I'm still having problems programming, so the majority of the blog is going to be about differential geometry at ASU. We went over our midterm this week and continued with lectures. Though the classes have all been really interesting, the schedule of a college student seems pretty routine. Go to class, learn the material, reread the book to make sure you actually get the concepts from lecture, solve practice problems, and repeat.
This week was a lot harder for me than the previous weeks in terms of keeping up with the material. I've had multivariable calculus at school (yay BASIS/Ms. Bailey) and have learnt a bit more afterwards, but the class requires a fluency in it that I don't have. I have the same problem with linear algebra in the class. Luckily, after a good amount of reading and rereading, I've been able to get through the material.
We've been looking at diffeomorphisms this week and how to create maps between two surfaces. A big part of the course studies how surfaces can be smoothly transformed. This week, our lecturer, Dr. Kotschwar, was out of the state for a conference, so we had Dr. Julien Paupert fill us in. This week, we focused on orientation of surfaces.
Orientation looks at how many 'sides' a surface has. With something like a hollow sphere, we could distinguish the sphere's inside and outside. But with surfaces like mobius strips (https://en.wikipedia.org/wiki/M%C3%B6bius_strip), we cannot distinguish 'sides' in the same way.
Also wikipedia isn't as bad as people think it is, especially in math.
For the most part, a lot of the theorems that we have proved have been intuitively 'obvious', but rather difficult to prove. Soon, we're going to get to the really cool stuff.
You guys are probably also wondering whats going on with my game theory research. I've still been programming/spending most of my time studying differential geometry, so I'll have cool results hopefully by the next post. I don't have much else to say about my project. Next time, I might try to keep my post more organized. I might try to keep myself limited to three things I've learnt at differential geometry and focus on my game theory project. I'll also share some of my (very ugly) recursive formulas I have.
I'll also post pictures (for real this time) since everyone else seems to be doing that. OK, thats all I got. Thanks for reading again.
This week was a lot harder for me than the previous weeks in terms of keeping up with the material. I've had multivariable calculus at school (yay BASIS/Ms. Bailey) and have learnt a bit more afterwards, but the class requires a fluency in it that I don't have. I have the same problem with linear algebra in the class. Luckily, after a good amount of reading and rereading, I've been able to get through the material.
We've been looking at diffeomorphisms this week and how to create maps between two surfaces. A big part of the course studies how surfaces can be smoothly transformed. This week, our lecturer, Dr. Kotschwar, was out of the state for a conference, so we had Dr. Julien Paupert fill us in. This week, we focused on orientation of surfaces.
Orientation looks at how many 'sides' a surface has. With something like a hollow sphere, we could distinguish the sphere's inside and outside. But with surfaces like mobius strips (https://en.wikipedia.org/wiki/M%C3%B6bius_strip), we cannot distinguish 'sides' in the same way.
Also wikipedia isn't as bad as people think it is, especially in math.
For the most part, a lot of the theorems that we have proved have been intuitively 'obvious', but rather difficult to prove. Soon, we're going to get to the really cool stuff.
You guys are probably also wondering whats going on with my game theory research. I've still been programming/spending most of my time studying differential geometry, so I'll have cool results hopefully by the next post. I don't have much else to say about my project. Next time, I might try to keep my post more organized. I might try to keep myself limited to three things I've learnt at differential geometry and focus on my game theory project. I'll also share some of my (very ugly) recursive formulas I have.
I'll also post pictures (for real this time) since everyone else seems to be doing that. OK, thats all I got. Thanks for reading again.
Whoa, sounds like you're learning a ton of math and stuff. What does it mean for a surface to be smoothly transformed?
ReplyDeleteDoes your schedule at ASU differ that much from at BASIS? I don't know about you, but I've pretty much been doing exactly what you described throughout high school, maybe minus dedicated rereading. I'd also like to offer myself as test subject for your player handicap, seeing as I know nothing about nim but what you've told me. If you can somehow get me to win then you'll definitely have succeeded.
ReplyDeleteNithin if you post pictures i'm gonna feel obligated to follow suit and frankly i dont know what to take a picture of~~ anyways, seems like you got a lot of interesting math stuffs going on in that class, although it seems rather impossible for the average human being
ReplyDelete