Back to Mathematics for Machine Learning: Multivariate Calculus

4.7

stars

4,026 ratings

•

714 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 04, 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 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.

Filter by:

By Gyamfi A K

•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 03, 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 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 01, 2019

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

By Maprang

•Jul 01, 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 Sven A

•Oct 07, 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 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 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 Thuy T N

•Aug 07, 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 Juan P M C

•Sep 01, 2020

Wonderful course! The teachers explain everything in such a clear way that if you pay enough attention and take notes throughout the videos you won't have many problems understanding the subjects. Also the assignments and tests help a lot in reinforcing what you just learned with all the clear instructions that guide you step-by-step through the several methods and algorithms of 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 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 04, 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 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 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 Adithya P

•Sep 26, 2020

The instructors are amazing, they make things quite easy to understand and the assignments would give a proper measure of your understanding of the lectures. The content covered in the course gives you a perfect idea of visualizing 3d or multidimensional models(data). The forum has a healthy discussion on the subject.

By Idris R

•Oct 28, 2019

Fun and challenging course! It's priceless to learn all the math behind neural networks and other machine learning algorithms without having to learn all of calculus and all of linear algebra. Those are large fields and having the material presented in a way that focuses on the most relevant pieces is hugely valuable.

By Agamjyot S C

•Jun 16, 2020

This is a must take course, if you want an insight into how the world of machine learning really works. This MOOC focused more on the intuition rather than just deriving out expressions for the heck of it. Everything has been explained in a very nice and simple manner, I have learned a great deal from this course.

- Finding Purpose & Meaning in Life
- Understanding Medical Research
- Japanese for Beginners
- Introduction to Cloud Computing
- Foundations of Mindfulness
- Fundamentals of Finance
- Machine Learning
- Machine Learning Using Sas Viya
- The Science of Well Being
- Covid-19 Contact Tracing
- AI for Everyone
- Financial Markets
- Introduction to Psychology
- Getting Started with AWS
- International Marketing
- C++
- Predictive Analytics & Data Mining
- UCSD Learning How to Learn
- Michigan Programming for Everybody
- JHU R Programming
- Google CBRS CPI Training

- Natural Language Processing (NLP)
- AI for Medicine
- Good with Words: Writing & Editing
- Infections Disease Modeling
- The Pronounciation of American English
- Software Testing Automation
- Deep Learning
- Python for Everybody
- Data Science
- Business Foundations
- Excel Skills for Business
- Data Science with Python
- Finance for Everyone
- Communication Skills for Engineers
- Sales Training
- Career Brand Management
- Wharton Business Analytics
- Penn Positive Psychology
- Washington Machine Learning
- CalArts Graphic Design

- Professional Certificates
- MasterTrack Certificates
- Google IT Support
- IBM Data Science
- Google Cloud Data Engineering
- IBM Applied AI
- Google Cloud Architecture
- IBM Cybersecurity Analyst
- Google IT Automation with Python
- IBM z/OS Mainframe Practitioner
- UCI Applied Project Management
- Instructional Design Certificate
- Construction Engineering and Management Certificate
- Big Data Certificate
- Machine Learning for Analytics Certificate
- Innovation Management & Entrepreneurship Certificate
- Sustainabaility and Development Certificate
- Social Work Certificate
- AI and Machine Learning Certificate
- Spatial Data Analysis and Visualization Certificate

- Computer Science Degrees
- Business Degrees
- Public Health Degrees
- Data Science Degrees
- Bachelor's Degrees
- Bachelor of Computer Science
- MS Electrical Engineering
- Bachelor Completion Degree
- MS Management
- MS Computer Science
- MPH
- Accounting Master's Degree
- MCIT
- MBA Online
- Master of Applied Data Science
- Global MBA
- Master's of Innovation & Entrepreneurship
- MCS Data Science
- Master's in Computer Science
- Master's in Public Health