KF Math Thread - Discuss Math

[Anti Snigger]

Imaginaries would also be like that and obviously complex numbers, since even if you presuppose the ability to make an infinite list, you can always come up with a number that isn't in that list, i.e. go down the entire list, take the first digit of the first number, change it, second, change it, until you now have a number that isn't in the original list. And of course you can keep doing that forever. That was Cantor's idea.

Damn you are a renaissance man, did you study any math in undergrad by chance?

 

[AnOminous]

Damn you are a renaissance man, did you study any math in undergrad by chance?

Just calculus, because I was embarrassed by how badly I fucked it up in high school. I did ace that, but no number theory or anything really advanced. And I still suck at it. The most advanced math I've used after school was a little trig for some simple land surveying shit.

 

[soup peddler]

My brother is a mathematician, so our collective Thanksgiving usually hosts 4-5 international mathematicians who want to celebrate the holiday. For those who had a suspicion, I can personally verify that the number theorist is the most autistic of them all by a landslide

 

[Private Tag Reporter]

Hello Gentlekiwis,

I have been generously invited to this thread by @y a t s . I've been told to ask here for recommendations in order to learn maths.

My working experience of mathematics doesn't extend meaningfully beyond that of an American High-School, so I don't really know where to start, other than a passing interest in learning Calculus. What's the most interesting fields and where should one start to improve their knowledge?

Merry Christmas.

 

[名無し]

What's the most interesting fields and where should one start to improve their knowledge?

Linear Algebra was my first foray into harder mathematics. It is used to solve nontrivial problems, and the thinking behind it is broadly applicable to higher math. Two books I can recommend on the subject are Linear Algebra and Its Applications by David C. Lay, a basic textbook that is meant to be accessible, and Linear Algebra by Kenneth Hoffman and Ray Kunze, a much moral formal text that tries instead to ground itself in rigorous proofs.

You may also find the above complemented by an understanding of logic as presented in Logic the Laws of Truth by Nicholas J. J. Smith.

If all else fails you can also consult:
https://wiki.installgentoo.com/wiki/Math_Textbook_Recommendations
https://wiki.installgentoo.com/wiki/Mathematics

 

[Kosher Dill]

What's the most interesting fields and where should one start to improve their knowledge?

If you're looking to go deeper in math, the first thing you should do is learn the language of abstract mathematics.

I liked this book well enough:

https://www.math.uwaterloo.ca/~wgilbert/Books/MathThinking.html

(Surely available on your local pirate ship)

This will get you started with the ABCs of further mathematics: proofs, induction, defining the number systems and functions, and some of the most famous classical results. (You don't need to finish the entire book)

The topic in general might variously be called "intro to discrete mathematics", "classical algebra", or similar.

 

[y a t s]

I liked this book well enough:
https://www.math.uwaterloo.ca/~wgilbert/Books/MathThinking.html (Surely available on your local pirate ship)

This looks very similar to waterloo's (free) in-house book for their Math 135 class, which covers the same intro topics. Good book made by some nice lads.

 

[Belisarius Cawl]

My working experience of mathematics doesn't extend meaningfully beyond that of an American High-School, so I don't really know where to start, other than a passing interest in learning Calculus. What's the most interesting fields and where should one start to improve their knowledge?

There are a bunch of people in this thread who are waaaaay better at math than I am but I just wanted to say that programming is definitely a way to make math more accessible and even more vivid. I don't do too well with the axiom-theorem-proof format except with the style of logic proofs you can see in books like Copi and others, where it's possible to check the correctness of an inference by syntax alone. (In general, writing proofs seems to me a bit more of an art form, if you can believe it, even though there are hard rules.) I'm under the impression a lot of people find the axiom-theorem-proof format kinda dull too, even if it is necessary. Programming will definitely put the rigor of your thinking to the test, as you will get nonsense answers or the compiler shitting itself if every detail isn't hammered down, and the result is often something that you can immediately benefit from in other ways. Also, writing in human languages inevitably leads to vagueness, even when the author is careful. As a result, even in some Springer books that tend towards a more traditional approach to exposition, you will see passages that look like this:

It's definitely a very valid different point of view as compared to math as one typically learns it in school. It occurred to me while programming Smalltalk, which does not have algebraic order of operations like most other programming languages do (that instead has to be enforced with parentheses where not typically used) that PEMDAS is just one possible convention out of many. (I suspect prioritizing the "EMD" part over the "AS" part might have to do with the fact that traditionally applied math pretty much all had to do with physics and chemistry where the former operations are more important than the latter, though there could be other reasons.) When you learn to program, no field of mathematics or area of application (or lack thereof) will be off limits to you. Logic (obviously), set theory, probability, calculus, linear algebra, you name it. You can even explore the very foundations of mathematics, though that's best left for others here to explain. Also, SageMath is a very nice free and open source computer algebra system that ties a zillion different software packages together with Python. One last thing to consider: "Beware of bugs in the above code; I have only proved it correct, not tried it." —Donald Knuth

 

[Belisarius Cawl]

One other point which my last one reminded me of: here is an excerpt from the preface of Raymond Smullyan's puzzle book The Lady or the Tiger:


You can find a lot of good math and logic puzzle books out there. (You can even DM me for the complete list of what I have which can be found on Annas Archive or whatever.) Some of these puzzles can be solved by bright middle or even grade schoolers but it's possible to really go off the deep end with others.

 

[y a t s]

PEMDAS is just one possible convention out of many. (I suspect prioritizing the "EMD" part over the "AS" part might have to do with the fact that traditionally applied math pretty much all had to do with physics and chemistry where the former operations are more important than the latter, though there could be other reasons.

I believe this is more a result of how linear systems behave in general, like how the unique representation theorem states that for any vector v, we can express v as a unique linear combination of its basis vectors. The AND/OR relationship between multiplication and addition appears everywhere, and I argue you can derive the rest of the operation ordering from this.

 

[Belisarius Cawl]

I believe this is more a result of how general linear systems behave, like how the unique representation theorem states that for any vector v, we can express v as a linear combination of its basis vectors. The AND/OR relationship between multiplication and addition appears everywhere, and you can arguably derive the rest of the operation ordering from this.

I did see something like that while doing a little research. Sometimes there can be multiple reasons for the same outcome!

 

[Anti Snigger]

What's the most interesting fields and where should one start to improve their knowledge?

'Interesting' is going to be subjective. My honest recommendation would be to find things in the world that you're already curious about and familiar with, and look into the mathematical backing behind it. I like to think of math as the study of games, of things with rules, and if you approach it with that attitude it'll just be fun.
I know this is a bit of a cop out, but I do think necessity and intrigue are great catalysts for understanding.

 

[AnOminous]

'Interesting' is going to be subjective. My honest recommendation would be to find things in the world that you're already curious about and familiar with, and look into the mathematical backing behind it. I like to think of math as the study of games, of things with rules, and if you approach it with that attitude it'll just be fun.
I know this is a bit of a cop out, but I do think necessity and intrigue are great catalysts for understanding.

I think a perfect example of this is Feynman's QED, about quantum electrodynamics. It's a pop science book, about light and matter, but it explained fairly complex mathematical ideas to me in a way I thought I was too retarded to understand beforehand.

 

[Sulla]

A math thread?

Math is for NERDS

 

[Alex Hogendorp]

Mathematics interest me the same way language does. I love to fuck around with numbers, graphs and other shit and experiment with them.

 

[Sparkletor 2.0]

Can anyone check the math here and see if @SamanthaPrater is correct?

( 1* 1 ) 6 + 5= ?

1 X1 EQUALS 1 SO DIVIDE THAT BY SIX. PLUS FIVE.12.

THE ANSWER IS 12.

EASY PEASY.

(1 x 1)6 + 5 = 12?

 

[Vecr]

Can anyone check the math here and see if @SamanthaPrater is correct?


(1 x 1)6 + 5 = 12?

I don't see a divide in there at all. It's either 11 if you assume it's supposed to be a multiply or 5.1666... if you somehow insert a divide.

Or maybe it's supposed to be 0.090909090... if the divide is a horizontal bar and 6 + 5 is below it.

 

[Sparkletor 2.0]

I don't see a divide in there at all. It's either 11 if you assume it's supposed to be a multiply or 5.1666... if you somehow insert a divide.

Or maybe it's supposed to be 0.090909090... if the divide is a horizontal bar and 6 + 5 is below it.

One times six, plus five.

 

[Sulla]

Can anyone check the math here and see if @SamanthaPrater is correct?


(1 x 1)6 + 5 = 12?

Most of the mathematically illiterate on this site will say "Um acktually, it adds up to 11, so 12 can't be the answer."

I being an enlightened physicist have been trained to know that there is a hidden dark number in the equation that lets it add up to the observed 12.

 

[Anti Snigger]

Can anyone check the math here and see if @SamanthaPrater is correct?


(1 x 1)6 + 5 = 12?

1 x 1 = 2, per Terryology