Об этом курсе

100% онлайн

Начните сейчас и учитесь по собственному графику.

Гибкие сроки

Назначьте сроки сдачи в соответствии со своим графиком.

Начальный уровень

Прибл. 21 часа на выполнение

Предполагаемая нагрузка: 6 weeks of study, 2-5 hours/week...


Субтитры: Английский, Греческий, Испанский

Приобретаемые навыки

Linear RegressionVector CalculusMultivariable CalculusGradient Descent

100% онлайн

Начните сейчас и учитесь по собственному графику.

Гибкие сроки

Назначьте сроки сдачи в соответствии со своим графиком.

Начальный уровень

Прибл. 21 часа на выполнение

Предполагаемая нагрузка: 6 weeks of study, 2-5 hours/week...


Субтитры: Английский, Греческий, Испанский

Программа курса: что вы изучите

4 ч. на завершение

What is calculus?

Understanding calculus is central to understanding machine learning! You can think of calculus as simply a set of tools for analysing the relationship between functions and their inputs. Often, in machine learning, we are trying to find the inputs which enable a function to best match the data. We start this module from the basics, by recalling what a function is and where we might encounter one. Following this, we talk about the how, when sketching a function on a graph, the slope describes the rate of change of the output with respect to an input. Using this visual intuition we next derive a robust mathematical definition of a derivative, which we then use to differentiate some interesting functions. Finally, by studying a few examples, we develop four handy time saving rules that enable us to speed up differentiation for many common scenarios. ...
10 видео ((всего 46 мин.)), 4 материалов для самостоятельного изучения, 6 тестов
10 видео
Welcome to Module 1!1мин
Rise Over Run4мин
Definition of a derivative10мин
Differentiation examples & special cases7мин
Product rule4мин
Chain rule5мин
Taming a beast5мин
See you next module!39
4 материала для самостоятельного изучения
About Imperial College & the team5мин
How to be successful in this course5мин
Grading Policy5мин
Additional Readings & Helpful References5мин
6 практического упражнения
Matching functions visually20мин
Matching the graph of a function to the graph of its derivative20мин
Let's differentiate some functions20мин
Practicing the product rule20мин
Practicing the chain rule20мин
Unleashing the toolbox20мин
3 ч. на завершение

Multivariate calculus

Building on the foundations of the previous module, we now generalise our calculus tools to handle multivariable systems. This means we can take a function with multiple inputs and determine the influence of each of them separately. It would not be unusual for a machine learning method to require the analysis of a function with thousands of inputs, so we will also introduce the linear algebra structures necessary for storing the results of our multivariate calculus analysis in an orderly fashion. ...
9 видео ((всего 41 мин.)), 5 тестов
9 видео
Variables, constants & context7мин
Differentiate with respect to anything4мин
The Jacobian5мин
Jacobian applied6мин
The Sandpit4мин
The Hessian5мин
Reality is hard4мин
See you next module!23
5 практического упражнения
Practicing partial differentiation20мин
Calculating the Jacobian20мин
Bigger Jacobians!20мин
Calculating Hessians20мин
Assessment: Jacobians and Hessians20мин
3 ч. на завершение

Multivariate chain rule and its applications

Having seen that multivariate calculus is really no more complicated than the univariate case, we now focus on applications of the chain rule. Neural networks are one of the most popular and successful conceptual structures in machine learning. They are build up from a connected web of neurons and inspired by the structure of biological brains. The behaviour of each neuron is influenced by a set of control parameters, each of which needs to be optimised to best fit the data. The multivariate chain rule can be used to calculate the influence of each parameter of the networks, allow them to be updated during training. ...
6 видео ((всего 19 мин.)), 4 тестов
6 видео
Multivariate chain rule2мин
More multivariate chain rule5мин
Simple neural networks5мин
More simple neural networks4мин
See you next module!34
3 практического упражнения
Multivariate chain rule exercise20мин
Simple Artificial Neural Networks20мин
Training Neural Networks25мин
2 ч. на завершение

Taylor series and linearisation

The Taylor series is a method for re-expressing functions as polynomial series. This approach is the rational behind the use of simple linear approximations to complicated functions. In this module, we will derive the formal expression for the univariate Taylor series and discuss some important consequences of this result relevant to machine learning. Finally, we will discuss the multivariate case and see how the Jacobian and the Hessian come in to play. ...
9 видео ((всего 41 мин.)), 5 тестов
9 видео
Building approximate functions3мин
Power series3мин
Power series derivation9мин
Power series details6мин
Multivariate Taylor6мин
See you next module!28
5 практического упражнения
Matching functions and approximations20мин
Applying the Taylor series15мин
Taylor series - Special cases10мин
2D Taylor series15мин
Taylor Series Assessment20мин
2 ч. на завершение

Intro to optimisation

If we want to find the minimum and maximum points of a function then we can use multivariate calculus to do this, say to optimise the parameters (the space) of a function to fit some data. First we’ll do this in one dimension and use the gradient to give us estimates of where the zero points of that function are, and then iterate in the Newton-Raphson method. Then we’ll extend the idea to multiple dimensions by finding the gradient vector, Grad, which is the vector of the Jacobian. This will then let us find our way to the minima and maxima in what is called the gradient descent method. We’ll then take a moment to use Grad to find the minima and maxima along a constraint in the space, which is the Lagrange multipliers method....
4 видео ((всего 28 мин.)), 4 тестов
4 видео
Gradient Descent9мин
Constrained optimisation8мин
See you next module!2мин
4 практического упражнения
Newton-Raphson in one dimension20мин
Checking Newton-Raphson10мин
Lagrange multipliers20мин
Optimisation scenarios20мин
2 ч. на завершение


In order to optimise the fitting parameters of a fitting function to the best fit for some data, we need a way to define how good our fit is. This goodness of fit is called chi-squared, which we’ll first apply to fitting a straight line - linear regression. Then we’ll look at how to optimise our fitting function using chi-squared in the general case using the gradient descent method. Finally, we’ll look at how to do this easily in Python in just a few lines of code, which will wrap up the course....
4 видео ((всего 25 мин.)), 1 материал для самостоятельного изучения, 3 тестов
4 видео
General non linear least squares7мин
Doing least squares regression analysis in practice6мин
Wrap up of this course48
1 материал для самостоятельного изучения
Did you like the course? Let us know!10мин
2 практического упражнения
Linear regression25мин
Fitting a non-linear function15мин
Рецензии: 210Chevron Right


начал новую карьеру, пройдя эти курсы


получил значимые преимущества в карьере благодаря этому курсу

Лучшие рецензии

автор: DPNov 26th 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.

автор: JTNov 13th 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.



Samuel J. Cooper

Dyson School of Design Engineering

David Dye

Professor of Metallurgy
Department of Materials

A. Freddie Page

Strategic Teaching Fellow
Dyson School of Design Engineering

О Имперский колледж Лондона

Imperial College London is a world top ten university with an international reputation for excellence in science, engineering, medicine and business. located in the heart of London. Imperial is a multidisciplinary space for education, research, translation and commercialisation, harnessing science and innovation to tackle global challenges. Imperial students benefit from a world-leading, inclusive educational experience, rooted in the College’s world-leading research. Our online courses are designed to promote interactivity, learning and the development of core skills, through the use of cutting-edge digital technology....

О специализации ''Mathematics for Machine Learning'

For a lot of higher level courses in Machine Learning and Data Science, you find you need to freshen up on the basics in mathematics - stuff you may have studied before in school or university, but which was taught in another context, or not very intuitively, such that you struggle to relate it to how it’s used in Computer Science. This specialization aims to bridge that gap, getting you up to speed in the underlying mathematics, building an intuitive understanding, and relating it to Machine Learning and Data Science. In the first course on Linear Algebra we look at what linear algebra is and how it relates to data. Then we look through what vectors and matrices are and how to work with them. The second course, Multivariate Calculus, builds on this to look at how to optimize fitting functions to get good fits to data. It starts from introductory calculus and then uses the matrices and vectors from the first course to look at data fitting. The third course, Dimensionality Reduction with Principal Component Analysis, uses the mathematics from the first two courses to compress high-dimensional data. This course is of intermediate difficulty and will require basic Python and numpy knowledge. At the end of this specialization you will have gained the prerequisite mathematical knowledge to continue your journey and take more advanced courses in machine learning....
Mathematics for Machine Learning

Часто задаваемые вопросы

  • Зарегистрировавшись на сертификацию, вы получите доступ ко всем видео, тестам и заданиям по программированию (если они предусмотрены). Задания по взаимной оценке сокурсниками можно сдавать и проверять только после начала сессии. Если вы проходите курс без оплаты, некоторые задания могут быть недоступны.

  • Записавшись на курс, вы получите доступ ко всем курсам в специализации, а также возможность получить сертификат о его прохождении. После успешного прохождения курса на странице ваших достижений появится электронный сертификат. Оттуда его можно распечатать или прикрепить к профилю LinkedIn. Просто ознакомиться с содержанием курса можно бесплатно.

Остались вопросы? Посетите Центр поддержки учащихся.