Adventures in Education: An instant of revelation

In my last post, I discussed how strongly I wanted to understand abstract algebra. Today, I am getting closer.

Mathematics is a play. In this play, there is a character (appropriately named the characteristic) that seemed alien to me. Its definition was quite simple, but the character was mysterious. I knew what it did, but not how it worked or what it was capable of. But then, in an instant, I learned a side of the character previously hidden. As if in soliloquy, it divulged just enough information to give me a taste of it's ambitions and agendas. And then, the rest of the story began to make sense. Those mysterious theorems, those awkward propositions, and those questionable conclusions began to fit together in a cascade of connections. A grand mystery has been resolved, and I can still feel the afterglow of the euphoria in my rosy cheeks and my tingling fingers. It felt like the tipping point in a Sudoku solution, when the identification of a single entry immediately reveals all of the others.

This character reached out and handed me a key. It is not a key that opens the entire subject of abstract algebra, but it is a key to its front foyer. Finally, I could step inside and marvel at the intricate workings of the subject! I expected it to be complicated and detailed and expansive, much like a grand hall with gold leaf designs and high ceilings and fine Victorian architecture. Much to my surprise, it was simple, compact, and clean like a photo in an Ikea catalogue. Where I expected a grand cabinet of tools I found a small cupboard with a few multipurpose theorems. It is incredible that such a great set of perfect ideas can collapse easily into such a small yet robust framework of elegantly simple rules.

Today, I went to class and understood everything the prof said. I didn't find the minor error in his notes. I didn't ask the clever question about a strange definition. I couldn't repeat the lecture back to you. But I understood what he was talking about the entire time. Hallelujah!

Some weeks are good weeks and some weeks are bad weeks. This week is a good week.    

Adventures in Education: At the back of the pack

Abstract algebra has become both a favorite hobby and the bane of my existence. The nuances and caveats are so grand, they swallow me up like sink holes. It's difficult to appreciate the great landscape of the subject from deep inside the chasm of a single theorem. The detailed elegance of every  piece of the algebraic machine takes my breath away. But putting those pieces together... well that's a different story.

So far, I have struggled to tie the subject together. I puzzle over problems for days, only to find the solution to be, of course, simple and perfect and easy. Slowly, very slowly, these beautiful theorems and quaint definitions are weaving together. The other students in the class ask intelligent questions and correct small errors in the teacher's definitions. They nod and smile and assimilate the ideas quickly and gracefully. I write every word the prof says and pray that later on it will make sense. This course is the biggest mental challenge I have undertaken, and I am sitting at the back of the pack.

My primary goal is not to achieve a high score or out-compete my classmates (although an A would be nice.) This subject is so beautiful and every detail is so precise, that it would be immensely satisfying to open my eyes wide and behold the magnificence of the theory. That's what I want. Not the grade, but that satisfaction. The solution to the grand puzzle. The insight. Thankfully, this stuff is much more important than my big ego.

Adventures in Education: New Beginnings at UVic

A degree wasn't enough. My week now consists of commuting back and forth to Victoria to take undergraduate math and computer science courses. If all goes well, next September I'll be in a Masters program. If not, I get to spend eight months learning undergraduate mathematics from geniuses. Win-win.

I learned very quickly that VIU (my home institution) and UVic (my new school) have slightly different approaches to teaching math. At VIU, in-class solutions are often quite detailed. By contrast, yesterday a prof wrote a solution as follows: "Proof: Induction." This is analogous a recipe for chocolate chip cookies that reads "Method: Bake." The student is still expected to understand all of the details of the proof. A benefit to this method: I must keep up with the reading. The drawback: I must keep up with the reading. Independent study skills? Yes, I think I'll need those. This semester presents an opportunity for substantial personal growth.



When I arrived in my first Abstract Algebra II* class, the front row was full and the desks had been pushed forward as far as they could possibly go. Strange, I thought, since there were only seven students in the class. The keeners in the front knew something I didn't. The prof came in with a few notes scrawled on the back of a receipt and a used letter envelope, and then plunged into an amazing lecture. At least, the parts I could hear were amazing. He was quiet. Mental note: get a seat at the front for every lecture from this point forward. Anyways, this guy knew every detail about the theory he was describing, as if it was his first language. Amazing.

As I adjust to the expectations of a new department, my emotions transition between excitement, intimidation, fear, and hope. I remind myself of  these words of wisdom from a VIU math instructor (very, very paraphrased):

In math, it's not about smart you are. Success is the result of being able to keep your head in the game. Get immersed in a problem. Do your best. Sometimes you don't get results quickly. It happens to everyone. It's not your intelligence that will define you; it is far more important to be able to find your way back into a groove when you are lost. We do this because we love it. You have to love it to be good at it, because you have to have the patience to stick with a tricky problem, even if you aren't getting anywhere quickly. If you really want to, and if you are persistent, you will do well.

I'll try my best.



*Abstract algebra is a subject about algebra of objects that may or may not be numbers. These objects could be all of the numbers, certain types of numbers, remainders, symmetries, systems of equations, the arrangements of sets of objects, or something else entirely. It's easier than it sounds.

The best things about September

Cool evenings.

Cool mornings.

Hot coffee.

Cinnamon in coffee.

Cinnamon in hot apple juice.

Cinnamon in everything.

Scarves.

New jeans.

Sunny afternoons.

Walks in the forest.

Walks by the beach.

Camping at the beach.

Homework at the beach. (Yes, homework!)

Fresh school supplies.

New courses.

High expectations.

High work ethic.

Classmate reunions.

Potluck parties.

Curried zucchini and apple soup.

Comfort food.

Warm hearts.

Cool evenings.