Yes, I know it’s nearly February, I just write slowly (or more to the point, disjointedly)

In my earlier post I discussed my ambitions for learning some computer science, in order to be a more effective data scientist and statistician. In particular, my aim is to follow Cosma Shalizi’s advice that statisticians should at least be aware of how to program like a computer programmer.

To become a better data scientist/ statistician maths is also an important element. The maths that I think that I am most lacking is probably algebra, in terms of linear algebra and abstract algebra. From what I can see, most algorithms for data start in this area, also making use of probability theory. Whilst my knowledge of probability is also in need of renovation, my knowledge of algebra is much more dilipidated. Professor Shalizi has an area of his personal site devoted to maths he ought to learn – assuredly, if I had such a website, the corresponding area would be much larger.

Fortunately the internet is here to help.

With respect to linear algebra, we can start at saylor.org’s open university:

http://www.saylor.org/courses/ma211/.

Note that this features the winner of Saylor’s open textbook competition,

Click to access Elementary-Linear-Algebra-1-30-11-Kuttler-OTC.pdf

so it seems safe to assume this is one of the best of Saylor’s offerings.

Saylor also have Abstract Algebra I and Algebra II courses in modern and abstract algebra. It is in the Abstract Algebra II course that found the following great video, which discusses the links between group theory and data mining, especially with respect to classification problems. From this video I discovered the existence of John Diaconnis and his area of research in probability on groups, which unfortunately I am nowhere near understanding due to deficiencies in almost all of the pre-requisites, from the group theory perspective and the probability perspective.

A final course I am trying to follow, although the timing is not quite right, is Coursera’s Functional Analysis course. I have enjoyed the videos so far, and seem to mostly understand it. This area is also important for understanding probability on groups, hopefully I will be able to find the time keep following along.

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Tags: Abstract Algebra, probability theory

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