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The Freshman's Dream (extra) - Numberphile

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Some extra footage from our discussion with Kevin Tucker... See main video at • The Freshman's Dream (... --- More links & stuff in full description below ↓↓↓
Kevin Tucker at University of Illinois Chicago: kftucker.peopl...
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Опубликовано:

5 сен 2024

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Комментарии : 38

@omartechnologies Месяц назад

Would it be possible to bring this professor again to talk more about the applications of mod but also encryption.. He seems to be deeply knowledgeable and can break things down quite nicely.

@timlandscheidt Месяц назад

"p clock" reminds me of the time in my younger years when I wrote a software to control phosphorus content and innocently named it "PControl". :-)

@trueriver1950 Месяц назад

Notice that the 4 line is the opposite of the 1 line. That's because 4 = -1 mod 5.

@binbots Месяц назад

The infinite clock -0+ ( ) -0+

@BenDanYt Месяц назад

Or is it?

@cheeseboy8241 Месяц назад

I've had that profound-sciency-sounding piano loop from Clocks by Coldplay in my head for this whole video

@CepheidMadEngineer Месяц назад

What does Kevin focus on / major in? I'd enjoy more videos with him; though more importantly I learned something.

@mgintz Месяц назад

I'm a student of Kevin! I think the most easy-to-explain kind of thing he does is "what does geometry look like when p=0?" How to define shapes using equations in this world, how to define when they're "smooth" or not, things like this. This is really closely related to algebra - what kinds of addition-multiplication structures can we get in this world? What are different ways to describe how "nice" these structures are?

@jakemaranzatto6514 Месяц назад

@@mgintzpoggers

@chriswebster24 Месяц назад

I could come up with lots of different ways to describe how nice something is. That sounds extremely easy. I need his job.

@abigailcooling6604 Месяц назад

So early this hasn't even been released yet.

@samlevi4744 Месяц назад

Is there a reason why the non-zero values for rows and columns 3 and 4 were the inverse of rows and columns 1 and 2, respectively?

@samlevi4744 Месяц назад

Is there a reason why rows and columns 3 and 4 were the inverse of rows and columns 1 and 2, respectively?

@yisahak Месяц назад

😂 still my physics teacher do it (a-b)²=a²-b²

@iaagoarielschwoelklobo1894 Месяц назад

And this will never be

@the_eternal_student Месяц назад

a little confusing at the end.

@frankharr9466 Месяц назад

Somehow, I've missed what the the therum actuall is. I should have paid better attention.

@sebastiandierks7919 Месяц назад

1:50 nice unintentional pun

@olivier2553 Месяц назад

So a multiplication table mod 9 should be a sudoku.

@MuffinsAPlenty Месяц назад

Unfortunately, it is not, since 9 is not prime. In particular rows/columns corresponding to multiplication by 3 or 6 will break things.

@olivier2553 Месяц назад

@@MuffinsAPlenty Oh yes, of course :( I should not post about maths at 3 in the morning.

@landsgevaer Месяц назад

And the zero-column/row messes it up too. And the 3x3 blocks don't work out. The mod-17 table contains a 16x16 megasudoku though, if you ignore the 4x4 subblocks.

@MuffinsAPlenty Месяц назад

@@landsgevaer Thanks for this comment! Very interesting :D

@landsgevaer Месяц назад

@@MuffinsAPlenty If you ignore the blocks, the modulo-N *addition* tables always work for any N. Not the most exciting sudoku though... 😉

@NiekLipper Месяц назад

Wouldn't (a+b)^n and a^n+b^n in mod n be the same as: (a+b)^0 and a^0+b^0 which are never equal?

@drdca8263 Месяц назад

You can’t apply the modulo to the exponent like that

@cheweh842 Месяц назад

Finite fields? Galois fields? There's no mention of "field" at all in these videos but isn't that what these are??

@MuffinsAPlenty Месяц назад

There is a relation with finite fields, especially this extra bit. This extra bit proves Fermat's Little Theorem works, specifically, in F_p for primes p. However, the Freshman's Dream for p powers holds in any commutative unital ring of prime characteristic p, not just finite fields.

@iabervon Месяц назад

The ones that are fields are the simple case of Galois fields, but the ones that aren't primes are non-field rings, and the Galois fields whose size is a higher power of a prime do work, but their multiplication and addition tables are different from the clock-arithmetic tables of the same size (in addition to customarily using different notation for the numbers). That is, Z_5 is GF(5) and Z_7 is GF(7), but Z_9 is not GF(3²).

@JamalAhmadMalik Месяц назад

Are these videos always unlisted?

@SgtSupaman Месяц назад

They typically start off by posting these kinds of videos as unlisted with a link from the preceding video so people don't watch them out of order.

@kuriana100 Месяц назад

Comment as to how many times does he say "right". The correct person gets usd 1000

@ADITYA-qt8zd Месяц назад

@Juustoaivo55 Месяц назад

This is no longer the most liked comment on this video

@Psi_Fan123 Месяц назад

*3 days ago* Excuse me what?

@chriswebster24 Месяц назад

I’m pretty sure it is, actually.

@Juustoaivo55 Месяц назад

@@chriswebster24 it is not, it has 4 likes less than another comment reading "Or is it?" in response to this comment which was initially "This is the most liked comment on this video"