Back to Mathematics for Machine Learning: Multivariate Calculus

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5,564 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....

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.

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 Suman G

•Dec 26, 2020

pathetic course

By Piotr C

•Jul 21, 2023

A truly amazing course!

The Calculus course from the Mathematics for ML specialisation is a really fun and effective way of learning. I think that it takes lots of skills and hard work to prepare course like that. It starts very gentle so that it's easy for those who haven't done calculus for a long time, but after refresing on the basics, it jumps to more interesting topics to end up in Taylor series for approximations, Lagrange multipliers, the chain rule application for deriving backpropagation algorithm and some basic optimisation algorithms.

All along they way they're showing everything visually, so that we can build intuitions to have confidence in using the math later on, when there are too many dimensions to visualise the function. The exercises are enough to start feeling comfortable with doing calculations by hand, while the programming assignments shows how to do that in code. Really nice bonus are interactive materials where we can really feel what the math and the algorightms are about (it's great for building intuitions).

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 Nabil C

•Jun 25, 2022

David and Sam are amazing: The found the right balance between bulding up intuition and mathematical rigor. Also their use of coding labs is spot on: Not too much coding language related complexity that would distract from the real objectives of the course, while not making out of the labs a trivial exercise of code copy/paste.

While I did Multivariate Calculus in depth back in University, that was 30 years ago, and I needed a good refresher before taking on some advanced ML/AI courses. This Maths for ML specialization did hit the spot.

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 채영

•Jun 23, 2022

It took me at least 3 hours every day to understand and absorb the contents. It's that I'm not a native English speaker and I'm almost in the dark about mathmetics which is covered at university. Nevertheless, every step in the course was worth investing. I could know why I, as a would-be developer, should understand and keep mathmetics in my head. I downloaded all videos of this course and I'm gonna repeat them.

By Chloe 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 !

By Reeshad M

•Jul 6, 2021

The videos are well designed and are direct in teaching the course material. For those with Calculus experience, it acts as a nice refresher and further expands it through higher dimensions. For those planning to learn more about Machine Learning and data science, the course also bridges mathematical gaps. Overall, I learned a lot and had fun while taking the course.

By Onkar A

•May 20, 2020

Awesome course, so much to learn, and all concepts built up from basic, had fun with all assignments and stand-pit like interactive things, really boosted the understanding, i felt that prof. copper's speed of teaching was fast for me persoanlly , i had to pause many times and think what he said, but prof. david's pace was perfect for me, both instructors are great!

By Dennis M

•Sep 12, 2022

Great course to refresh multivariate calculus skills. I remember going through the traditional method of teaching this subject in college. And while taking the college courses many years ago I ways pondered how I would use the theorectical derivations. The methods used by David and Sam really opened my eyes and now I understand how to apply multivavriate calculus.

By David A E G

•Aug 21, 2020

A beautifully designed course, in which I could strongly settle the principles behind Linear Regression and Neural Networks. It did a wonderful job, filling the gaps I had from some other material I had checked on the web, but that was too technical, from a beginner's point of view. I feel so motivated by this course, that I will finish the specialization!

By Douglas W

•May 4, 2020

Such an impressive set of instructors! I loved the enthusiasm at which the material was taught and injections of British humor. Now, this is not an easy course, but one that requires work. Plan on reacquainting yourselves with pencil, paper and practice. So, do the work, repeat videos when required, rely on classmates in the forums and you'll do fine.

By Ludovic G

•Dec 7, 2020

Simply brilliant ! Although the exercises might tend to be fairly simplistic, the quality if this course is top-notch. I truly believe it is one of the best material out there to get a grasp on fundamental concepts underpinning machine learning and data science.

I would definitely recommend the entire specialisation to anyone interest in this field.

By Manas G

•Jul 15, 2020

This is legitimate the best course on coursera. The video production and animations are beyond words. Also the amount of efforts put into quizzes and assignments is clearly visible. They are soo much helpful in understanding and practicing of the concepts taught. I loved doing this course. I wish there were more courses like in this specialization.

By Carlo G

•Apr 12, 2022

Great course about multivariate calculus and its application in machine learning. This completes very well the math side of things with other courses about machine learning, like from Andrew Ng. The instructors are great, the explanations clear and I like very much the code exercises! Can't wait to start the 3rd course of this specialisation.

By Aileen F

•Nov 27, 2020

Highly recommend it for engineering students or even graduates, since some schools in my country do not teach some of these topics and programming in their engineering programs. The discussion accompanied by graphical and interactive tools really helped me understand some of concepts. The quizzes and assessment focus on the important points.

By Camilo M

•Jul 29, 2020

The explanations are very clear and intuitive, the teachers explain very well and give guidelines so that you can do your own analysis and experimentation. The programming exercises are not complex but you must pay attention and take notes. So far both courses (linear algebra and multivariate calculation) are very, very good.

By Natasha M

•Apr 10, 2021

Probably my favorite course series on Coursera! Even though I already took calculus and algebra years ago, I feel like I have gained a greater intuition through this and the previous algebra course. These are probably not introductory courses, but more to gain a deeper intuition of using calculus for machine learning.