Just to have this out for people to look at, here is my honors thesis from my degree. It is broadly about some of the mathematics behind a particular phenomenon in quantum mechanics.
Thesis
Thesis Formatted as a Book
Fun Coin Flips
I learned an interesting fact in my Stochastic Processes class the other day, and I managed to come up with an easier way to present it than using Markov chains (which are really cool, but not conducive to making a good blog post).
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Monty Hall and Gambler's Ruin: A Third Small Step into Mathematics
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”