What are you studying in math?

Question

I'm just curious, but what are you studying in math right now? Since I'm bored, just post some problems up here and I'll answer them for you.

Answer 1

First of all, I feel like helping "Forever" with her question:
Notice that your question first says: you can divide both sides by a non-zero number... and then goes on to say... "divide both sides by zero" that's the reason you don't get 5=4. You can't divide by zero. Ever. 0/0 is not equal to one. If anything, you would approach this problem by dividing both sides by a number APPROACHING 0. then you get infinity=infinity, which IS logical.
Anyways, on to the part where you help me.



I'm studying calculus in three dimensional planes. I want to see if you can answer some problems for me.

Evaluate the following double integral:

int[1,4](int[0,2]([x+sqrt(y)]dx)dy)



Next question:
1. Integrate f(x; y) = sin(sqrt[x^2 + y^2]) over:

(a) the closed unit disc;
(b) the annular region 1 <= x^2 + y^2 <= 4.

I can't wait for you to do these for me...

(EDIT) T M, you have a good point. But to somebody who doesn't want to do their homework, like me, they are real problems :P Just for you though, I'll take out the matrix question.

Answer 2

Too many students are overwhelmed by the symbology of mathematics... they think they have to memorize procedures, too. You like English and science likely because it is all conceptual to you. Well, treat math in the same way. See symbols not as a language but as a concept... or realize at least that math is a language of concepts. Every symbol stands for an idea, and every rule has an explanation. There really arent any definite procedures to solving a problem... in that math can be very creative, in how you approach a problem and how you choose to manipulate the symbols. Ultimately what matters is the final answer. As creative and original as you may be, as subjective that you may visualization a problem, the answer is an absolute. There is a lot of leeway, though. There are rules and restrictions... but they all have an understandable justification. Any rule can be reinforced with example, and any wrong rule has a counter example. A lot of the rules you can come up with on your own. I actually taught myself vector algebra during the final exam... I determined all the rules in the margins, then did the problems. Aced that test. I even finished it before anyone else, and got the best grade. How? By understanding concepts. Not by memorizing rules, nor by redundantly solving the same old problems. But by truly conceptualizing what the problems are asking, coupled with what I already know and what might be the next logical progression in my knowledge. Its possible. Most people on YA criticize me for my honest recommendations... but they are the ones that struggle, not I. Dont practice. Try to understand concepts. Discover proofs. Truly wrap your mind around a concept and explore it by asking your own questions. If you dont get something, figure out why you dont. Most students take an utterly wrong approach to learning math. They memorize. They repetitively do homework and practice problems. All it does is tire the mind and frustrate... you arent learning anything new when you practice stuff you dont know how to do in the first place. I literally never study. I ditch out on all homework, too, if I can get away with it. I never read the books. And I usually ditch out on math class too. And yet, I persistently maintain the highest grades in my class, showing up just to exams. People that I have tutored have loved my tutoring, my approach they appreciate and I help a lot... and yet I cant image what I do any different than anyone else... besides emphasize a conceptual understanding and convey those concepts as best as I can. I find out what the hold up is and I correct misconceptions. I deemphasize practice and overemphasize concept and proof. If you understand proof, you understand method, application, and all caveats and restrictions involved, it reinforces an appreciation for more basic ideas, and you are left satisfied knowing that you understand why something is true. There is no room for error after that. I do all my math with a pen, not a pencil. I have made it through 3 out of 4 calculus classes without a calculator. And I am bound to get down thumbs because people either dont believe it or they resent it for some reason. I enjoy math. I learn it at home in my free time independent of school. I end up enrolling in college classes already knowing the material. I read it once, online or in a book, or as part of someone elses YA answer, and I have the knowledge for life. I challenge myself to YA problems I dont even understand, and more often than not I get the BA in those problems.

Answer 3

my daughter is in sevemth grade pre algebra. here's a problem to think about: You can divide each side of an equation by the same nonzero value. Explain what would result from the equation 4 times 0 = 5 times 0 if you could divide each side by zero and if 0 over 0 = 1

Answer 4

Patrick, those are not problems, but mere exercises. To illustrate the difference, someone could just paste them into a program like Maple or Mathematica, adjust the syntax as necessary, and have an instant solution. They wouldn't need much understanding of the mathematics involved because your "problems" merely exercise the mechanics. A real problem requires one to think and decide what principles to apply. It could be a practical engineering problem with conflicting constraints and you have to make compromises and evaluate the most important factors.

Answer 5

Algebra II

Answer 6

Linear Programming and just lately Matrices -blahh

Answer 7

calculus 2, but right now it's all the reviews from calculus 1, boring

Answer 8

Physics of Sports, and yes, it is a real class here.

Answer 9

Find the inverse of this function:

f(x) = x^3 + 3

Answer 10

E=Za/2squrt1/4n solve for n