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Рецензии: 291
Специализация
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Часов на завершение

Прибл. 22 часа на выполнение

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

Английский

Субтитры: Английский...

Приобретаемые навыки

Eigenvalues And EigenvectorsBasis (Linear Algebra)Transformation MatrixLinear Algebra
Специализация
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Прибл. 22 часа на выполнение

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

Английский

Субтитры: Английский...

Программа курса: что вы изучите

Неделя
1
Часов на завершение
2 ч. на завершение

Introduction to Linear Algebra and to Mathematics for Machine Learning

In this first module we look at how linear algebra is relevant to machine learning and data science. Then we'll wind up the module with an initial introduction to vectors. Throughout, we're focussing on developing your mathematical intuition, not of crunching through algebra or doing long pen-and-paper examples. For many of these operations, there are callable functions in Python that can do the adding up - the point is to appreciate what they do and how they work so that, when things go wrong or there are special cases, you can understand why and what to do....
Reading
5 видео (всего 31 мин.), 4 материалов для самостоятельного изучения, 3 тестов
Video5 видео
Motivations for linear algebra3мин
Getting a handle on vectors9мин
Operations with vectors11мин
Summary1мин
Reading4 материала для самостоятельного изучения
About Imperial College & the team5мин
How to be successful in this course5мин
Grading policy5мин
Additional readings & helpful references10мин
Quiz3 практического упражнения
Solving some simultaneous equations15мин
Exploring parameter space20мин
Doing some vector operations12мин
Неделя
2
Часов на завершение
2 ч. на завершение

Vectors are objects that move around space

In this module, we look at operations we can do with vectors - finding the modulus (size), angle between vectors (dot or inner product) and projections of one vector onto another. We can then examine how the entries describing a vector will depend on what vectors we use to define the axes - the basis. That will then let us determine whether a proposed set of basis vectors are what's called 'linearly independent.' This will complete our examination of vectors, allowing us to move on to matrices in module 3 and then start to solve linear algebra problems....
Reading
8 видео (всего 44 мин.), 4 тестов
Video8 видео
Modulus & inner product9мин
Cosine & dot product5мин
Projection6мин
Changing basis11мин
Basis, vector space, and linear independence4мин
Applications of changing basis3мин
Summary1мин
Quiz4 практического упражнения
Dot product of vectors15мин
Changing basis15мин
Linear dependency of a set of vectors15мин
Vector operations assessment15мин
Неделя
3
Часов на завершение
3 ч. на завершение

Matrices in Linear Algebra: Objects that operate on Vectors

Now that we've looked at vectors, we can turn to matrices. First we look at how to use matrices as tools to solve linear algebra problems, and as objects that transform vectors. Then we look at how to solve systems of linear equations using matrices, which will then take us on to look at inverse matrices and determinants, and to think about what the determinant really is, intuitively speaking. Finally, we'll look at cases of special matrices that mean that the determinant is zero or where the matrix isn't invertible - cases where algorithms that need to invert a matrix will fail....
Reading
8 видео (всего 58 мин.), 3 тестов
Video8 видео
How matrices transform space5мин
Types of matrix transformation8мин
Composition or combination of matrix transformations7мин
Solving the apples and bananas problem: Gaussian elimination8мин
Going from Gaussian elimination to finding the inverse matrix8мин
Determinants and inverses12мин
Summaryмин
Quiz2 практического упражнения
Using matrices to make transformations12мин
Solving linear equations using the inverse matrix16мин
Неделя
4
Часов на завершение
6 ч. на завершение

Matrices make linear mappings

In Module 4, we continue our discussion of matrices; first we think about how to code up matrix multiplication and matrix operations using the Einstein Summation Convention, which is a widely used notation in more advanced linear algebra courses. Then, we look at how matrices can transform a description of a vector from one basis (set of axes) to another. This will allow us to, for example, figure out how to apply a reflection to an image and manipulate images. We'll also look at how to construct a convenient basis vector set in order to do such transformations. Then, we'll write some code to do these transformations and apply this work computationally....
Reading
6 видео (всего 56 мин.), 4 тестов
Video6 видео
Matrices changing basis11мин
Doing a transformation in a changed basis6мин
Orthogonal matrices8мин
The Gram–Schmidt process6мин
Example: Reflecting in a plane14мин
Quiz2 практического упражнения
Non-square matrix multiplication10мин
Mappings to spaces with different numbers of dimensions12мин
4.6
Формирование карьерного пути

20%

начал новую карьеру, пройдя эти курсы
Карьерные преимущества

83%

получил значимые преимущества в карьере благодаря этому курсу

Лучшие рецензии

автор: PLAug 26th 2018

Great way to learn about applied Linear Algebra. Should be fairly easy if you have any background with linear algebra, but looks at concepts through the scope of geometric application, which is fresh.

автор: CSApr 1st 2018

Amazing course, great instructors. The amount of working linear algebra knowledge you get from this single course is substantial. It has already helped solidify my learning in other ML and AI courses.

Преподавателя

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David Dye

Professor of Metallurgy
Department of Materials
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Samuel J. Cooper

Lecturer
Dyson School of Design Engineering
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A. Freddie Page

Strategic Teaching Fellow
Dyson School of Design Engineering

О 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....

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

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