Back to Mathematics for Machine Learning: Multivariate Calculus

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4,912 ratings

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879 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....

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.

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 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 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 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 Preetam S R

•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 D 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 Benjamin F

•Nov 1, 2019

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

By Maprang

•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 Steve

•Aug 5, 2020

The ideas the course hopes to present are good and relevant but the presentations are so poor that most of my learning of the material came from finding outside sources like Khan Academy. Often, important new ideas were roughly and quickly explained with not enough detail to give the student the intuitions needed for understanding. Often the practice quizes asked questions that were not properly covered in the videos so you need to go to the forums or elsewhere to gain the understanding needed.

By Sven A

•Oct 7, 2020

Extremely well built course. The quality of materials is excellent and practice exercises really help to deepen the understanding. But what I did like the most were programming assignments, where students are asked to implement mathematical equations as python scripts. The reason I liked such assignments so much was that I needed to build a general understanding (and sometimes come up with general solutions on paper) before writing the code. I did not need any background knowledge of python, because I only needed to write arithmetical equations, pretty much using python as a calculator. In that way I had a chance to focus on the subject matter while leaving python do all the calculations. Now, if I screwed up something in my equations, there were tests written for me, where I could check my solution (e.g. presenting visually how well my script did etc.). That really helped the learning process.

By Iacopo C

•Aug 26, 2020

Although the course doesn't cover all of the details of a traditional calculus course, it helps you build an understanding of the fundamentals in the language of calculus, as well as some intuition as to where it might be usefully applied in machine learning.

The lecture videos are top notch and overall both instructor do an amazing job in teaching and developing the intuition required to understand the meaning of the tools used in multivariate calculus. The quizzes are strongly related to what's taught and even what's best, the programming assignments (for which is not required any programming ability) show how to use in practice what you learned.

I think the enthusiasm of the instructor is the cherry on top since it makes a huge difference when it comes to delivering the content precisely and effectively.

By Magesh J

•May 23, 2021

The course gives an in-depth knowledge of vector calculus and how it used for fitting data by software programs like MATLAB and PYTHON. The course videos themselves may not suffice to complete the course and the tasks. I had to refer to KHAN ACADEMY and other internet resources to understand better the concepts being taught in the course. The assignment questions range from medium to hard type and require additional time and resources to complete them. The Python codes included in the assignments may look strange if you haven't done any courses on Python. Overall, the course meets my expectations, and I strongly recommend it to anyone looking to move to data science careers.

By Kaustubh L

•Jul 14, 2020

It's great, however if you are hoping that they would teach you to differentiate like teachers in high school then you are in the wrong place. But, if you want to build an intuition about calculus, optimization techniques, neural networks then you are in the right place. Personally, I was good at calculus in school so it was relatively easy for me, but if that's not the case for you I would recommend that you brush up your basic differentiation. Also basic knowledge of python numpy library would be super useful. Also this course will introduce some really scary looking formulas, so don't be intimidated they just look scary. Best of Luck !

By David S

•Feb 21, 2021

A solid course, recommended for those who want a deeper understanding of the math behind machine learning. It is well taught and organized, with many quizzes so students work through problems themselves,

However,

a) don't think for a moment that a six minute video can be absorbed in six minutes, or a quiz can be completed in the suggested time. From my experience, count on taking twice as long

b) there are so many concepts introduced that I needed to refer a number of times to outside resources like Khan Academy or 3 Blue 1 Brown

Overall, a worthwhile course.

D

By Khubaib A

•Jul 29, 2020

You will need the basics of Calculus in place. You can't just wake up and start Calculus with this course. With that said, the basics covered serve to be a good revision of the calculus. Certain applications such as the Neural Networks have been done hastily as others say on the forums (and I wholeheartedly agree) but then again this is not a course on Machine Learning. still some more examples from the instructors wouldn't hurt :) The exercises are great. Neither too hard nor too tough.

By Jaiber J

•Apr 17, 2020

Simply excellent course. The breadth of topics one needs to cover is astounding. I liked the way the topics and ordered, and following a common structure. The best part is the assignments - one really needs to understand every word of what the instructor says to solve it. They are tough in general to anyone who's done their bachelors/masters long time ago. For those who are not used to programming, the assignments can be difficult.

By Alina I H

•Dec 9, 2020

Amazing instructors and well designed course. Definitely a recommendable course to get intuitive knowledge on mathematical concepts that are relevant for machine learning. What I especially loved about it: it neither went too much into annoying and exhausting detail, nor was it simple. If you take this course, take some time to concentrate and get the brain cells running - will be a satisfying and rewarding experience! 11/10!

By Thuy T N

•Aug 7, 2020

This is my first encounter with Multivariate Calculus and surely the course has been extremely helpful beginner-friendly. I recommend investing in practical mathematics courses as this specialization if you are new to machine learning field. You will be equipped with enough math background and should feel confident to enter more technical machine learning/deep learning courses.

A truly fundamental stepping stone!

By Kerem E Y

•Dec 31, 2020

I learned limit, derivatives and integrals in high school. Afterwards, I took a few calculus lessons at university. However; I have never got a chance to see this theoretical background to put into practice. For this reason, I have never learned the essence of which means is calculus. I wouldn't have gotten a detailed education on this topic anywhere in Turkey. It was crucial for me, thank you for all !

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