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Back to Mathematics for Machine Learning: Multivariate Calculus

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5,349 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 Nushaine F

•Jul 18, 2019

This is my first time learning calculus (I'm a 16 y/o high-school sophomore), and I'm satisfied with this course. The instructors were great, and the assignments are awesome.

If I would suggest one improvement, it would be to give more examples in the lectures. Some lectures were packed with examples, and some had none at all. I had to often refer to Khan Academy and YouTube to learn the concepts which the instructors did not provide an example for. (Especially in Week 4). Sometimes this would frustrate me because it would take me hours to grasp a concept.

Having said this, this course is for you if: (1) - you want a refresher on fundamental calculus concepts that relate to machine learning, or (2) - if you want to learn calculus for the first time, and you have a strong desire to learn these concepts. But no matter what, DON'T GIVE UP and don't stop until you've completed the course.

I hoped this has helped and good luck on your ML journey!

By Jonathan C

•Oct 24, 2019

I don't want to be too hard on this course since I really liked some parts of it. Especially, the instructor in Week 1 - 4 did a good job explaining the concepts and overall one can clearly see that a lot of effort was put into the creation of this course. However, I found that a lot of topics could be handled a lot more in-depth.

The assessment at the end of a week was not really challenging and does not require a deep understanding of the concepts. Some of the quizzes were more challenging but in the assessments it was often only required to answer questions based on graphs or other images of functions. Most of the programming assignments only required the student to fill in some easier blanks.

I still do not know what the Taylor Series Chapter was about. I guess this is an important concept but I was not sure how this relates to machine learning. If you call a course Math for Machine Learning, I would expect that you relate the concepts to Machine Learning.

Maybe, it is just me but I would have been glad if this course had offered more depth and took at least double the amount of time to complete. This would have been more rewarding, as I do not feel that I learned as much as I hoped for when I started this course.

By Tanuj J

•Jan 18, 2019

Topics need to be covered more in depth. Too much information packed into this course. Instructor's explanations are also not clear most of the time. It will be hard to follow this course if you don't have some background with calculus.

By Marc P

•Apr 28, 2019

The course is led by two instructor and my ratings is an average of the two performances. The videos in week 1 to 4 are absolutely outstanding and a pleasure to follow. The ones in week 5 and 6 are ok but not great. The use of quizzes and coding assignments throughout the course is very engaging and of great use for retention and application of the learned subjects.

By James T

•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.

By Valeria B

•Jun 17, 2019

The first part of the course is fine. Towards the end, lots of interesting concepts explained too quickly. I'd rather have more detailed explanations, especially about linear and non-linear regression.

The examples are quite good.

By Samresh

•Aug 4, 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.

By Yan

•Mar 30, 2019

Some errors confused many students. And they are remained unfixed.

By Daniel P

•Nov 26, 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.

By Oleg B

•Dec 11, 2018

Excellent summaries of important points.

By Derek T

•Apr 4, 2022

-> Consider this course only when you want to have a brief introduction into intermediate calculus

The course is poorly explained and many details are skipped. The lecturer taught as if students've known everything and just needed a brief remind.

I've already had knowledge in calculus and deep learning, but I still get confused by the way the lecturer taught. Jacobian was taught without mentioning directional derivative, Hessian matrix without any idea what it really is, neural network in 5 minutes,... beginners would struggle to understand if they have no prior knowledge.

This course is not for beginners because it skips details and no deep explains, but it's also not for intermediate level since there's not much to notice if you've known calculus.

By Seongwoo K

•Sep 24, 2019

This specialization consists of the courses which deliver essential mathematical background to ML learners. I think learners would feel confident and solid when diving into ML after taking this course.

Video lectures are great with clear graphics and lecturers are passionate with energy. The most outstanding part is the programming assignments: They are designed so elegantly that you can get intuition right away once you go through them. They are simply amazing.

Meanwhile, be aware that learning curves are often steep at some points. Without some basic python skill and ML knowledge, I guess quite many people would feel frustrated. But please don't give up and push it through to completion. You will be absolutely rewarded at the end.

Thank you for great contents, David and Sam.

By Eric P

•Apr 9, 2019

Challenging in places but another great speedy introduction to the relevant maths and how they are applied to ML. The best thing about this course is that you learn the general mathematical concepts and then see them in action in ML through examples and exercises. It's great. I used this course to refresh my maths skills learned long ago. I also found the pace good: neither too slow or too fast. The course would probably be quite challenging for someone who never had exposure to the concept of matrix algebra or derivatives.

By Artem D

•Aug 10, 2018

I really liked the teachers and everything they prepared for the students.

Lectures are entertaining, not boring.

Assignments are interesting. Especially, i've found very useful the structure of learning: (1) you have a short lecture, (2) you have a small quiz which continue to intriduce you to the topic and in parallel let you to try it on practice - it was really great!

Thank you a lot! I loved this course (as a previous one) so much!

By Deleted A

•May 13, 2019

The first four weeks are excellently prepared and the programming assignments are almost too easy at some points. The last two weeks and a part on backpropagation in the first four weeks give a nice intro on how to apply the learned methods. In the last two weeks there were some minor flaws in some slides and it is less easy to follow but it is still very well presented.

By Ilja S S E C L

•Nov 20, 2019

Really like the approach that a learner should get the intuition and understand how things work graphically. Then a learner should understand how numerical methods work and how math concepts can be used in Python code to do some optimization. Also, the sandpit exercises are great to easily understand how gradient descent works, which is a very important concept in ML.

By Nelson S S

•Dec 22, 2019

Excelente.

Muchas gracias por compartir generosamente su conocimiento.

Ha sido muy grato para mí repasar temas de cálculo multivariado, álgebra lineal y optimización.

Gracias COURSERA, Gracias MINTIC y Gracias a The Imperial College of London. Un abrazo a cada profesor que ha dado lo mejor de su enseñanza en cada uno de los videos que he observado.

By laszlo

•Apr 30, 2018

Really helpful and informative course. Different from the traditional math course, this course focuses on the intuitive understanding of math rather than the calculation. The calculation part are done by python code, which lays a foundation for further machine learning course and shows how the mathematical concepts are used in practice.

By Yiran X

•Jan 6, 2019

This is a great course! I have learnt a lot in this course. I have leant single variable calculus and linear algebra (freshman year difficulty), and this course is challenging but doable for me! All the assignments are designed carefully and interesting to complete! I would like to say thank you to all the instructors of this course:D

By Lee F

•Sep 18, 2018

This course was perfect for me. I took calculus years ago in high school and college, but had forgotten most of it. This course got me back to Jacobians and Hessians quickly . These are essential tools for optimizing multivariate functions and fitting data sets with lots of features to models. Really enjoyed the course!

By Andrii S

•Jan 20, 2019

Excellent.

By Khai T

•Mar 5, 2022

I do not recommend this course for anyone who are true beginners in calculus. Although the course states that it is for beginners, it is not. You must have a strong background in calculus, numerical methods and mathematical optimization to understand what the instructors are saying. There are also a huge gap between theory and exercises (for example, none mentioned about the convergence condition for Newton - Raphson method, but in the exercises, you have to cope with this condition). The resource sheet is quite oversimplifed, beginners cannot get any useful information from the sheet (as you mentioned in the beginning of the course, you want the learners to capture the intuition of the problem, but there are no intuitions fact in the sheet). Overall, if you are a veteran of Calculus, Numerical methods and Mathematical optimization, this course will help you revise your understanding about the fields; otherwise, you should take "true beginner courses" by watching 3Blues1Brown on Youtube or take Khan Academy courses before enrolling for this one.

By Tyler W

•Jun 18, 2022

Some interactive components were interesting to work through and the videos themselves were well polished and fairly engaging. However, much of the in-depth working throughs (particularly in later weeks as things get more difficult) are omitted in favor of having nicely packaged 5-10 minute videos. As a result, assignments can have Qs that are exceedingly easy or impossibly difficult (without needing to consult external resources, which you will have to do to fully grasp these concepts).

Much of the "programming" is also just implementing the pure math in Python; the actual programming you'd need to implement these concepts is pre-written, so you don't get any experience with this. I realize this isn't a programming course, but I don't think it's unreasonable for a course specifically targetting people looking to do ML can write their own functions / practice implementation.

By Mahwish A

•Apr 26, 2020

Second professor David is waste of time while the first one is excellent.

By Carsten H

•Mar 31, 2018

Too many derivatives of pointless functions.

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