Mathematics

Github code and YouTube lecture series on mathematics

This is a lecture series on YouTube® about multivariable calculus.  I start off by looking at sequences and series.  The course picks up pace with discussions on vector calculus, directional derivatives, Taylor series, double and triple integrals and finally the theorems of Green, Stokes and Gauss.

Linear algebra lectures on YouTube

Linear algebra is an essential topic in statistics and data science.  In this lecture series I cover all of the introductory topics in linear algebra.

In this first course on differential equation I start of by explaining what a differential equations is.  In these 113 lectures I discuss separable variables, linear equations, homogeneity, linear models, order reduction, second order equations, superposition, the annihilator approach, variation of parameters, the Cauchy-Euler equation and systems of linear equations.

I end off by looking at a variety of real world examples and Laplace transforms..

In this first course on differential equation I start of by explaining what a differential equations is.  In these 113 lectures I discuss separable variables, linear equations, homogeneity, linear models, order reduction, second order equations, superposition, the annihilator approach, variation of parameters, the Cauchy-Euler equation and systems of linear equations.

I end off by looking at a variety of real world examples and Laplace transforms..

In this lecture series on more advanced topics in differential equations I take a look at linear systems, eigenvalues and eigenvectors and the method of variation of parameters.

In the second section I discuss a variety of numerical methods for solving systems of linear differential equations.

This is a new lecture series that is still under construction.  It is all about the exiting world of abstract algebra.  Take a look at the first few lectures.

In this YouTube lecture series I take a look at vector calculus.

This is my second course on the massive open online platform, Coursera.  Together with Dr Henri Laurie, we teach you how to code in this super-fast and exciting new language for scientific computing.

This four-module course introduces users to Julia as a first language. Julia is a high-level, high-performance dynamic programming language developed specifically for scientific computing. This language will be particularly useful for applications in physics, chemistry, astronomy, engineering, data science, bioinformatics and many more. As open source software, you will always have it available throughout your working life. It can also be used from the command line, program files or a new type of interface known as a Jupyter notebook (which is freely available as a service from JuliaBox.com). Julia is designed to address the requirements of high-performance numerical and scientific computing while also being effective for general-purpose programming. You will be able to access all the available processors and memory, scrape data from anywhere on the web, and have it always accessible through any device you care to use as long as it has a browser. Join us to discover new computing possibilities. Let’s get started on learning Julia. By the end of the course you will be able to: – Programme using the Julia language by practising through assignments – Write your own simple Julia programs from scratch – Understand the advantages and capacities of Julia as a computing language – Work in Jupyter notebooks using the Julia language – Use various Julia packages such as Plots, DataFrames and Stats The course is delivered through video lectures, on-screen demonstrations, quizzes and practical peer-reviewed projects designed to give you an opportunity to work with the packages.

You can also earn a certificate from the University of Cape Town.

This is a link to my popular Jupyter notebook lecture notes and code for the MIT 18.06 course on linear algebra.

This is a link to my Jupyter notebooks on discrete mathematics.

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