User rorty | chat.stackexchange.com

rorty

Jul 21, 2017 04:30

I have 1.6 months or so to prepare for it and am wondering how to spend my time. I have covered introductory analysis, linear algebra, abstract algebra; I have been working through the basics of point set topology for fun mainly

rorty

Jul 21, 2017 04:29

Does anybody have any experience taking the math subject GRE?

3

rorty

Sep 5, 2016 22:16

any advice for not forgetting old mathematics? does anyone use spaced repetition programs like anki?

rorty

May 1, 2016 05:08

i want to make him a poster

rorty

May 1, 2016 05:08

does anybody have good suggestions of math objects to put on a graphic to a math-oriented friend for his birthday?

rorty

Apr 29, 2016 05:11

yes, ur right

rorty

Apr 29, 2016 05:10

I wish not to, because I haven't learned continuity yet... I'm towards the beginning of a very intro analysis text.

rorty

Apr 29, 2016 05:04

I come to seek guidance on a proof. I want to show that if $A$ and $B$ are compact sets, then $A+B$ (that is, the set $\{a+b : a \in A , b \in B\}$) is compact. I know that $A+B$ is bounded, but am having trouble showing that it is closed. That is, I am having trouble showing that if $x = \lim (a_n + b_n)$, then $x \in A+B$.

My attempt: Bolzano-Weierstrass guarantees that $(a_n)$ has some subsequence $(a_{n_k})$ that converges to some $a \in A$. Likewise, there is some subsequence $(b_{n_j})$ that converges to some $b \in B$. Consider the indexing set $I = \{n_k\} \cap \{n_j\}$. If $I$ is …

rorty

Apr 29, 2016 05:03

Do you guys mind if I interject with a question of my own?

rorty

Apr 14, 2016 19:43

I am feeling frustrated because I don't think my problem solving skills are getting better despite many months of self study. I keep getting stuck on seemingly trivial problems, and my impulse after 30 min or so is to get hints. I want to get through a certain body of math within a time limit so I can't take forever on a single problem, but at the same time I want to improve my problem solving skills. Any advice?

rorty

Apr 14, 2016 06:46

but how do i use these facts?

rorty

Apr 14, 2016 06:46

and the series sum(1/(2n-1)) diverges

rorty

Apr 14, 2016 06:45

well the series sum(-1/(2n)^2) converges to 0

rorty

Apr 14, 2016 06:42

scratches head

rorty

Apr 14, 2016 06:42

but.........HOW

rorty

Apr 14, 2016 06:40

(at least, i think it does not apply in an obvious way...)

rorty

Apr 14, 2016 06:39

yes, but that does not apply here because the absolute values of the terms of the sum is not decreasing.

rorty

Apr 14, 2016 06:38

I'm trying to prove whether or not the series 1 - 1/2^2 + 1/3 - 1/4^2 + ... converges. I think it diverges because there is more positive "fuel" than negative fuel, but am uncertain how to approach the proof.

rorty

Apr 14, 2016 01:06

The quasi-alternating signs leads me to think I should find some way to use the alternating series test

rorty

Apr 14, 2016 01:04

I am having trouble deciding whether the following series converges: 1 + 1/2 - 1/3 + 1/4 + 1/5 - 1/6... (two positive terms followed by negative term)

rorty

Apr 11, 2016 00:43

@TedShifrin I went to Yale, but I only took a few math courses on the side (now studying math more "seriously" in my free time). However, I do have many friends who struggled through your book, and are glad they did.

rorty

Apr 11, 2016 00:41

@TedShifrin O GOD. I just realized you wrote the textbook of the freshman honors math course at my university (which I did not take, though I do own your book).

rorty

Apr 11, 2016 00:37

have any of you met other math.se users in person (whom you previously had only known through the site)

rorty

Apr 11, 2016 00:31

thanks!

rorty

Apr 11, 2016 00:31

how do you align expressions after equals signs in mathjax? e.g. 5 = 3 + 2 = 1 + 1 + 1 + 1 + 1, but having each equal sign sitting on top of each other, if that makes sense

rorty

Apr 10, 2016 02:46

Do you think that all math undergraduates should take a course in topology? Topology is not required at my university (some treatment is given through analysis of course). But I've heard that topology is one of the pillars of a math foundation (along with analysis and algebra)

rorty

Mar 31, 2016 18:45

If you refer to it later, do you say $(1)$ or is there a more elegant way to refer?

rorty

Mar 31, 2016 18:34

how do you number equations in mathjax (like in a question post)

rorty

Mar 30, 2016 04:03

I am wondering how long it would take to do the Analysis text just because I have 4 months of free time left and am trying to allocate my time properly (I want to do other things too, math and otherwise)

rorty

Mar 30, 2016 04:02

@MikeMiller In undergrad I took only a few proofy math courses (linear algebra, discrete math, intro probability theory, etc) but was a poor math student (not very mature). I am now trying to build a solid undergrad math foundation through self study. I just finished Pinter's abstract algebra book and did 90% of the exercises (with a lot of help from math.se), which took me 4 months (including weeks where i would be too lazy / distracted).

rorty

Mar 30, 2016 03:19

Hi all, do you think it's unreasonable to work through a introductory analysis text in a month? specifically Abbott's text

rorty

Mar 30, 2016 00:14

Is there anyone here that primarily works in statistics or a related field?

rorty

Mar 28, 2016 02:52

i know that the basis of $V$ spans the subspace, but that basis might include vectors in $V-H$

rorty

Mar 28, 2016 02:51

there would be no finite set of vectors spanning it

rorty

Mar 28, 2016 02:49

I'm trying to show that if $V$ is finite dimensional, then the subspaces of $V$ are finite dimensional

rorty

Mar 28, 2016 02:46

Let $V$ be a finite dimensional vector space, and $H$ a subspace of $V$. How do I show that $H$ has a basis? This seems obvious but I am having trouble proving it.

rorty

Mar 26, 2016 23:29

"Prove that for every prime number $p$, there is an irreducible quadratic in $\mathbb{Z}_p[x]$." I don't think there's a particular polynomial that's irreducible over $\mathbb{Z}_p[x]$ for all $p$. Any other approaches I can try?

rorty

Mar 26, 2016 17:35

Help! I can't see how $F(\sqrt{a+b+2\sqrt{ab}})$ contains $\sqrt{a}$ and $\sqrt{b}$!

rorty

Mar 26, 2016 16:23

@BalarkaSen Thanks, you had the right approach. To be more precise I think you have to write $\pi = f(\pi^3)/g(\pi^3)$ because $\mathbb{Q}(\pi^3)$ requires quotients to be a field.

rorty

Mar 26, 2016 03:22

Hey all, looking for some help... I am having trouble showing that $\pi \notin \mathbb{Q}(\pi^3)$. Any tips?

rorty

Mar 24, 2016 08:12

i.e., is it clear enough to say that $\sqrt{1+\sqrt[3]{2}}$ is not expressible as $\sum a_i (\sqrt[3]{2})^i, a_i \in \mathbb{Q}$?

rorty

Mar 24, 2016 08:09

Why is $x^2-(1+\sqrt[3]{2})$ irreducible over $\mathbb{Q}(\sqrt[3]{2})[x]$?

rorty

Mar 20, 2016 20:17

Let $F^*$ be the multiplicative group of nonzero elements of the field $F$. Consider the subgroup $H=\{x^2:x \in F^*\}$. Why is it that any element $x^2 \in H$ is the square of only $x$ and $-x$? Why can't $x^2=y^2$ for some $y \notin \{x, -x\}$?

rorty

Mar 19, 2016 23:51

Hi all, I'm having trouble seeing why the irreducibility of polynomial $p(x)$ over some field $F$ implies the irreducibility of $p(x+c) $ where $c \in F$.

rorty

Mar 19, 2016 09:23

@EricStucky Thanks for your help. I'll think about what you suggested some more.

rorty

Mar 19, 2016 09:09

what method are you referring to by bash it through?

rorty

Mar 19, 2016 09:05

@EricStucky I'm still failing to connect the dots. if $x$ is already "assigned" to $c$ under $\phi$, how am I supposed to find which element in $F[x]/<p(x)>$ is assigned to $d$?

rorty

Mar 19, 2016 07:05

I'm having trouble getting to the end of this proof...

rorty

Mar 19, 2016 07:04

(^because each is isomorphic to F[x]/<p(x)>)

rorty

Mar 19, 2016 07:04

Say $c,d$ are the roots of $p(x)$. Then I know $F(c)$ is isomorphic to $F(d)$.

rorty

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