Be skeptical. Never blindly trust. Don’t believe that everything I say is true in math is true. Don’t believe everything you read on the AoPS wiki. Don’t blindly believe everything any other math teacher, in school or extracurricular, says. Don’t believe every bit of math you read on the internet, no matter how reputable the source. Everyone is human. Everyone makes mistakes. Always try to find counterexamples to new theorems you learn, even if they are well known theorems. If a certain theorem seems to be true for n=1,2,3…10, try to figure out if you can understand if it is always true, and if so, why. If you slowly digest and don’t believe anything in math until you can fully convince yourself of every “fact” you learn, you will gain a much deeper understanding of things.
Developing a healthy skepticism of the news you see on tv or hear on the radio or read is also a very crucial skill the develop. Don’t blindly trust the news.
2. Work hard in high school. Choose something that interests you. Work hard on it. It doesn’t have to be math competitions, though it can be. Even if you don’t pursue it later in life, the act and experience of having worked hard at something (even if you fail at it) is invaluable later in life. Don’t go through high school with no goals in mind. Choose something and work hard at it. Then, even if you fail, it will have been worth the experience
3. Take charge of your own education. Don’t rely on just taking some math classes to carry you to do well in math competitions. Most of your learning should come from you doing problems, thinking, checking your understanding, digesting proofs, reflecting, checking the rigour of your understanding, etc, on your own.
This goes not just for math competitions, but for anything you do later in life. Never stop learning. Learning does not end at the completion of college. In fact, I would argue that real learning starts (or continues) once you finish college. Don’t rely on getting your education solely from education institutions. Take charge of your own education. Pursue learning about whatever interests you at the time.
4. Make lots of friends. Make lots of friends in life. Make lots of friends in your area(s) of interest.
If you try to bury yourself in your work, like math and math competitions, you’ll find you’re lacking a lot of things later in life that require friends’ support, both for morally and emotional/mental health. While I encourage everyone to work hard, I also encourage you to vigorously make friends whenever you get the chance.
Don’t lose friends outside of math either. I can’t tell you how grateful every time I can to a friend to ask about tech related things or where is the cheapest place to buy item X. One person can only keep track of so much in life, and having friends with a variety of personalities and interests will help you immensely later in your road of life.
Advice for Current Students:
Please ask me lots of questions!
That’s the main point of taking lessons from me.
If you are in class and don’t understand something I said, please do ask!
I don’t bite. Really!
It is very helpful feedback to hear that someone in class doesn’t understand something. Chances are, if you don’t understand, several other people don’t understand either. Also, I won’t get angry or think you are stupid or anything like that. Instead, I will take this into account and try to explain it a different way (or just again).
Oftentimes, if someone doesn’t understand something, it is good feedback for me, indicating I didn’t explain it that well.
I try to place everyone in classes as best as a I can, so I try to avoid scenarios where you don’t have the background to understanding something I’m explaining.
2. Please do the suggested homework! You won’t improve if you only do math during my classes. Most of math improvement comes from doing problems on your own. So when I suggest homework, please do it! Really! Even 1-2 hours a week reinforcing what we learned the last less will help in spades.
I don’t really force anyone to do any homework, as my classes themselves are optional to begin with, but if you really want to improve, you should do the homework, or choose better homework you think is more suited to yourself at the current time.
My Philosophy: you doing the problem on your own in 15 minutes is 10 times more valuable than me guiding you through it it 5 minutes. I want everyone to come to their own understanding of math, even if it’s different from my own. (as long as it’s correct) It’s not easy to come to this level of mathematical maturity and depth of understanding, but if you can get there, you don’t need to hear me explain anything- you can guide and travel your own math journey. Thus, I always think the least important parts of class are when I explain, and the most important parts of class are for you to play around and come to your own understanding of the problem (often in silence).
You may also be interested in some of my previous posts I have made on AoPS giving advice: hurdler’s AoPS page
Don’t play the college admissions game. Just don’t. It’s not worth it. In particular avoid choosing classes for GPA boosts, avoid EC’s you have no interest in for the resume building, etc.
AMC overview, tips,