Studying Math

Grad school has been very difficult. I'm constantly learning how to "be" a mathematician.

I'll be frank, undergraduate classes were simple. Most of the work required was just getting the hang of whatever you were doing. This worked fabulously back at the University of Minnesota, Duluth. Especially in the philosophy program. I'd skim/read the material, doing my best to get the general impression. Then, I'd attend class and the professor would cement the general ideas in my mind. The details mattered only every once in a while. In fact, this process even worked backwards: I could attend class, get the general idea from the professor, then read the book and I'd be ready for an exam.

It doesn't work that way now. No matter how many times I read through a chapter, even if I use different books to get many different angles on a subject, it isn't enough. It's still difficult to follow lectures. I still have trouble completing the homework.

Today, I finally had the courage to ask one of my professors for advice. He said you've got to read a sentence, set the book aside, then play with it.

For example, here's the first sentence from Set Theory (Jech 2002).

Intuitively, a set is a collection of all elements that satisfy a certain given property.

Like most definitions in mathematics, I'd basically try to memorize it, and that's not necessarily wrong. But according to my professor, you've got to start testing the definition out. "What kind of property would work?" you might ask. "What about the property 'numbers less than 5'?" So, that means a set would be the numbers 0, 1, 2, 3, and 4. "Is that okay? Are numbers 'elements'?" I'm supposed to ask. "What if the property was not being equal to itself?" No number (or anything in the universe, for that matter) isn't equal to itself, so that would be an empty collection.

Of course this is the obvious thing to do. But it's hard in practice to do it. It's painful to stop reading a book every sentence, put the book aside and actually think. It reminds me of the saying "You can send them to college, but you can't make them think."

I suppose studying math is like exercising. Watching, listening and reading other people do mathematics is like watching someone on a treadmill. You don't gain anything unless you're on the treadmill yourself.

I sure hope I get the hang of it. I'm very proud of where I am and I want follow the path in front of me. It's just strange having to admit that I still need to improve my studying habits.

Cool Ad

This is a bus stop vestibule filled with coffee cups. I think it's very clever, as posters normally don't capture my attention. Also, when the light shines through from the other side, it's really pretty.

Tylenol has some great ads. I like being told to "Feel better."

(If you're curious, this is on the north side of 34th street, near the corner of 5th avenue. The building along the right side is the Empire State Building.)

Update #6

Hello! Here's what's going on with me:

The Great News: I'm 24! As you may recall, my birthday was Sunday. I had a great Birthday. I woke up to breakfast in bed prepared by Alicia. She even made me a menu, which options. I had big eyes, bringing me to order french toast, scambled eggs, and potatoes. It was fabulous.

Alicia and I then walked around Manhattan, spending money where we normally wouldn't. For instance, I bought a Futurama comic at Barnes and Noble for 2.99. Normally, I'd say "blah, I don't need it." But on my birthday, dall garn it, I blew the money. We started in SoHo (SOuth of HOuston street), moving from the east side of Manhattan to the west, all the while walking up to about 23rd Street.

Some of my swag include new rubber coasters, some new jeans, a book about casinos, and a new Nintendo DS game. Hurray!

The Good News: The middle of the semester is here. Today is officially spring, and the semester is going fast. I'll be giving my students their midterm in just over a week, then I'll jet home to Minnesota to enjoy Spring Break and Easter weekend.

The Bad News: Every semester, a full professor attends one of the classes I teach to give feedback. Normally, I get great comments. This semester, I was evaluated the day after my birthday, which gave me less time to prepare. As a result, three of the four problems I put on the board at the beginning of the day had typos. (I always put a few math problems on the board for students to work through while I take attendence and answer questions). I think the rest of the class went just fine, but that first twenty minutes really shook me.

I haven't actually heard what my evaluater has to say yet. I'll meet with her Monday to discuss how it went and what suggestions she has for me. I'm preparing for the worst now, though.

What I'm Thinking About: I'm thinking a lot about Set Theory. We're working on Forcing Arguments. Now, forcing is a prerequisite for the class but I haven't ever studied it before. So I am at a disadvantage. But I'm extremely interested in the subject, so I've been sticking with it. But this class is why I've been so busy lately. I don't think I've ever felt so busy studying. Even taking over 20 credits at UMD was easier than this.

Here's my quicky explaination of forcing. Suppose we have a mathematics (we do!). It's a system where some sentences are certainly false (like 2 + 2 = 3) and other sentences are true. In the early 1900's, Godel proved that there are sentences that can't be proven true or false in a mathematical system. (Whether these sentences are true or not can't be determined within the system... but we're humans, so we can certainly have beliefs). Forcing allows us to make "Stronger" mathematics, that can show whether those sentences above are true or false.

How's that? Clear as mud? Prof. Hamkins, my set theory instructor, described forcing as "Profound, but extremely difficult." So far, my experience with forcing suggests he's right.

What I've Enjoyed: I've been playing my Nintendo DS a lot more lately. It's perfect for subway rides. I should be reading a book or studying my flash cards (you'd be surprised how much there is to memorize in higher level mathematics). But the subway rides go really, really fast with a video game. And it's about the only time I don't feel guilty about wasting.

Cabinet is finished!

As you can see, we received the front pieces of the drawers. Alicia did a fabulous job putting them on, didn't she? She even had to drill holes for the handles. Way to go, Alicia!

Ikea Stuff!

Alicia and I have a pretty recognizable pattern. Every time we have a craving to move to a new apartment, we decide we don't want to pay the rent increase, thus staying put where we are. We then turn our attention to our apartment and begin debating what we can improve. You may remember last summer when we purchased those two giant wardrobes for the bed room.

Two weeks ago, Alicia and I saw two different apartments. They were both a step up in price, but they had their advantages. All that kept going through my mind as I looked at the space was "Where would the couch and the lovesac go?" After we were home and decided to not move, I started thinking about how much space we could free up. Not only will it make the apartment feel bigger, but it will make a future move much easier. On the chopping block, the couch. Our lovesac had been hiding in the storage space for awhile.



We realized that if we got rid of the couch, the lovesac could return from exile and be the main focus of the living room. The problem with this solution is that it removes all other sitting in the living room.

With my birthday coming up, we decided it was time for another Ikea trip! We purchased a Poang chair to add extra seating to the living room:



And now the lovesac has a prominent place in our living room:



In the above photo, you can see the new Lack table (only 11.99!). "Where's the coffee table?" you might ask. Well, here it is!:



Yes, this means the entertainment center is no more. It was a black TV stand with great slots for my games and gaming systems. But, it isn't entirely gone!



I built this makeshift counter from the wood of the entertainment center (the black legs) and the wood from a small shelf Alicia was throwing out. I can't believe how perfect the size is. It isn't terribly pretty, but it gives the kitchen a ton more room. As does this:



This is our new kitchen cabinet from Ikea. The front of the drawers will be Black-brown, just like my desk and bookshelf. They said they were in stock, but weren't when we tried to pick them up. So they'll be arriving in a week. Oh well.

The drawers are great. They have the dampeners that prevent the cabinet from being slammed shut.

The top of the cabinet is custom made by me. They wanted approximately $90 for any kind of top. Alicia and I noticed that there were Ikea cutting boards for $10. Of course, the size didn't match. But for $10 dollars, we decided we'd try cutting it to fit. And it worked perfectly! You can see the back of the cutting board doesn't match the front. That piece is what I cut off the side and glued onto the back. All that's left to do now is oil the cutting board to make it perfect.



Prior to these two counters, our only kitchen space for working was that tiny drawer between the stove and the sink, as well as the stove and the sink. Now, we've moved the fridge over 15 inches, and added two counters. The kitchen feels a thousand times better.

Two last surprises from Ikea.



We found a tent for Livia! She goes crazy in there.



We found these two chairs. One of them was in the As-is section. It was $20 instead of $30, which is super cheap. The other one took some tracking down. But these are fabulous chairs. We bought them to go outside, but we keep using inside.

So that's where the apartment is. There were no changes in the bedroom. My desk moved in January, and I suppose I didn't blog about it. So here's a picture:



I've been a little lazy and a lot of busy, so it's kind of a mess. But you can see Alicia's Birthday decorations! She's so sweet to me.

I also put shelves up in the storage area:



You can barely see it at the top of the photo, but the shelves go up to the ceiling. The lack table in this picture was free, as someone in the building moved out and left it in the hallway. This is our little storage area, now.

Well, what do you think? I think the apartment breathes better. By that, I mean it feels more open! Yay!

It's my birthday...

...and I can cry if I want to. So I choose to exercise that right!



I woke up to breakfast in bed this morning. Yay Alicia. Now we're on our way out the door to explore Manhattan a bit. Hope everyone has a good day for me, since it's my day.

Happy Pi Day!

Take any circle! The distance all the way around is called the circumference. The diameter is the distance from one end of the circle to the other (how wide the circle is). Amazing, if you divide the circumference by the diameter, you'll always get approximately 3.14.

Today is March 14th, or 3/14. Thus, today is Pi Day! Happy pi day!

Today, Alicia made me an Apple pie to celebrate. We didn't measure the circumference or the diameter, but I'm pretty confident we'd have gotten pi (apple pi!).

Also, to celebrate, I've told my students that there will be a pop quiz on Monday. Every ten digits of pi they successfully memorize, I'm giving them 1 point extra credit. Of course, there will be a cap at 5 points. I'd hate to give a student an A just because he or she memorized pi to a thousand digits.

To finish the post off, here's a very small part of pi:

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196
4428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273
724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609...