiz have huge amount of calculated amount which I really spent a lot time to verify the answer.

Finally, I hope more detailed explanations could be given if I made mistakes in some quiz so I could boost what I've learned so far.

Thanks,

Fang

By Hermes J D R P

•Feb 28, 2020

The first 4 weeks of the course were amazing: great content, clear explanations and fair and interactive assessment activities. However, the last 2 weeks weren't as good as the previous ones. That's why I don't give this course 5 stars. By and large, the first two courses of this specialization are the best resources available on the internet to learn the foundations of mathematics for Machine Learning. I recommend that instead of doing the last course, you had better try to read the related book wrote by Deisenroth.

By Christiano d S

•Aug 3, 2020

this course contains good lessons, and the level of assignments is proportional to what is being taught. there are some minor issues at some of the videos, but it´s possible to clear the doubts in foruns, in general, I´ve found this course the best one by far compared to other courses in coursera in which you have to spend a lot of time searching for extra information and content to accomplish the assignments. for the first time I felt the instructors actually taught the content.

By Wu X

•Apr 21, 2020

This course teaches multivariate calculus and its applications. In particular, Jacobian and Hessian Matrix are introduced as Matrix versioned derivatives (first order and second order), along with gradient descent optimization based on them. The structure of the course is a little bit loose, so it's not a good choice for those who want to seek systemically arranged learning materials. But it still worth taking for a better perspective and ideas.

By Saras A

•Jan 29, 2020

Good course. I wish it had more sections as in a total of 12 sections or weeks and more steps to gain a more thorough graphical understanding (and perhaps even a more mathematical/algebraic understanding however overall that's much easier for me on that front...).

From a Data Science or Machine Learning perspective Week 6 (linear regression and non linear regression with chi-squared methods etc) were the most interesting.

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 Habib K

•Aug 29, 2021

This course gives a great intuition about the calculus required for machine learning. Meanwhile the lecturers do not explain some concepts completely which is really bothering. In those situations always check the forum because you are not alone and other students probably had the same problem and someone would have explained it in more details or posted a link to a video that explains that concept in more details.

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 Walter S

•Feb 3, 2021

This is a good calculus refresher and exploration of optimization processes and techniques. It goes rather fast and if you are rusty on the concepts you will need help from other sources such as Khan academy. I would have liked hands-on examples of using the functions in python libraries and matlab, as this was just a footnote on the last lecture.

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 Radu 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 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 Christian S

•Apr 17, 2021

Very solid introduction into Calculus. Keep in mind that this is a course meant to give you an intuition and basic understanding. Sometimes there are small gaps in the curriculum to the quiz (but you will easily be able to make up for them by just reading the according Wikipedia page). Was a pleasure.

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).