Mathematics for Machine Learning: Multivariate Calculus

Start Date: 07/05/2020

Course Type: Common Course

Course Link:

About Course

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.

Course Syllabus

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. Typically, 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 off 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.

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Course Introduction

Mathematics for Machine Learning: Multivariate Calculus Mathematics is for everyone who wants to understand the fundamentals of mathematics, including math majors and non-math majors alike. Designed to help non-mathematicians understand the concepts and notation of mathematics, this course includes a large number of lectures and hands-on exercises. The course is primarily targeted at the non-mathematician who wants to understand the fundamentals of mathematics, and is motivated by a desire to learn more. After completing this course, you will: * Understand the basics of matrix algebra and how to use trigonometric identities * Know the essentials of vector spaces and their applications * Know how to construct vectors and how to use linearization * Know how to construct vectors and how to use linearization * Know how to construct linearized control structures and their associated dependent variables * Know the essentials of linearized control structures and their associated dependent variables * Know the basics of matrix factorization and how to use trigonometric identities * Know how to construct vectors and how to use linearization * Know the essentials of vector spaces and their applications * Know how to construct vectors and how to use linearization * Know the basics of linearized control structures and their associated dependent variables * Know the basics of vector spaces and their applications * Know how to construct control structures and how to use trigonometric identities * Know the basics of linearized control structures and their associated dependent

Course Tag

Machine Learning Mathematics Mathematics for Machine Learning Multivariate Calculus Calculus Math Linear Regression Vector Calculus Multivariable Calculus Gradient Descent

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