EPTAnyway, I've written quite a bit about the other two, and though I've written a Treatise on Mental Arithmetic, I believe it's time I wrote a blog about my adventures with math.
Ever since a young age, math was always my forte. It was just one of those things that really clicked and made sense to me. In fact, the preschool I went to in Taiwan was a private one, and the teacher noticed I was doing exceptionally well and decided to speed me up - so when I got to America, apparently I knew everything that they had learned up until 5th grade.
Math wasn't that fun for me at first though - mindless computations were forced upon me by my mother [of the Asian tradition], and it was really not-fun as I had to spend my summer afternoons holed up in my room multiplying things together.
All throughout elementary and middle school, math was never really that interesting for me. I was just good at it. That was it. My mom didn't really know much about math competitions and stuff, since she had just moved here with us, so there wasn't a lot of that. I didn't really have much to do about math - I would sometimes think about it, and do my little mental arithmetic stuff, but that was it.
Then I entered Pre-Calculus, in the 10th grade - the first math class that I've ever had trouble with. I don't know why, but all of a sudden I was making really stupid mistakes that I normally didn't and everything just seemed somewhat suffocating. I actually started studying for tests, which was a practice that I reserved exclusively for other subjects - or I just let my grade tank so I could play Starcraft XD
At the end of Pre-Calc, however, even though I got a B in the class - something clicked. Something clicked inside me. I made the stupid realization that so long as every single part of my work was correct - there could not be anything wrong in the solution. I had always feared that even though my work was "right," I would still make mistakes, because that's what it kept feeling like. Since then, my mistakes have declined dramatically - and I only ever made them because I was being a dingus.
Then came Calculus, the first year of math that I truly loved and enjoyed. Everything made sense to me, and everything was so interesting. As a class specifically to prepare us for the BC test, however, proofs were glossed over - but I always stayed after class to ask the teacher to prove it to me if it wasn't in the book. I loved reading the proofs in the book and knowing why things were the way they were, instead of just accepting it at face value the way I had my whole life.
That year, I also started taking the CAML tests at lunch, which were kind of a shock to me - I had never seen problems like that before; all the problems on my homework were pretty easily solveable, since I knew the rough subject matter that they were related to, and it was just a twist on the method that I had to employ. The thing with the CAML tests were that I had to create the method completely. That was a new experience. All my experience problem solving in Starcraft: Brood War campaign editor were starting to come into play LOL
Anyway, that year, I took the AMC12 A for the first time (in 2011). That was a brutal awakening. I had never prepared for these exams, mind you, but I did correctly answer 13 of the problems, and I incorrectly answered 8 of them lol. I was very intrigued by these types of questions - they were actually fun, and I actually really liked doing them. I decided to join the math team, but I didn't really know who to talk to, so I didn't that year.
The next year, time for college decisions. I was really on the fence about what to do - I had no idea, but I was doing well in my Multi class and I asked the teacher what I should do - and he told me to be a math major, to get the basic tools down, and THEN specialize in something, or stick with math if I liked it. AMC was fun, so I decided to stick with math. And boy, was that the best decision I've made since then.
I decided to prepare for the AMC12 this year, mainly by doing old problems. I also joined the math team [because my love interest was in it LOL] Boy, was that fun.
I still didn't know how to properly study for these competitions, and the solutions seemed to be so alien, not accessible, and just difficult in general.
I did, however, beat the whole school that year :D
But I didn't qualify for the AIME :/
I also did Math Day at the Beach that year. That was the first time I'd ever seen high-level math, since there was a talk about Elliptic Curves, and the problem about Cannonballs stacked in squares, and they collapsed into a perfect square. [Find integer solution to 1^2 + 2^2 + ... + n^2 = y^2]
SO THEN, on a whim, I decided to sign up for Physics C for the shits and giggles. I didn't start studying until 2 weeks before the tests - and I somehow managed a 5 on both :O. It was THEN that I really got the motivation to begin my favorite thing ever - self-studying.
The focus was on martial arts that summer, so not a lot of math-related things occurred, but when I got to college, there was one thing on my mind...
The Putnam.
My high school multi teacher had told me a lot about the Putnam, and it seemed like something that I really wanted to do. As a freshman without significant math contest experience, however, I needed to really push myself in order to get anything done.
So I picked up some books - the first one being Linear Algebra 2e, by Axler. Boy was that thing difficult to read - I had never been subjected to formal proofs of anything of that nature, and I was reading that in addition to Problem Solving Through Problems by Larson, and Putnam and Beyond by Gelca and Andreescu. I also read random articles on certain math topics, and tried to do as much as I could to hopefully even score a point on it. It was really difficult. But I persevered.
I also really liked number theory, so I read some stuff about that.
So I talked to the professor in charge of the Putnam team, and she arranged to have me attend the practice sessions every Friday afternoon. I was the only freshman. I didn't really have a clue what was going on half the time, but I was able to reason my way through certain problems, and I was even able to solve one of them :D
[The old one about five points on a sphere, 4 of them lying in the same hemisphere]
I got pretty close with a few of the integral problems, and there was a similar triangles one that I solved, but that was it. Everything else was too difficult.
I was repeating multi that quarter which was boring, so I devoted most of my efforts to the Putnam.
Then came the actual test, in 2012. My love interest had written me a letter and sent it to me and I was super pumped. As a person who sucks at getting up, I arrived 2 minutes late. Good thing the test hadn't started yet XD
I took a good look at the first 6 problems in the A portion, and I decided to focus my attention on A1, A2, and A6. A6 I later dropped because I couldn't solve, and A1 I tried to use some Pigeonhole Principle argument but I don't think what I wrote worked. I tried to do a contradiction using the obtuse triangle side length square inequality thing but I ran out of time.
I presented a solution for A2 relying mainly on a lot of "clever" algebraic manipulation which was super sloppy, but I kept trying shit until something worked. And something DID work. It was very poorly written though since I had no rigorous proof experience.
I couldn't solve any of the B problems, but I did try.
I got a 1 :D
I AM NOT A NONSCORER ON THE PUTNAM YEAHHHHHHHHHHHHHHHH
I then taught myself Set Theory and Logic in hopes of skipping that class. I read a book called the "Book of Proof," and everything made PERFECT sense and I loved it, but I didn't really have a resource to go to for feedback on my proofs, but they made a lot of sense to me, and I really scrutinized them and made sure that there were no holes. I tried to skip the class, but the dean managed to talk me out of it - so when I actually took the class, everything was easy and I slept and scored over 100%. I should've skipped the class.
So then summer came and I didn't do a lot of math. But fall came, and with it came Topology and the History of math. I LOVED Topology. It was so interesting and everything was super cool, but I don't really see why everyone gets so mad. Sure it's a lot of definitions, but it all makes perfect sense at the end of the day...Hitler loves Topology was pretty funny though; I agree they could've chosen better terminology as opposed to "clopen" XD
I didn't do so well on the Putnam in 2013, [I think I scored 0, but I didn't find out my score yet LOL wayyy after the fact] because I think at that point I wasn't as "free" as I had been the year before - I was looking for Euclidean Expositions to everything, which was obviously the wrong approach. I didn't really have a lot of time that school year thanks to working to pay for school, but now that it's summer - I have a lot more time, and I'm really devoting a lot of time to problem solving.
With a formal understanding of proofs, analysis, and groups now [I still haven't taken the class yet - I read a book LOL] I decided to pick up a few problem-solving books. I'm coaching a friend of mine to take the AMC 10A, so I read through the Art of Problem Solving Volumes 1 and 2, and I also am working on "How to Solve It" by Polya, and am working through Problem Solving Through Problems as well as Putnam and Beyond again. This time, it's actually doing something for me - and I'm actually able to solve the occasional problem here and there! [The ones used in IMO at least - though it's taking me way longer than I'd like]
Now that my arsenal is slightly developed, and I have a lot more heuristic tools to work with, problem solving is become more of an accessible thing, and I'm really having a lot of fun with it. I'm going to do Combinatorics this fall, and I'm super excited because I feel like that would really help me a lot. My goal is to score at least a 10 this year, but at this rate, maybe I'll get more, I don't know XD
Yayyy problem solvingggggg
