Today we will be looking at two problems in probability: the Monty Hall problem and Gambler’s Ruin. These are two common probability “brain teasers”. For the Monty Hall problem, it feels paradoxical when you first learn about it, while the Gambler’s Ruin is instructive and important as you go forward in life. With that brief introduction, let us begin!
There was a game show (so I have been told, though I am too young to have watched it) hosted by Monty Hall. One of the main elements of the show was a classic three-door setup, where behind two doors there were goats, and behind the third door there was a brand new car waiting to be won. The way this would go is that Monty Hall would ask you, the contestant, what door you wished to select. You picked door one, two or three. Then Monty Hall, bold and clever, would open up one of the two doors that you did not pick, only to reveal one of the goats! At this point in the game he would come back to you with a smirk, asking if you wished to stay with the door you picked at first, or if you wanted to switch to the other closed door. The problem is: in order to maximize the probability that you win the car, do you switch or stay (or does it even matter)?
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Mathmagic Land: A Second Small Step into Mathematics
Mathematics is the alphabet with which God has written the universe.
-Galileo
In our second small step into mathematics, I wish to explore that wonderful world that many generations of students will hopefully be familiar with: Mathmagic Land. This was an Academy Award nominated short film featuring Donald Duck, adventuring through a place entirely unfamiliar to him. After first asserting that math is for “eggheads”, a friendly narrator guides him through the math involved in music, architecture, art and games. In my first post I said I wished to go beyond the utility of math, and I believe this movie transcends utility to explore the natural wonder of math and where it appears in the wild.
This video is just under half an hour and is freely available on YouTube (linked above) so I recommend that you watch it as a prerequisite to this post. I hope to extend some of the concepts that are so nicely presented in the video, while also adding some of the places where I love seeing math show up in organic ways. So without further delay, let us begin!
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"Oh, You're Studying Math?" A First Small Step into Mathematics
“That sounds hard. I used to like math, but then I had a bad teacher and realized I just wasn’t any good at it anymore. I think it’s really cool that you like it though, and that you can teach other people about it. That’s what you want to do, right? Become a math teacher? That sounds really great. I couldn’t be a teacher, especially for math, that sounds way too difficult. Continue reading “"Oh, You're Studying Math?" A First Small Step into Mathematics”
The Election and Change (Election Processing Part 3)
One of the main themes that has come up in the two days after the election is change.
Many people believe that much of what occurred is a result of people wanting change after having eight (or more) years of the government not listening to them. The Democratic party did not listen to this, putting up a candidate that was perceived as having no potential for anything different from what President Obama has done, while the Republicans were taken by someone who spoke of nothing but radical change, all the change against the current system that anyone could possibly want. Protecting the borders, opening up trade, reducing government expenditure and regulations, as well as social issues. As a result there was a significant part of the populace who gravitated towards Trump, wanting change and believing he was the only candidate who could make it happen.
As I thought about this, I did not want to focus too much on particular policies so I apologize if I become too critical of certain proposals. There is no proof that any policy, conservative or liberal, actually works as well as anyone wants. There are so many factors and much coincidence involved in when a certain policy is enacted during a period of time that, to me, much of what has gone on (in particular, economically) in our nation has become a wash. In my math jargon, it is an undecidable problem. Due to this, I want to focus on the dynamics of change in general and how reasonable it is to expect change, as well as how the change being called for by Trump supporters compares to the change that was hoped for by many Americans who opposed him.
The Election and Education (Election Processing Part 2)
Read part 1 here.
In light of the election, I have been on a bit of a thought and writing spree. While I recently processed through a fair bit of the election as a whole, there is so much that will be affected that I need to take it bit by bit. Right now I am thinking about education, particularly mathematics education, as this is something very near to me and something I have a strong passion for.
Regarding the Election (Election Processing Part 1)
While I have no doubt that these words will likely fade into the backdrop of the political discourse that is occurring as a result of the recent election, I need to write this for my own sake, to make sense of what America will become over the next four years and beyond.
Continue reading “Regarding the Election (Election Processing Part 1)”