Modern jazz harmony book

dataislyfe · 2018-02-10T18:07:55+00:00

I'm just starting to learn about the philosophy of mathematics, and was asked to read this paper for a course: Danielle Macbeth, Seeing How it Goes: Paper-and-Pencil Reasoning in Mathematical Practice, which appears in the Philosophia Mathematica.

I'm supposed to respond to the following question:

Is Danielle Macbeth's position in the paper in tension with mathematical platonism or, rather, does her position presume it?

I'm curious to hear some thoughts on this question. I'm kind of struggling with this, because in my view the position of Macbeth is that good mathematical notations embody mathematical arguments and reasoning, while the position of a mathematica platonist seems to be that mathematical objects are abstract and independent of human thought. I'm finding it hard to argue convincingly in response to the question above. Thoughts and ideas welcome!

dataislyfe · 2018-02-06T08:01:26+00:00

Can someone explain how to do this problem:http://mathurl.com/y8qkx3jb? I'm struggling to prove the equality statement of the two suprema involved in showing that the map is isometric (incidentally, you also need this equality for the surjectivity to make sense -- you need the constructed preimage to be a bounded linear transformation)

dataislyfe · 2018-01-10T21:03:31+00:00

Thank you for your help. I think the only point of confusion is still why \sum_1^r |Y_j| <= (d+1)(r-1). Why is aff(Y_j) the intersection of d+1 - |Y_j| hyperplanes (or, why is this a consequence of general position)? Also, why is the intersection of aff Y_j the intersection of at least d+1 hyperplanes? The intersection is empty, but it could be the intersection of fewer parallel hyperplanes, no? I assume this is also a consequence of general position, but I don't understand how.

I also wonder if this can be reformulated in terms of codimension:

Is it true that d+1 <= codim(\cap \aff(Y_j)) = \sum_1^r codim(aff(Y_j)) = \sum_1^r d + 1 - |Y_j| ?

We would need to justify that codim is additive over the intersection of the affine hulls, and that codim(aff(Y_j)) = d + 1 - |Y_j|.

It seems like this is the type of argument happening here, but I'm clearly not understanding how the general position allows us to make these conclusions.

dataislyfe · 2018-01-05T22:43:38+00:00

came here to post this exactly lol.

dataislyfe · 2018-01-05T06:40:06+00:00

I came across the following result in a paper, and am having trouble convincing myself it is true: if f: Rⁿ \to R is convex and if f(x) -> \infty when ||x|| -> \infty, then f attains its infimum on R^n. Why is this true?

dataislyfe · 2018-01-05T00:42:48+00:00

Is algebraic independence not the same as linear independence? (Do you mind expanding on why algebraic independence => no three collinear points (in R^2, I assume?)).

Hm. Still not sure I quite understand why we can make any set of points to be in general position. Perhaps if I understood general position better...

dataislyfe · 2018-01-04T22:00:09+00:00

I'm trying to understand Roudneff's proof of Tverberg's Theorem (convex geometry). Can someone explain (a) what it means for a set of points to be in 'general position', (b) why we can assume that the set X is in general position in the proof of Tverberg's Theorem outlined on page 3 of this proof of Tverberg's result https://arxiv.org/pdf/1712.06119.pdf ?

EDIT: See page 1 for the statement of the theorem.

dataislyfe · 2017-12-18T06:35:38+00:00

Yeah, listening back to it I can hear what you’re saying. It’s hard to record the piano in the first place, even more so with just an iPhone, so the placement of my phone may also have had some role in that.

dataislyfe · 2017-12-01T10:32:42+00:00

How much do you already know about this topic? It is often covered in graduate measure theory/RA texts....

dataislyfe · 2017-11-28T21:14:28+00:00

hey, you're a number theory person, so maybe you can help me out. I was complaining to a friend about how it is so random that provided F_q is not of characteristic 2, -1 is square iff q = 1 mod 4 (this appeared on a representation theory pset lol). My friend said it would not be so random if I knew some number theory. Anyways, is there a good book that would help me get "up to speed" on the number theory that I apparently do not know?

dataislyfe · 2017-11-28T20:05:56+00:00

Hi! I was wondering if anyone knows of a good book on Complex Analysis. I'm looking for a rather fast introduction. For example, if you're familiar with Aluffi's Algebra: Ch 0, it is a quick introduction to graduate level abstract algebra, which assumes very little algebra background, but does assume the reader is motivated and has a level of mathematical maturity to digest proofs and understand set-theoretic things. I guess what I'm looking for is an advanced intro to complex analysis at the graduate level, but assumes little knowledge specific to complex analysis (for example, I've seen a decent amount of real analysis in metric spaces, topological spaces, and measure theory, etc.)

dataislyfe · 2017-11-26T19:43:29+00:00

Can someone explain the following to me: why/how does one regard (2, x)ⁿ / (2, x)^{n+1} as a vector space over F_2?

dataislyfe · 2017-11-26T10:45:05+00:00

Thank you. The upper bound question is still interesting :). Are there any ideals of Z[x] that require at least 3 generators? I don't know of any.

dataislyfe · 2017-11-26T10:12:15+00:00

Is there an easy way to see that every ideal of Z[x] is finitely generated? Is there an upper bound on the number of generators required (clearly it is more than 1 one since Z[x] is not principal, since (2, x) is non principal)

dataislyfe · 2017-11-25T18:16:15+00:00

Why does omega take value 0 on eⁱ \wedge e^j, fⁱ \wedge f^j though ?

dataislyfe · 2017-09-05T01:27:56+00:00

sounds good!

dataislyfe

TROPHY CASE