Christmas video idea: Integration by substitution, video title: "All I want for Christmas is u"

@hotlatte1222

3 жыл бұрын

And which means, on Christmas day, u are just a substitute.

@drpeyam

3 жыл бұрын

I like that! I had something else planned, but this is good too!!!

I love topology! This stuff always has me thinking, and the way Dr. Peyam explains it makes it so easy to understand!

I knew the discrete metric would be involved here! He's a funky little fella, always loves to be the counterexample lol

Using *exclusive or (XOR)* as an analogy might make the concept of *discrete metric* more stomachable for any CS student.

Will you consider a collab like mathvengers or something else (obviously math related), for the Christmas video? I'd recommend something weird, like 100 PDE's in one video, or just something out of the box. Anyways, wishing you happy times throughout this season.

@drpeyam

3 жыл бұрын

I have some ideas! Not a collab, but probably something fun

I've really got to learn some topology! I'm a first year undergraduate (though, being the smarty pants I am I do a some 3rd year courses :-) ). I have a topology book and a very interesting looking book (Stone spaces) which I have been wanting to read for a while now. Now Dr. Peyam I have a personal question for you: I want to do mathematics research, and I kind of want the bragging rights of saying I published in first year. Though I don't know if the stuff I have is good enough. I know at least one result I derived last year was good enough, because someone else managed to publish it a few months ago. I have a lot of personal projects which have a lot of promise (in my eyes) but I don't know if I can make the jump from 'something that would be interesting to put on arxiv' and 'something interesting enough to be published'. Some of my projects are like follows: - I have done a lot of stuff regarding the arithmetic derivative (cool function) and extended it to most rings. - I made an extension of logic from {0, 1} -> C. In the range [0,1] it has the same properties as probability. However in the range C you have 'eigenvalues' of logical statements (Imagine a system of logic gates, L, with some output O - then there exists some z in C s.t. L(z,...,z)=O. for all O). And a bijection between some polynomials and all systems of logic gates. - Treating shapes of polynomials (I have a fullish explanation of this one down below because it reminds me of topology) - I derived some stuff using fractional calculus, the shape polynomials, and analytic continuation to answer the question 'what if fractional euclidean dimensions existed'. Fun fact: Given a half dimensional square which encloses a half dimensional sphere, it follows that the sphere always has a greater area than the square. this is only true in dimensions 0 A lot of these are interesting but I worry are they interesting enough? I worry about my capability, despite being so young (19 yo). ==== polynomial explanation === Though speaking of topology I have had a little project of treating shapes as polynomials (as an injection, so some shapes are 'equal', like an infinite plane and a sphere are 'equal'). This allows you to have a little topology like thing in which your invariant is sharp edges rather than holes. You can then multiply and add these polynomials together which equates to actions on the shapes. For example - x^n is an infinite plane in n dimensions. (x+1)^n is a positive infinite plane (imagine a plane of positive real numbers - sort of like a cube which goes on infinitely in one direction) in n dimensions. (x+2)^n is a cube in n dimensions. Making this rigorous has proven difficult but I've tried and I'm getting there. The polynomials work like this: the coefficient of X^k is the number of 'k dimensional edges' in your shape. so the coefficient of x^0 is the number of points, x^1 is the number of lines, x^2 is the number of surfaces etc. I have managed to prove that multuiplying two polynomials is equivelent of 'joining' one shape at any orientation onto every point of the other shape. A line is x + 2 (1 line segment, and two delimiting points) a square is x^2+4x+4 (1 surface, 4 lines, 4 points). You can notice that a square factorises into (x+2)^2 which is two lines multiplied. Now if you get two finite lines - and sort of stick one onto the other at right angles and run it along - you will get a filled in square (or any rectangle depending on the length of the lines). Things get weird if you allow negative powers of x (and I even have an intuitiveish way of looking at negative powers). There are a lot of theorems you can prove about these polynomials - I find it really interesting.

Haven't watched it yet but I'm curious

Cool!

3:13 I'm surprised there wasn't a BOI comment made! Always love it when funny words happen to show up in the question and Peyam makes his little pun, but you missed it! I thought that was funny, haha

@drpeyam

3 жыл бұрын

Not my type of humor haha

Weird. Thanks.

but would that be consideed as a norme?, i just took topology so i am cofused as to weather or not we can find such counter examples using normes that follow the three axioms

@tomkerruish2982

3 жыл бұрын

It's a metric. It's nonnegative, 0 iff both points are the same, symmetric, and satisfies the triangle Inequality. Presumably, if you've taken topology, you were introduced to the discrete topology, in which every set is open; this is (roughly speaking) the analogue for a metric space.

8-6÷2×3=?

That's crazy ngl

@gregheffeley4922

3 жыл бұрын

Wait...how'd you comment 5 days ago if this was released 8 minutes ago......????

@massimoaster9407

3 жыл бұрын

*Confused screaming*

@codebulletin

3 жыл бұрын

@@gregheffeley4922 Paterion or member

@drpeyam

3 жыл бұрын

Code Bulletin Nope

What exactly is a discrete metric? Is it one that can take on only finitely many values?

@user-yw7cm4yf8m

3 жыл бұрын

Discrete means that your distance function d(x, y) not continuous ig

@toaj868

3 жыл бұрын

@@user-yw7cm4yf8m Thank you.

Dr. Peyman, I have encountered a new way to prove the Fermat's last theorem, nevertheless, I obnoxiously do not have enough information to know whether or not my chosen prepositions are mathematically correct. There are another ones as well, but they are not of the current opportunity.

A bit too much for my attention span to handle.

@drpeyam

3 жыл бұрын

Dude 😂😂😂

@frozenmoon998

3 жыл бұрын

I think we must all agree that Dr P has to introduce a red pen, to ensure our friend bprp could follow :D. Nice having you here.

Shows how much I know...a ball is not a sphere ! Is this just a game of semantics...forgive me, I'm just a thicko.

@Qermaq

3 жыл бұрын

I remember it this way. Spheres are 2-D manifolds. Balls are 3-D. So the surface of the planet is a sphere, but the whole planet is a ball.

Discreet matrix. You make it so easy. How to master it?? Any hints.

@elfabri666

3 жыл бұрын

Discrete metric

I will not post this comment . And even if I do... the P(you reading this)=1