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8:00 AM
I've actually wanted to take some category theory, but none one at my college seems to have any interest in it.

So you could be the first one :D

I probably will take a course in it down the road. I'm coming up on applying for graduate school.

That's cool. What is your area of interest?

Mainly algebra, with some additional interest in topology, geometry, and analysis.

Hahaha that's funny. Take a look at my profile description.

8:10 AM
Hehe, almost exactly the same.

Jan 21 '17 at 6:17, by Secret
List of maths fields I have interest in:
1. Group theory in terms of orbits and actions
2. Zero term algebra and division by zero algebra
3. Integration in the language of abstract algebra and as a functional, symmetry of integrands
4. Optimising proofs given axiomatic systems
5. Category theory
6. Unnatural algebraic structures
7. Patterns in expanding multiplications of polynomials
8. Set of all counterexamples given a proposition
9. Tensor visualisation and intuitions
10. Numerical analysis methods to explore special regions or points of mathematical functions or systems of equations
Updated version:

Is it true that if $R$ is a division ring, then $(R\setminus\{0\},\cdot)$ is cancellative? It feels like that should be obviously true, but I've made mistakes about this sort of stuff in the past, so I like to make sure.

By "cancellative" you mean $ab = ac \implies b=c$ ?
(and the analogous statement with right multiplication)

Exactly

If $R$ is even an integral domain it is cancellative

8:20 AM
That uh,should be straightforward proof for associative rings

Yeah, that is a simple proof.

For nonassociative rings...
I need to check...

Alright, I thought so.

why will the presence of zero divisors screw up cancellation in nonassociative rings...
Ah...
$0c= (ab)x$ but $c\neq x$
but... what if that nonassociative ring has only one pair of zero divisors?
nope that does not work, because you can still produce 0 with sums
ok done

8:48 AM
2

In university I have learnt about the concept of tensors, which are multilinear maps in that it is a map such that it is linear with respect to all its arguments $$f(a+b+c+d+e+f+g....)=f(a)+f(b)+...+f(g)+...$$ and in physics, it is geometric in that it is independent of basis In biophysics I l...

Probably anything that has to do with the exponential map

9:43 AM
Hi chat.

hi

Can you guys recommend me books on analysis and linear algebra? Like from calculus 1 to formal integrals and beyond, polynomial bounding and stuff that’s more than calculus.
On linear algebra I’m already using @TedShifrin’s book. I’m trying to learn everything about the first year of uni so I can do scientific research.

Well, people often refer to Rudin for real anlysis

10:05 AM
Are there a finite number of combinations of $a, b$, where $a, b$ are palindromic primes that do not contain the digit 1 and $ab$ is a palindrome?

Let $a,b$. compute $💥(a)$. From this we get:

@TedShifrin following up on the other day -- So if I'm reading this problem correctly, what I ended up having (and again, I don't think the lecturer himself understands what he's asking, since his matrices are not even well defined) is two sets of orthogonal columns -- a set of column vectors for the even functions -- call their span $F$, and a set of column vectors for the odd functions -- call their span $G$, whence $F \perp G$. The question asks how many even left singular vectors in the SVD decomposition of $A$ (where $A$ is not well defined mind you). What I was trying to do is force i

(Also glad they finally added a horizontal scroll bar else the chat will be screwed)

yup.. 2 in a row huh

Here is an identity about numbers of tuples $(a,b,c)$ with $a,b,c\in [1,n]$ such that $ab=c$:
$$|\{(a,b,c)\in [1,n]^3|ab=c\}|=2\sum_{i=1}^{\lfloor\sqrt{n}\rfloor}\Big(\lfloor\frac ni\rfloor-i\Big)+\lfloor\sqrt{n}\rfloor$$
I'm not sure how to get this. Does anyone have any idea about the counting method?

10:20 AM
Is it possible for $X := S^1 \vee S^1$ to have a covering space $E$ such that $\pi_1(E) \cong \Bbb{Z}$?

10:46 AM
(Next time I saw another palidrome question out here that is boring unlike the 3 starred one, you are out of my view. Cannot kept on being banned by producing a rant)
(Of course, I already knew at least 3 users have pressed the ignore button on me, but that will not affect my workings)
now to study the above two questions...
@user193319 Intuitively I can think of a loop that covers that, but it will require the point where it joined to be cover by the loop twice. I am not sure if paths like these are legal

@Secret im sorry i didn't give context
1

While discussing about prime numbers with other users, I noticed that: $(1)$ There are very few combinations palindromic prime numbers that have products which are palindromes. Ex : [2, 3], [2, 30203], [2, 30403] $(2)$ For the large range I tested on PARI/GP, I noticed that all the palindromi...

here is some

11:01 AM
Until I have a formula that allow me to say even one thing about all odd palidromes, I don't know if there is a systematic way to investigate these

i was planning to give it earlier and explain my question better but i got involved in proving it myself
sorry for the inconvenience @Secret

sorry for being rude, but ever since a long time ago some homework vampired drained me in my tutoring, I have very low patience for pure computation type questions
Regarding palidromes, similar to primes, I don't know if there exist a way to study them systematically. It seems it suffers the same hard problems as transcendental number theory

hmm
actually it turns out that my 3 star question was a conjecture

One thing that is clear to me is algebraic methods don't really work on these because the digits are so sensitive to carryovers

and it demonstrated that there are infinite types of those prime numbers

11:07 AM
and regarding that 3 starred question, I thought it would have been easier to solve since it is the subset of the actual open question of whether there are finite palidrome numbers

Hi
$\displaystyle \lim_{n \to \infty} \frac{-z^2}{(1+z^2)^n} = 1$... shouldnt be equal to zero?

@Secret well there are infinite palindrome numbers, but yes the three star question in fact is a subset of another open question

@Odestheory12 ah yes, careless mistake. In that case, your originally suggested n has to hold
@Mathphile whether there are infinite palidrome primes, that one?

yes
Fermat Number Conjecture it is a subset of this @Secret

1 hour later…
12:29 PM
chat.stackexchange.com/rooms/92782/… Friends i have created this room so that a beginner or any one on Math SE can discuss question (before posting it ,if he wants to discuss )
4

2 hours later…
2:03 PM
0

Problem: Let $F$ be a field with $\text{char} F = p$ for some prime $p$. Show that if $X^p - X - a$ is reducible in $F[X]$, then it splits into distinct factors in $F[X]$ Solution in back of the book: This solution confuses me slightly. Why is $f(X)$ splitting as two monic polynomials? ...

I now see why reducibility is necessary, but I am wondering if someone can critique my proof.

2:41 PM
Prove that a sequence of continuous functions $f_n : [0,1] → \Bbb R$ converges uniformly to a continuous function $f$ then $f_n (x_n ) → f(x)$ whenever $x_n → x$.
Fixing $i$ in $f_i(x_n)$, we see by continuity of $f_i$ that $f_i(x_n)\to f_i(x)$ as $x_n\to x$ and now $f_i(x)\to f(x)$ by uniform convergence. Am I correct?

@Silent so far so good
be wary though of the bi-sequence $a_{ij} := \delta_{ij} = \begin{cases}1&i=j \\ 0&i \ne j \end{cases}$ where $\displaystyle\lim_{j \to \infty} a_{ij} = 0$ for every $i$, and $\displaystyle \lim_{i \to \infty} a_{ii} = 1$

that $\delta$ is not even continuous

3:02 PM
@LeakyNun I am sorry but can't get what you are pointing with this

well you argued that $f_i(x_n) \to f_i(x)$ and $f_i(x) \to f(x)$
I'm saying that you cannot conclude that $f_i(x_i) \to f(x)$

oh!!
So, how to show?

3:28 PM
$|f_n(x_n)-f(x)|\le|f_n(x_n)-f_n(x)|+|f_n(x)-f(x)|$

3:54 PM
in Group Theory, 1 min ago, by Shaun
Does anyone know of an encyclopedia or miscellany of group presentations?

4:13 PM

@Thorgott Wow!! Thank you very much

np

4:41 PM
Thank you, @Silent; more specifically: gap-system.org/Datalib/datalib.html
@Secret (Sorry.)

For any irrational number $α$ such that $α^ 2 ∈ \Bbb N$, we define $\Bbb Q(α) := \{a + bα : a,b ∈ Q\}$. Show that $\Bbb Q(α)$ is a field.
Is this answer correct: $\Bbb Q(\alpha)$ field because $(x^2-\alpha)$ irreducible over $\Bbb Q$?

4:58 PM
Apropos of nothing: Travelocity’s customer service can kindly go f*** itself

Use a map to convert Travelocity into an infinite dedekind finite set to be onion skinned

@Thorgott, will you please verify my above question?

One of my connecting flights on the return trip got cancelled by the airline. That’s annoying but not Travelocity’s fault
So I contact Travelocity to get the flight changed to one that will work. There is an obvious fix
But it takes days (via their Facebook IM support) for them to convey that info to me correctly
They first quoted the flight as coming from LGA aka Laguardia NY. probably what they meant was LGW aka Gatwick in London. But that’s exactly the same info as the cancelled flight, and they finally confirmed that it should have been LHR aka Heathrow in London
So I finally confirmed that with them, and asked them to schedule it
They tried, but that was on Friday which is apparently is a holiday for Icelandair and they’ll have to wait until Monday. Again, annoying, but not in their control

Where are you flying?
You're in London?

This morning they reply to me with my updated itinerary... which is exactly the same itinerary as I had before I contacted them
They didn’t book any new flight. They just quoted back the itinerary I’d already told them was not acceptable

5:12 PM
@Silent $x^2-\alpha$ isn't even a polynomial over $\Bbb Q$. You mean $x^2-\alpha^2$?

@AkivaWeinberger not yet. I’ll be flying out there in a month, and flying back a week later

Ah
What're you doing there?

So yeah. They’ve taken a week to get back to the same itinerary that I told them was the problem in the first place

5:14 PM
Sorry to hear your travel agency website is shit

Yeah.
in retrospect, maybe I should’ve done it via their twitter account
If only so that potentially I could have gotten other people knowing they’re dumb

5:39 PM
I'm not versed in the theory of field extensions, so can't really comment

2 hours later…
7:38 PM
Hello chat

Hello, Can someone help with little question in set-theory?

7:52 PM

8:33 PM
1

Problem: Let $F$ be a field with $\text{char} F = p$ for some prime $p$. Show that if $X^p - X - a$ is reducible in $F[X]$, then it splits into distinct factors in $F[X]$ Solution in back of the book: This solution confuses me slightly. Why is $f(X)$ splitting as two monic polynomials? ...

I now see why reducibility is necessary (I was being a knucklehead), but I am wondering if someone can critique my proof that $\alpha \in F$.

9:08 PM
1

Consider the following problem 5 below. I am trying to construct the stated function f. I tried many functions one which sends the matrix of the form below to xy. I also tried to send the matrices of the form below to x + y. None of them work. Recall a left uniform continuous function f on G i...

If someone could help that would be niceeeee

9:58 PM
1

Consider the following problem 5 below. I am trying to construct the stated function f. I tried many functions one which sends the matrix of the form below to xy. I also tried to send the matrices of the form below to x + y. None of them work. Recall a left uniform continuous function f on G i...

10:20 PM
If $p(x,t)=x^n+a_1(t)x^{n-1}+...+a_n(t)$ is a family of parametrized polynomials, where t lies in a compact interval and all the $a_i(t)$ are continuous, then why do the roots of $p(x,t)$ in $x$ for all $t$ form a bounded set?

2 hours later…
11:57 PM
@Thorgott Because the roots of a polynomial vary continuously with the coefficients. This can be proved, for example, with Rouché's Theorem in complex analysis.

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