KF Math Thread - Discuss Math

Belisarius Cawl said:
But if you've ever solved problems on a site like Project Euler, you'll know that even just integers can be riddled with insanely autistic patterns. (Perfect numbers? What the hell is this shit?)
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lmao yeah. I know. Number theory and combinatorics are what first got me into maths, and I can personally attest to the fact that the most innocent and simply stated questions can have autistically deep elaborations or proofs. Fermat's Theorem comes to mind regarding this. The statement is innocent enough, and plausible with some experimentation, but the real proof only occurred centuries later with an exploiting of some very modern fields of research. Galois Theory and Elliptic Curves come to mind as involved topics.

Belisarius Cawl said:
when I learned about the distinction between countable and uncountable infinity
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The kvetching over this is funny to me now that I read about it. To me, as an analyst, countable infinity is something I can completely enumerate by a sequence (like the integers or rational numbers), while uncountable infinity is something I cannot do that with. That's tangibly what it means to me when doing analysis.

It's a shame Cantor got so much trouble for that. To me, the idea of finitists or ultra-finitists trying to get some "final victory" over mathematicians who accept infinity, or those who accept the Axiom of Choice, is pretty silly. If a mathematician rejects any proof with a notion of infinity, or just the concept of infinity as a whole, I find the provocative idea to be not how this somehow replaces the canonical mathematics but that it presents an alternative way to prove/show certain theorems and that this is possible tells us something about the theorems.

For instance, for some theorems in maths, you require the Axiom of Choice. This is usually seen in practice with invoking Zorn's Lemma. You can plug that in as an axiom in the model, things work out, and it's all good. But sometimes you can come up with an alternate proof that doesn't use the Axiom of Choice, that sidesteps it somehow. Doing so isn't motivated by dispelling the Axiom of Choice in general, as some absolutists on the matter would do, but to show the role that the Axiom of Choice plays in the proof and, by inference, the nature of the theorem being proved.

Belisarius Cawl said:
Same goes for the argument over sqrt(2) that allegedly got a member of the Pythagorean cult killed (though this just might be a sick / amusing story).
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I remember reading a book going over some classical history of mathematics where the author insinuated that the murder was prototypical of the mafia heritage and culture of Sicily, where the Pythagorean cult was based at the time.

Also thanks for the book recommendation! I'll take a look at it later when I got time.
 
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Doubly Punished Snigger said:
Diagonalization
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I'm basically just now hearing about perturbation theory and so can't comment on how it applies to different infinities
Lurker Child said:
It's a shame Cantor got so much trouble for that. To me, the idea of finitists or ultra-finitists trying to get some "final victory" over mathematicians who accept infinity, or those who accept the Axiom of Choice, is pretty silly. If a mathematician rejects any proof with a notion of infinity, or just the concept of infinity as a whole, I find the provocative idea to be not how this somehow replaces the canonical mathematics but that it presents an alternative way to prove/show certain theorems and that this is possible tells us something about the theorems.
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Well basically the long and short of it is that if even someone like me can easily understand how there are infinitely many (but still presumably countably many) prime numbers then a fact like this shouldn't be lost on those who make an entire profession out of mathematics
Lurker Child said:
Also thanks for the book recommendation! I'll take a look at it later when I got time.
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I found the excerpt I was looking for. It would be pretty autismal to quote the entire thing but basically there was a vizier in the court of the caliph in the story who was like "lol get rekt nerd" and the titular "Man Who Counted", one Beremiz Samir, responded:
Beremiz paused briefly and then continued, with a smile, “When the mathematician makes his calculations or looks for new relations among numbers, he does not look for truth with a practical purpose. To cultivate science only for its practical purpose is to despoil the soul of science. The theory that we study today, and that appears to us impractical, might have implications in the future that are unimaginable to us. Who can imagine the repercussions of an enigma through the centuries? Who can solve the unknowns of the future with the equations of the present? Only Allah knows the truth. And it is possible that the theoretical investigations of today may provide, within one or two thousand years, precious practical uses.
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...except in reality here was basically something a bit like G.H. Hardy's A Mathematician's Apology, published not too much later, and we did not have to wait for a few thousand years, only a few decades ... which, in the scheme of things, is basically nothing.
 
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Named User said:
Math is the subject of study for real men because you cannot innovate, design, or build complex things without an understanding of math.

People who want to learn how to code miss the forest for the trees. A programming language is just a tool in the same way a hammer is just a tool. You cannot design Gothic cathedral by just knowing how to use a hammer. Likewise, you cannot create your own graphics engine by just knowing Python syntax.

Whether you’re interested in computer audio, machine learning, ray tracing, data compression, computer architecture, or whatever nerdy thing, math is the shibboleth that distinguishes the real niggas from the bitches. And I’m not talking YouTube trivia math that fake nerds spout, like Gödel’s incomplete whatever the fuck.

Without math, you will be a slave to whatever tool you are using. It’s no wonder four of the seven liberal arts are focused on mathematics.
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What field of math do you think is most important?
 
Advanced combinatorics still haunts me. My female professor was also insane, so that didn't help.
 
Justtocheck said:
Advanced combinatorics still haunts me. My female professor was also insane, so that didn't help.
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I can't comment on the professor part but one of the things I remember being difficult about combinatorics was affirming what I thought was true with some sort of empirical simulation that closely matches what I did with pure mathematics. Then again that was quite a few years ago so maybe techniques I've learned since would help out much more in that regard.
 
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Belisarius Cawl said:
I can't comment on the professor part but one of the things I remember being difficult about combinatorics was affirming what I thought was true with some sort of empirical simulation that closely matches what I did with pure mathematics. Then again that was quite a few years ago so maybe techniques I've learned since would help out much more in that regard.
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Speaking of combinatorics, a thermal physics class is fun, because you're using such big numbers and shit like Stirling's approximation, that being within ten orders of magnitude is considered accurate
 
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MarvinTheParanoidAndroid said:
What field of math do you think is most important?
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PDEs & numerical analysis (the latter of which depends heavily on linear algebra) for physics & engineering.
Algebra (including algebraic number theory & all things combinatorics-related) for computer science.

They're kind of all coupled to physics in the end. I mean you also need statistics & probability theory for physics, too. And engineering. And just like...stuff.

So I guess the answer is, "all of them except topology," because topology's just gay, who cares about shapes.
 
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Hey, if there are any fellow smooth brains trying to learn math above a fifth grade level, I was wondering if you'd be interested in my epic groundbreaking work-in-progress paper titled "Algebra for Retards." I'm learning (or I guess relearning) algebra and I'm also learning how to use LaTeX which is a typesetting thingy for technical documents and math papers and stuff. I learn best by writing the new information down in a semi-formal, well formatted way as if I'm writing notes to teach a class or give a lecture or something. I'm writing a paper in LaTeX that is basically the Wondrium (formerly known as Great Courses Plus) Algebra I course with examples and maybe some exercises to do (the LaTeX math notation is pretty as fuck). Maybe it could add some wrinkles to your brain as I hope it does mine. If this idea's gay and stupid rate me autistic or something and I'll keep it to myself. Seasoned math autists here can impart their wisdom as well and let me know if I'm a retard who's misunderstood the material.

Edit: If people like it I might do the same for Algebra II, Trigonometry, and Calculus. I can see it now; The smash hit free use Kiwi Farms "Math for Retards" series, used in schools across the English-speaking world.
 
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Tsar Nicky said:
Hey, if there are any fellow smooth brains trying to learn math above a fifth grade level, I was wondering if you'd be interested in my epic groundbreaking work-in-progress paper titled "Algebra for Retards." I'm learning (or I guess relearning) algebra and I'm also learning how to use LaTeX which is a typesetting thingy for technical documents and math papers and stuff. I learn best by writing the new information down in a semi-formal, well formatted way as if I'm writing notes to teach a class or give a lecture or something. I'm writing a paper in LaTeX that is basically the Wondrium (formerly known as Great Courses Plus) Algebra I course with examples and maybe some exercises to do (the LaTeX math notation is pretty as fuck). Maybe it could add some wrinkles to your brain as I hope it does mine. If this idea's gay and stupid rate me autistic or something and I'll keep it to myself. Seasoned math autists here can impart their wisdom as well and let me know if I'm a retard who's misunderstood the material.

Edit: If people like it I might do the same for Algebra II, Trigonometry, and Calculus. I can see it now; The smash hit free use Kiwi Farms "Math for Retards" series, used in schools across the English-speaking world.
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LaTeX is based, I don't use docx anymore, I use markdown for quick shit and LaTeX otherwise
 
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Doubly Punished Snigger said:
LaTeX is based, I don't use docx anymore, I use markdown for quick shit and LaTeX otherwise
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Yeah, I really like LaTeX. I've got no practical use for it but I enjoy it a lot because it works a lot like Lilypond, a typesetting program for musical notation which looks a lot nicer than easier-to-use programs like Musescore and Sibelius. Good typesetting scratches my 'tism nicely.
 
OP, please explain to me what a lagrangian is. I do not understand it.

Also please present a proof that 1 > 0. Please help me understand what the hell "delta is greater than epsilon" means, prove the fundamental theorem of calculus, and walk me through the definitions of derivatives and integrals.

ty
 
revenge of rebecca said:
in what ways was she insane? could she at least speak english properly?
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Well, imagine trying to learn math from someone who's having a mild DMT trip and never stops writing numbers or examples. Something like that. It doesn't sound that bad, until you get 3 hours of that with only a 15 min break.

On a sidenote, the Simplex algo was the coolest applied math thing I've ever learned, from the story of its origin to its use in the Berlin Airlift. I just hated the fact that they made us do it by hand in the exam in for 1st year Algebra. I thought it would show how much smarter we were if they gave us a laptop and made us program the simplex algorithm in python and make it work. If a student can do that, he's good. But I understand, not everyone knows programming and it's math so...
 
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I spent my entire morning sick off work making this shit. I'm writing it to help me remember what I'm learning online (I am mathematically handicapped) and to amuse myself as I revise the material but if it could be helpful to other Kiwis I can post it here or elsewhere when I'm done. I've only done three pages because I'm still learning LaTeX but lemme know what you think if you want to, especially if I've made some error like a retard.
 

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Tsar Nicky said:
Hey, if there are any fellow smooth brains trying to learn math above a fifth grade level, I was wondering if you'd be interested in my epic groundbreaking work-in-progress paper titled "Algebra for Retards." I'm learning (or I guess relearning) algebra and I'm also learning how to use LaTeX which is a typesetting thingy for technical documents and math papers and stuff. I learn best by writing the new information down in a semi-formal, well formatted way as if I'm writing notes to teach a class or give a lecture or something. I'm writing a paper in LaTeX that is basically the Wondrium (formerly known as Great Courses Plus) Algebra I course with examples and maybe some exercises to do (the LaTeX math notation is pretty as fuck). Maybe it could add some wrinkles to your brain as I hope it does mine. If this idea's gay and stupid rate me autistic or something and I'll keep it to myself. Seasoned math autists here can impart their wisdom as well and let me know if I'm a retard who's misunderstood the material.

Edit: If people like it I might do the same for Algebra II, Trigonometry, and Calculus. I can see it now; The smash hit free use Kiwi Farms "Math for Retards" series, used in schools across the English-speaking world.
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Here's a free LaTeX header:

Code: 
\documentclass[12pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[urw-garamond]{mathdesign}
\usepackage[margin=1in]{geometry}
\pagenumbering{gobble}

Garamond looks much nicer than Computer Modern Roman
 
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