Homework Statement
Define the interior A◦ and the closure A¯ of a subset of X.
Show that x ∈ A◦ if and only if there exists ε > 0 such that B(x,ε) ⊂ A.The Attempt at a Solution
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Here is my new solution, but I'm not sure if the graph I put is of any use, but if you can, please put up a similar graph to the one I put to help better understand.
Right now, I am studying Advanced Calculus (proof based), and it is hard thinking through some of the definitions without first thinking about it concretely (meaning how to visualize it better geometrically, if that makes any sense?). I need help with this definition.
Definition
Let X be a...
Classical or modern physics? Basically, which branch is responsible for all modern inventions: Cars, airplanes, modern sea ships, spacecraft s, microwaves, ovens, computers, televisions, smartphones, etc. (Also, how did we get to the moon, using concepts from classical or modern physics?)...
When I asked this question in another forum, some people argued that scientific and mathematical discoveries are born out of curiosity and a way to explain unknown elements that surrounds us. Others say it comes from originality. In my opinion, I think it does come from curiosity, but you have...
I don't know why I think purer math is more important for CS majors while applied math is more important for Physics majors. Only because for CS, you need to be able to do logic and think logically and be able to do proofs (but then again, I'm not a CS major, nor have I taken discrete math, but...
What about for computer scientists? As far as I have seen in a few colleges with different requirements, it seems that discrete math is the only required math course. Some colleges I've looked at also require students to take Linear Algebra (especially those specializing in graphics) and two...
As I stated before, I'd imagine that computer scientists know more of the abstract kinds of math that deal with logic and algorithms while physicists know more of the applied math topics that apply to everyday phenomenon. Those pure math courses (real analysis, abstract algebra, topology) seem...
I am wondering, what is the math level of your average CS or physics major? Like how much math do these two take beyond stuff like the Calculus sequence, differential equations and linear algebra?
I was having a discussion with one of my old math professors from my community college (I'm in a...
Didn't know where to put this question. but just wanted to ask quickly. All i know is that in Calculus 3, you use double, triple or multiple integrals for 3D models. But what other higher level math course uses or involves multiple integrals?
That is what I'm trying to point out. Along with an advisors note of my promises, I want to show them my plan for the next year as well to support my appeal.
How would it not be helpful? At least I am letting them know my plan for the upcoming Junior Year? Do I have to tell them the hours I plan on studying as well. What about telling them that I will take advantage of the resources given to me such as tutors, going to professors office for help, etc?
But should I provide my plan for the following Junior year, like the classes I plan on taking for both the fall and spring semester. Should I let them know I am re-studying my Calculus and Chemistry notes for when I am taking the next classes?
What do I say to make them believe? Should I say by turning off my house computer and only studying at the library? Being at home is my comfort zone and can be very distracting.