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  1. Exercises 3.1.1, 3.1.2, 3.1.3, 3.1.5, 3.1.6, 3.1.8
  2. Exercises 3.3.1, 3.3.3, 3.3.4, 3.3.5, 3.3.7, 3.3.8, 3.3.10, 3.3.11
  3. Exercises 3.7.4
  4. Create Venn diagrams for the following sets:
    • A \cap C
    • A \cup B \cup C
    • ((A \cap B) \cup C')
    • (A \cup B) \cap C
    • A' \cap B' \cap C'
    • B \cup C

Quiz: 19 September 2018 (at the beginning of class)

Do the following exercises from the textbook (Kohar).

  • 1.4.2
  • 1.6.2, 1.6.4
  • 1.7.1, 1.7.3, 1.7.4 (c), 1.7.5, 1.7.6, 1.7.7, 1.7.8, 1.7.9, 1.7.10, 1.7.12, 1.7.16
  • 1.8.6
  • 2.2.3 (a), (b), 2.2.4, 2.2.5, 2.2.6, 2.2.7, 2.2.8, 2.2.9, 2.2.14, 2.2.15, 2.2.17, 2.2.19

These are some highlights from a talk that E. O. Wilson gave at TED.

Keep your eyes lifted and your head turning. The search for knowledge is in our genes. It was put there by our distant ancestors who spread across the world, and it’s never going to be quenched. To understand and use it sanely, as a part of the civilization yet to evolve requires a vastly larger population of scientifically trained people like you. In education, medicine, law, diplomacy, government, business and the media that exist today.

Our political leaders need at least a modest degree of scientific literacy, which most badly lack today — no applause, please. It will be better for all if they prepare before entering office rather than learning on the job. Therefore you will do well to act on the side, no matter how far into the laboratory you may go, to serve as teachers during the span of your career.

I found out that in science and all its applications, what is crucial is not that technical ability, but it is imagination in all of its applications. The ability to form concepts with images of entities and processes pictured by intuition. I found out that advances in science rarely come upstream from an ability to stand at a blackboard and conjure images from unfolding mathematical propositions and equations. They are instead the products of downstream imagination leading to hard work, during which mathematical reasoning may or may not prove to be relevant. Ideas emerge when a part of the real or imagined world is studied for its own sake.

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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?

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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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