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GhostStalker posted:Advanced classes in middle school (plus some help from an Asian test prep school) helped me get into the best public high school in New York, with the year's credit of Algebra I that's practically a requirement to get in there, and then I really had no problems with math in school afterwards except for failing to hand in some research assignments in an "advanced" Algebra II class Sophomore year that had a research component. Oh hey, sup fellow Stuy grad. Read the Math Team comment and I immediately knew what school you were talking about. GhostStalker posted:I feel like I'm a terrible math major because I had no problems with using algorithms to calculate things when given actual numbers, but I pretty much fall apart when it comes to doing proofs. I mean, I head a hell of a time during Abstract Algebra, because while I could see where my professor was going with proofs done as examples and could follow it then, when it came time to take the exam, I'd be pretty lost on a bunch of problems. The Numerical Analysis course I took this past semester wasn't much better. Like I understand that proofs are pretty much the thing you have to do when it comes to higher level math, and I just can't help but feel like I made a terrible mistake deciding to be a math major. Yeah higher level math classes can be brutal. Most people don't get the context of pure math (I know I didn't as an applied math undergrad) and will view proofs really rigidly. The best way to think like a pure mathematician is to put yourself in the shoes of someone like Cantor or Godel. You're seeing ideas/algorithms applied to novel situations that only exist in your head and you have to try to prove it to the mathematical community. Developing intuition plays a huge part in grounding yourself in these types of proof classes. The very first thing to do is understand what you're trying to prove and have examples and counter-examples help you limit the search space. Or else you're just staring at the page going WTF because you have an 'infinite' search space (yes this is a fuzzy concept, maybe the better idea is combinatoric to the tools that you have to mash together to prove a concept.) Intuition 'grounds' the 'degrees of freedom' so you're not performing an insane exhaustive search. For Abstract Algebra in college, the context is that you're working with regular algebra but generalized so you relax constraints (assumptions) and get new generalized results. So extra cases could come to mind and help you visualize what you're trying to solve. For Real Analysis, I tried to 'brute force' the class and it was not pretty. Rudin is a hell of a book to learn from starting out. Also definitely branch out to other sources/intuition/diagrams when the book just doesn't make any sense. In the end of the day, you're objective is to get the material and that's the goal to not lose sight of. Tezzeract fucked around with this message at 18:12 on May 28, 2014 |
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May 28, 2014 18:08
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| # ¿ Jul 13, 2025 11:19 |
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