#math Definition and Topics - 13 Discussions

Math rock is a style of progressive and indie rock with roots in bands such as King Crimson and Rush as well as 20th-century minimal music composers such as Steve Reich. It is characterized by complex, atypical rhythmic structures (including irregular stopping and starting), counterpoint, odd time signatures, angular melodies, and extended, often dissonant, chords. It bears similarities to post-rock.

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1. I Writing down an explicit homotopy

I understand that a homotopy is a continuous deformation. The only thing I really remember is something in my notes like this: F(s, 0) = a(s) for 0≤s≤1 and F(s, 1) = a * Id(s). Basically I have to construct some sort of piece-wise function such that I go something like two loops half of the time...
2. I Proof involving Identity maps

So, this problem I sort of get conceptually but I don't know how I can possibly rewrite (idX)∗ : π1(X) → π1(X). Does this involve group theory? It's supposed to be simple but I honestly I don't see how. Again, any help is greatly appreciated. Thanks.
3. I Describing homeomorphisms with the π1 function

Here is what the problem looks like. The thing is I don't remember what π1is exactly and I don't really know much group theory or know what equivalence classes are. I remember learning some group theory fact that f*(n) = n*f*(1). So, I think (a) was just equal to m since f(1) = 1 and (b) was...
4. I Doing proofs with the variety function and the Zariski topology

I included this image because it is easier than typing it out. Anyway, this is an old problem I need to catch up on. I have a clue as to how to do part a. I could say given an x that is a member of ∩V(Ai) which implies that x is a member of V(Ai) for ∀i. Then we can say ∀i all polynomials are in...
5. I Proving a function f is continuous given A U B = X

Basically with this problem, I need to show that f is continuous if A and B are open and if A and B are closed. My initial thoughts are that in the first case X must be open since unions of open sets are open. My question is that am I allowed to assume open sets exist in Y? Because then I can...
6. I Show that (0, oo) is homeomorphic to (0, 1)

So, I already have a function in mind: tan(pi*x - pi/2) that maps (0, 1) to (0, oo). I just forget how to rigorously show that a function is continuous. I was hoping to get some help on showing that this tangent function I just wrote is continuous (not the topological definition, just like the...
7. I Show R^2 \{(0,0)} and {(x,y) | 1 < sqrt(x^2+y^2) < 3} are homeomorphic

As I said in the summary, I don't really know how to even figure out which function would be appropriate to map the two sets that I described in the title. I'm using the book called Basic Topology by M.A. Armstrong. The book can sometimes be really dense. I am having a really hard time knowing...
8. Find the roots of x^5=10

Mentor note: Member reminded that some effort must be shown. Real root is 1.858. Just dont know which method to use to find the 4 complex roots
9. A math problem related to circles

Summary:: If a circle can be inscribed in a parallelogram how will the parallelogram change? Explain. It is a 10th grade math question in case you want to know.
10. The sum of this series of the product of 2 sine functions

Homework Statement I have encountered this problem from the book The Physics of Waves and in the end of chapter six, it asks me to prove the following identity as part of the operation to prove that as the limit of ##W## tends to infinity, the series becomes an integral. The series involved is...
11. Programs Physics degrees in the world?

So I'm looking to do a bachelor's degree which involves a lot of physics and math but one that is not engineering, maybe like a BSc in physics? Idk Anyone got any suggestions?
12. J

I Why mathematicians do not solve mathematical theories?

Why mathematicians do not solve mathematical theories in different fields, name quantum mechanics that tries to describe gravity or any other theory such as multiverse/lqg/branes etc. It's just pure mathematics, only this language can fully describe universe, so why is it still just a theory...
13. Schools Mean girls at the university!

hello all i've just started university about a month ago (studying for a single major in mathematics) and in desperate need for some advice from the wiser and older. since i've started at the second semester (you can do that in my uni), we are a relatively small group of people, only about 20-30...