These notes were developed as I was learning how to program in Fortran 90. Matlab is a great scripting language; however, when you need to do a lot of numerical computations, nothing beats Fortran (or C).

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This is a great introduction in understanding Markov chains with the running example of calculating how many hops a knight can make around a chess before it returns to its starting position. Check it out.

I was reading Prediction, Learning, and Games by Cesa-Bianchi and Lugosi (2006), when I came across the following quote in their preface:

. . beware of mathematicians, and all those who make empty prophecies.
St. Augustine, De Genesi ad Litteram libri duodecim.

This was a bit bizarre, because I had read St. Augustine’s De doctrina christiana where he uses logic. Now, logic didn’t become part of mathematics (mathematical logic) until around the 19th century when De Morgan and Boole started to publish their work. (Leibniz had been working on logic in the 17th century, but it was not widely circulated.)  But still, St. Augustine had been using mathematical ideas, and then yet warned Christians against the evils of mathematics?

It appears that Morris Kline (a wonderful mathematics teacher by the way) might have started the myth with a bad translation from Latin into English.

From wikiquote

De Genesi ad Litteram

  • Quapropter bono christiano, sive mathematici, sive quilibet impie divinantium, maxime dicentes vera, cavendi sunt, ne consortio daemoniorum animam deceptam, pacto quodam societatis irretiant.
    • II, xvii, 37
    • Translation published in Mathematics in Western Culture (1953): The good Christian should beware the mathematician and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of hell.
    • Modern translation by J.H. Taylor in Ancient Christian Writers (1982): Hence, a devout Christian must avoid astrologers and all impious soothsayers, especially when they tell the truth, for fear of leading his soul into error by consorting with demons and entangling himself with the bonds of such association.
    • Note: The well known, but incorrect English translation was published on page 3 of Morris Kline’s Mathematics in Western Culture (1953). This book is a favorite with math students and is still in print. The Latin word mathematici derives from the Greek meaning of “something learned” and refers mainly to astrologers. This was the chief branch of mathematics at the time but has been replaced in modern times by a plethora of other branches. According to the Shorter Oxford English Dictionary, 3rd edition, the word “mathematician” still meant astrologer as late as 1710.

These are my notes from the YouTube video below about using Org-mode in Emacs.

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Beamer

I have been writing a couple of presentations in Beamer. Because I am so used to working in LaTeX now, it’s very frustrating to have to switch back to a Microsoft product such as Microsoft Powerpoint.

Slowly, I’m learning tricks to make my Beamer presentations more dynamic by revealing or hiding bullets or parts of a figure.

I wish I had found this post, How To Make a Presentation with Beamer, sooner. It would have saved me a lot of time!

The most useful tip for me was the \onslide command.

\onslide<4->{ content }  This will reveal the content from slide 4 onwards.

\onslide<2-4>{ content }  This will reveal the content only on slides 2 to 4.

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So begins another school year, and the Basic Discrete Mathematics course is in full swing. This Monty Python clip is almost mandatory viewing for a logic course. It’s a twist on the classic comedic sketch: a man walks into a shop and wants something strange—this time it’s an argument.

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This is a beautiful video from 3blue1brown. He shows a connection between measure theory (a topic studied in mathematical analysis), and music. Have a look.

I even got a chance to email him to ask about how he does his animations. It was clear that he used LaTeX to typeset his equations, but he told me that the animations are done using a Python script he developed. He has posted his code on his gitHub account. The animation results are so impressive, it’s tempting me to pick up and learn Python just so that I can do this.

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I have a real interest in artificial intelligence and in particular, I like working on the ideas that govern self-learning or autonomous learning. [This can be a difficult idea to express to people as I have tried before, and I only see confused faces after I’m done talking.] It’s trying to come up with algorithms that would allow an agent to change internal parameters or settings so that, through experience, they can get better (or learn) at performing a task.

This is an interesting clip (from 4 years ago!) that shows autonomously learning robots.  They are learning to control their own bodies and developing their own language. Hopefully, this better explains this idea better than I could.

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Errata

This is where I collect all of my blunders, flaws, fallacies, miscalculations, inaccuracies, and other miscellaneous grammatical and mathematical howlers in Basic Discrete Mathematics. The name of the person who found the erratum is listed at the end. RK is me.

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