Brett Hutley's Blog

I've had a lot of sequential maths assignments due lately, and I haven't been doing much other than to study maths! Most of my other work has fallen by the wayside, unfortunately. My exams are starting in a month, and then my study will be over for the year!

I've been loving devoting so much time to just doing maths, but I feel a bit guilty about letting all my other stuff go. Oh well. I'll get back to doing lots of coding soon!

It's been a few weeks since I last posted. I've been totally absorbed in doing assignments for my Masters. Much to the detriment of all the other stuff I need to do! I've been avoiding doing a lot of tasks on my todo list, so a lot of my day-to-day routine has been disrupted. I'm slowly getting back to normal now.

Recently I've started studying maths using a Jupyter notebook. What I do is to review my coursework, and while I go through each theorem/proof, I code it up in the IPython notebook and experiment with the maths. I've found it a good way to come to grips with complex ideas. I'm currently studying Dirichlet Characters, and am finding the technique invaluable.

I've started studying daily using Anki Flash Cards to revise. Every day I add at least one card to my study deck. Every day the study deck gets more valuable to me.

Today I discovered the sheer awesomeness that is Emacs with EIN. This lets my Emacs environment to to Jupyter Notebooks. Through it, I have the power of Emacs Python completion and editing while writing iPython functions. It works really well! I can display matplotlib graphs inline in my Emacs buffer. There is even symbolic computation via the sympy package! Bliss!

Today I was thinking about creating a mathematical model to represent my own personal "Klout" score. Instead of providing a measure of social influence, it would actually be a day-to-day score of how social I had been. Lately I have been quite reclusive. Other than Helen, I haven't had much contact with people. I have also been a lurker on social media, such as Twitter and Facebook. In order to encourage more social interaction, my score would keep track of how many interactions I have. Whether the people I interact with are new people to me, or whether they are friends. If I construct the model properly and use it on a daily basis with an aim to improving my score, it should get me out of this reclusive rut I am currently in.

I have been studying continuously for many years now. I am still refining my studying technique though. One of the things that I am being forced to do with the maths I am doing at the moment, is to read and re-read the course materials over and over again. My workflow at the moment is:

1. Skim the chapter. Scan the headings and sub-headings and try to build up the outline in my head.
2. Skim through the problems within the chapter.
3. Speed read the chapter. Get more of an idea of what is going on.
4. Read through the problems and the answers.
5. Read the chapter more thoroughly. Try and get a good understanding.
6. Work through the problems.
7. Repeat 5 and 6 until either clarity or the exam arrives!

I just found Ram Murty's short course on YouTube - Introduction to Analytic Number Theory. So good! I am studying Apostol's book "Introduction to Number Theory" at the moment, and it is fantastic to get an insight into the subject from someone so brilliant! I ordered Murty's book "Problems in Analytic Number Theory" after watching the first lecture.

Today has been a day of Analytic Number Theory study. I have a couple of assignments due next week on the Calculus of Variation and Analytic Number Theory. I'm a bit behind in my study plan, but that is nothing new. I found some excellent YouTube videos on various topics that I am working on - it really is an amazing resource!

Continue reading “Analytic Number Theory”

I read a really interesting post on Reddit explaining Markov Chain Monte Carlo, which drew the analogy between MCMC and a long game of Frogger.

Continue reading “Markov Chain Monte Carlo as Frogger”