Informações sobre o curso

100% online

Comece imediatamente e aprenda em seu próprio cronograma.

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.

Nível iniciante

Aprox. 21 horas para completar

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


Legendas: Inglês, Grego, Espanhol

Habilidades que você terá

Linear RegressionVector CalculusMultivariable CalculusGradient Descent

100% online

Comece imediatamente e aprenda em seu próprio cronograma.

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.

Nível iniciante

Aprox. 21 horas para completar

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


Legendas: Inglês, Grego, Espanhol

Programa - O que você aprenderá com este curso

4 horas para concluir

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 vídeos (total de (Total 46 mín.) min), 4 leituras, 6 testes
10 videos
Welcome to Module 1!1min
Rise Over Run4min
Definition of a derivative10min
Differentiation examples & special cases7min
Product rule4min
Chain rule5min
Taming a beast5min
See you next module!39s
4 leituras
About Imperial College & the team5min
How to be successful in this course5min
Grading Policy5min
Additional Readings & Helpful References5min
6 exercícios práticos
Matching functions visually20min
Matching the graph of a function to the graph of its derivative20min
Let's differentiate some functions20min
Practicing the product rule20min
Practicing the chain rule20min
Unleashing the toolbox20min
3 horas para concluir

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 vídeos (total de (Total 41 mín.) min), 5 testes
9 videos
Variables, constants & context7min
Differentiate with respect to anything4min
The Jacobian5min
Jacobian applied6min
The Sandpit4min
The Hessian5min
Reality is hard4min
See you next module!23s
5 exercícios práticos
Practicing partial differentiation20min
Calculating the Jacobian20min
Bigger Jacobians!20min
Calculating Hessians20min
Assessment: Jacobians and Hessians20min
3 horas para concluir

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 vídeos (total de (Total 19 mín.) min), 4 testes
6 videos
Multivariate chain rule2min
More multivariate chain rule5min
Simple neural networks5min
More simple neural networks4min
See you next module!34s
3 exercícios práticos
Multivariate chain rule exercise20min
Simple Artificial Neural Networks20min
Training Neural Networks25min
2 horas para concluir

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 vídeos (total de (Total 41 mín.) min), 5 testes
9 videos
Building approximate functions3min
Power series3min
Power series derivation9min
Power series details6min
Multivariate Taylor6min
See you next module!28s
5 exercícios práticos
Matching functions and approximations20min
Applying the Taylor series15min
Taylor series - Special cases10min
2D Taylor series15min
Taylor Series Assessment20min
2 horas para concluir

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 vídeos (total de (Total 28 mín.) min), 4 testes
4 videos
Gradient Descent9min
Constrained optimisation8min
See you next module!2min
4 exercícios práticos
Newton-Raphson in one dimension20min
Checking Newton-Raphson10min
Lagrange multipliers20min
Optimisation scenarios20min
2 horas para concluir


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 vídeos (total de (Total 25 mín.) min), 1 leitura, 3 testes
4 videos
General non linear least squares7min
Doing least squares regression analysis in practice6min
Wrap up of this course48s
1 leituras
Did you like the course? Let us know!10min
2 exercícios práticos
Linear regression25min
Fitting a non-linear function15min
212 avaliaçõesChevron Right


comecei uma nova carreira após concluir estes cursos


consegui um benefício significativo de carreira com este curso

Melhores avaliações

por 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.

por 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

Sobre Imperial College London

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....

Sobre o Programa de cursos integrados 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

Perguntas Frequentes – FAQ

  • Ao se inscrever para um Certificado, você terá acesso a todos os vídeos, testes e tarefas de programação (se aplicável). Tarefas avaliadas pelos colegas apenas podem ser enviadas e avaliadas após o início da sessão. Caso escolha explorar o curso sem adquiri-lo, talvez você não consiga acessar certas tarefas.

  • Quando você se inscreve no curso, tem acesso a todos os cursos na Especialização e pode obter um certificado quando concluir o trabalho. Seu Certificado eletrônico será adicionado à sua página de Participações e você poderá imprimi-lo ou adicioná-lo ao seu perfil no LinkedIn. Se quiser apenas ler e assistir o conteúdo do curso, você poderá frequentá-lo como ouvinte sem custo.

Mais dúvidas? Visite o Central de Ajuda ao Aprendiz.