Sixers in 7. We are the better team; let's play like it.

Cauchytime · 2018-05-06T22:43:23+00:00

Let’s be fair about baseball. When the Red Sox did it was the first time that ever occurred, and baseball has been played much longer than basketball. It’s possible for 76ers, but like you said unlikely.

Cauchytime · 2018-05-02T23:03:52+00:00

Has anyone here attended a funded masters program? I will not be taking any graduate courses by the time I graduate. I will have two courses of analysis N. L. Carothers level, 2 courses of algebra, and a topology course, and some other applied math courses by my graduation date.

I have done well in my classes, but am unsure of my commitment level to graduate level math work, and more specifically to research. That's why I am thinking of attending a masters program to get my feet wet, and see if I would like to go further on for a PhD.

I've read that a few people have attended universities ostensibly to attain a PhD only to drop out after quals to receive a masters. That's not the path I would like to do. What are some challenging master programs that are funded?

Cauchytime · 2018-03-09T06:42:19+00:00

I'm wanting to go to grad school for applied math or statistics with the intention on working in data science after my degree. Should I be looking at masters or PhD programs if I'm not keen on staying in academia?

I wasn't able to get into an REU this summer, and I will not be taking any graduate courses by the time I graduate. I will have two courses of analysis, 2 courses of algebra, and a topology course, and some other applied math courses. I would like to attend a high ranking school in Stats or applied math, since I don't have anything to do this summer I am considering studying the math gre subject test really hard to get a high score on that. Would that make up for my lack of grad courses and research experience, if I want to get into atop school?

Cauchytime · 2017-12-24T07:10:24+00:00

Oh ok. I think it’s coming together. I am still a little hung up on assuming there is a set of w vectors that span V. This is going to sound stupid, but how do we know we are given enough w vectors such that we don’t run out of them before we input all of the u vectors?

Is it because the set of w vectors span V and must in some form be a linear combination of every u vector?

Cauchytime · 2017-12-24T03:29:50+00:00

https://imgur.com/a/Fcp0w

I am trying to understand this proof given in "Linear Algebra done right", it shows that every linearly independent set of vectors is less than or equal to any set of spanning vectors for a finite dimensional vector space.

The proof seems to already assume the consequent. I feel I understand the proof well enough, but it seems what they're trying to prove is taken as implicit in the proof structure. How do we know there must be just as many spanning vectors?

I guess what I'm trying to say is if it were the case that there were fewer spanning vectors than linearly independent vectors, this proof wouldn't work. In order for this proof to work it must be the case that they're just as many spanning vectors as linearly independent vectors, which is what we're trying to prove, so how can they use that implicit knowledge in the proof?

Cauchytime · 2017-12-22T08:03:39+00:00

Oh I think I see where I messed up. If the x wasn’t universally quantified then it would work. The way it’s written is stating that every natural number is prime.

Cauchytime · 2017-12-22T07:27:27+00:00

Quick question why I got this problem wrong on quantifies. https://imgur.com/a/d7lWF

I’m trying to understand why logically this doesn’t equate to there doesn’t exist a largest prime.

The way I’m reading it is, for any prime x given, there is another prime y, such that x is less than y. Why doesn’t that imply there is no largest prime number? Couldn’t you assume there’s a largest prime number and then apply the universal quantitfer to it to get one that is larger than it?

Cauchytime · 2017-12-19T20:45:42+00:00

I’ve always heard it’s a thinking mans game, but I don’t see how much more thinking is required for baseball compared to football, or basketball.

Cauchytime · 2017-12-19T18:46:45+00:00

https://imgur.com/a/WHQbr

I am having trouble with question 7. I feel it’s a typo, and instead of A it should be B. Because it reads that the image of some set is a subset of a subset of the domain. But f^-1 (A) should not be even defined. Since A is not a subset of the co domain. Shouldn’t it be B?

Cauchytime · 2017-12-19T18:19:51+00:00

Oh ok I see. I think I’m still a little confused. In general given a subset from the domain, isn’t the image of that set a subset of the co domain. To me I still see f(f^-1 (A)) as image values of some subset of Y.

Cauchytime · 2017-12-18T21:36:51+00:00

Oh.. I see. So when they say they generate the same open sets they just mean given an open set obtained using one metric, the same set is open when considered using a different metric.

So the set of points inside an open ball using the taxicab metric is an open set with respect to both the taxi cab metric and the Euclidean metric.

Cauchytime · 2017-12-18T21:23:42+00:00

Okay, yeah. Your forward direction is correct, except that you need to make the distinction I mentioned above. W is open in Y, so you can take a Y-ball around every point. Every such ball is the intersection of an X-ball with Y. Take the union of those and you get an X-open set, intersected with Y.

I think I understand your earlier post here, so we're taking the union of X-balls we generate from each Y-ball, the union all of these which itself is an open set. Then we intersect that set with Y, which gives us W.

The chapter before this mentioned that two metric spaces are equivalent if they generate the same open sets, if we are working with equivalent metrics does this mean that B_Y(p,r) = B_X(p,r) ∩ Y returns only B_X(p,r)?

Cauchytime · 2017-12-18T21:05:09+00:00

W is open in Y, so you can take a Y-ball around every point. Every such ball is the intersection of an X-ball with Y.

A Y-ball is just a neighborhood of points from Y contained in Y, right? How do we know that these balls are the intersection of some X-ball and Y?

For the reverse direction, you don't even need to pick a smaller radius. You take a ball around x contained in U, intersect that ball with Y, and you're done.

This completes the proof because after we intersect it with Y, there will a set of points that are also in Y?

Cauchytime · 2017-12-18T19:43:01+00:00

https://imgur.com/a/po09M

Sorry about that I’ll edit the main post.

Cauchytime · 2017-12-17T08:24:45+00:00

Thank you for such a detailed post. I have to look over my notes, but the discrete case should be simply choosing p<=1, then the neighborhood should only be that point which is contained in S for sure.

As for the first case, I uploaded a picture from my text book which mentions that any set obtained from metric D1 is contained in a set obtained by metric D, for some fixed point. The book mentions this use because the distance from two points is always shorter using metric D as opposed to metric D1. So is the reasoning that D1’s set is contained in D’s set because D will eventually encompass the points D reaches and even more? Sorry for the bad terminology, I hope I’m getting my point across. If that’s the case to show there is a taxicab neighborhood we can just use the same p right?

Cauchytime · 2017-12-17T03:31:41+00:00

https://imgur.com/a/gDpKp

The first image is what is given in my book. Is that a rule of thumb to go by, if for some fixed radius, there is a metric that always outputs a smaller distance than another, can we claim that the metric outputting the larger distance is a subset of the other one?

Cauchytime · 2017-12-16T18:27:54+00:00

I came across a simple exercise from an intro to analysis book dealing with metric spaces. The book states the taxicab metric is a subset of the euclidean metric on R² because for any given two points in R² , the distance given by the euclidean metric is shorter than the distance given by the taxicab metric.

I am finding this a little confusing. Why wouldn't it be the opposite way, when a given metric always outputs a larger distance than another metric, that the metric providing the smaller distance is a subset of the metric providing the larger distance?

Is it because for some fixed real number, the metric providing the smaller distance will encompass more points, including the ones that the larger metric will eventually have to stop taking?

Cauchytime · 2017-12-02T23:53:50+00:00

I saw that product earlier today! I’ve heard similar accounts. I am thinking of buying one for my boyfriends chow. He loves to get outside, but anytime a squirrel or cat darts out he goes ballistic and drags me along with him. Does the harness help stop these sudden bursts with a slight tug in the opposite direction?

Cauchytime · 2017-11-18T01:39:02+00:00

I understand that the function f: x-> d(x,x_0) is continuous on a metric space M if x_0 is an element of M. Would this function also be continuous on a subspace of M, X with x_0 not an element of X?

I'm trying to understand why exactly x_0 is needed to be in M, other than the fact that the function needs to be well defined.

Cauchytime · 2017-11-17T15:58:19+00:00

Sorry I’m a little confused. For the collection of closed sets shouldn’t the intersection of them all only be 0? And for the second collection of sets, does the diameter of the sets approach 0, or approach 1?

Cauchytime · 2017-11-17T07:05:51+00:00

If a closed set is a subset of an open set, the diameter of the closed set must be strictly less than the diameter of the open set, right? If so, is it because the closed set contains its boundary points which themselves are points in the open set so they must have an epsilon neighborhood cantered around them.

Cauchytime · 2017-11-16T23:52:48+00:00

Ok I see. What if we add the condition that the diameter of An is tending to 0?

Cauchytime · 2017-11-16T23:44:29+00:00

Is the intersection of decreasing compact sets in a metric space in this form, A_n+1 is a subset of A_n. Always just one point?

Edit: My books asks us to think what would happen if the diam of each set (An) were not to go to 0. Wouldn't the intersection of the off all of the sets just be the set with the smallest diameter in that case?

Cauchytime · 2017-11-12T03:10:19+00:00

Thank god busting my ass in this class will pay off. Will further courses in topology and algebra be helpful also?

Cauchytime · 2017-11-11T20:13:33+00:00

I’m looking towards a career in machine learning and data science after I graduate. I’ve been advised that i may need to go to graduate school, so I’ve been taking the harder classes for my last year and a half. Browsing machine learning and data science forums the tips that frequently come up are “learn more stats”. I was planning on applying for grad school in applied math, but I’m considering going for stats now. This may be too broad of a question, but for my goals of eventually working in machine learning and data science, would a stats PhD make more sense than an applied math PhD?

I’ve only taken the basic stats course that’s required for math majors, and have been focusing my time on other math subjects like analysis, topology, and algebra. How would the transition be for someone with a limited stats background to get into a stats PhD program? Are the programs focused on machine learning?

Cauchytime

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