>>16859832 Have you taken physics classes and how did you do in them? I thought I was good at math (aced calc as a sophomore in highschool) but now that I'm in college, the physics class for engineering majors is kicking my ass and I don't understand how I am so bad at something that most people consider to be an offshoot of mathematics.
Also any advice for succeeding in a physics (mechanics) class?
>>16859850 Well, I'm an undergraduate. So, all kinds: real and complex analysis, ring theory, group theory, field theory, logic, number theory, linear algebra, differential equations.
>>16859859 Infinity isn't a number so you can't take its derivative.
>>16859868 I've taken some physics classes. Physics is hard because you have to develop the intuition according to the theory and then really think about the things you're doing. In some ways, physics can be harder than mathematics... a lot of the time, at least in undergraduate mathematics, you don't really have to understand what you're learning to complete something. In physics, doing that is not so easy.
In order to get better at physics, memorize theorems by really, really, really learning them. Do lots of problems. Don't do problems just to get them done - do the problems to prove to yourself that you understand the material. Review solutions.
>>16859873 It's definitely one of the most pathetic.
Is there something like an inner product but that takes more than two elements? I've been thinking that all of its axioms could be extended to more than two elements, and then p-norms could be defined from p-inner products.
>>16859935 Interesting. It doesn't generalize it exactly in the way I was thinking. I was thinking something in line with <x1,x2,...xn> with it becoming its complex conjugate when you take an odd permutation of the xi's, and it being linear in it's first element. And real and positive if all the elements are the same.
>>16859937 I can only find a paper by a certain Misiak, and I need to pay for it and I'm not currently in the mood to figure out how to access it through my university.
>>16860026 Why would you think it would generalize to something so convoluted and complicated?
>>16860034 Graphs are cool but graph theory is for the most part tedious in my opinion. Some graph theory is pretty nice. I took a course in graph theory and got an A in it. We covered some neat stuff.
And for the anon that requested it, the sad picture is included. Not sure if this one is sadder or my OP pic... but both are pretty sad.
>>16859901 Yeah, I understand that feeling. Math is abstract based solely on intuitive reasoning, but physics requires more knowledge and connects abstract reasoning with concrete examples, if that explanation makes sense.
Math has always been my strongest subject (I have consistently placed in the upper 5th percentile in almost every math-related test I take), and my ability to do it is mostly based on natural talent. Half of the time I complete problems without remembering exactly how I even solved them (and eventually I will hear the names of the theories at a later time and be able to recognize them, but not having names for them and just doing them makes it harder to instruct and tutor people), but in physics it seems like I have to do more practice problems in order to develop an understanding of how the theories relate to each other.
What was your score on your AP exam and what career do you plan on going into? I'm currently a high school senior taking AP Calculus BC, if you scored a 4 or above could you please share some advice on preparing for them? Standardized tests are easy but AP style questions are really conceptual and application based so I feel like I can't just wing them like I can for a lot of tests.
>>16860050 I don't see how it's convoluted (or less convoluted than the way it's generalized in that paper anyway). I just took the 4 axioms and basically said what they will be if there were more than two elements.
Of course it may be useless, but I think that it may be seen as a way to get p-norms from something like a inner product.
>>16860066 That's right. Math is just a tool you use to do physics. Solving physical problems depends more on what's upstairs than anything... at least in undergraduate physics. It can be a bit of a shock at first. You'll get it.
I didn't take AP stuff because I'm not American. I want to be a professor eventually. I'm really not sure what's contained in the AP exam, but if you have a sample test, I can go over some questions with you here and solve them with you. I could try to give you a look into how I solve them which might help you solve the problems yourself.
So far, it seems as though you're good at following an algorithm to solve a mathematical problem but you aren't practiced at actually doing mathematics. This kind of thing is rarely natural and comes with lots of practice. You need a large working memory, to think about connections between things, to know how proofs work, be creative, and even a little lucky to get good at those kinds of questions. Practice.
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