/mg/ maths general Koblitz edition

talk maths

sites.math.washington.edu/~koblitz/

Other urls found in this thread:

losangeles.cbslocal.com/video/channel/322-cbs2-live-newscasts-and-breaking-news/
en.wikipedia.org/wiki/Linear_map
stitz-zeager.com/),
cimat.mx/~luis/seminarios/Teoria-K/Atiyah_K_theory_Advanced.pdf),
twitter.com/NSFWRedditVideo

I had this guy for calc 1. Couldn't read a god damn thing he wrote on his projector slides.

Could graph theory be applied to find a winning strategy for a car chase?

losangeles.cbslocal.com/video/channel/322-cbs2-live-newscasts-and-breaking-news/

No, but you could use coding and algorithms

Sorry, I'm not mentally diseased.

>implying

So what are you trying to achieve again?

Since you're too autistic to understand, I'm saying you are mentally diseased
It's not funny when I have to explain it user

You're trying to claim that I'm a "platonist" or an "intuitionist". Neither of these hold since I'm not mentally diseased.

t. Actual retard
You think I'm the same person, who followed you from that thread?
>you're too autistic to understand
This statement still stands, and is amplified by the proof you have just willingly provided

>You think I'm the same person
It's a post made by the same account so it doesn't really matter.
>This statement still stands
How so? I'm neither of those things, nor am I mentally diseased.

>nor am I mentally diseased.
Your posts signal otherwise.

definitive texts for precalc?

For calc you hear about stewart, apostol, spivak

for lin alg, theres axler, strang and a bunch of others

For analysis you hear about tao and rudin

are there any books like those for precalculus?

The doctors signal otherwise.

>The doctors signal otherwise.
They likely have not read your posts.

Axler has a book on precalculus, if i recall correctly.

Lang - Basic Mathematics, the canonical precalc textbook.
BTW, there's a cretin lurking here that keeps posting "Lang is a meme", don't listen to him.

>Lang - Basic Mathematics
Lang is a meme.

>BTW, there's a cretin lurking here that keeps posting "Lang is a meme", don't listen to him.
I'm not a "him".

How can I get better for euclidean geometry (as in, 5 Euclid's postulates+some equivalences)? For some reason the first 3 weeks of my Intro to Geometry course is about euclidean geometry.

Most books propose their own axiomatic system, but I want to practice with the one I mentioned earlier. Which book can help me solve some problems? My prof is autistic so there's no (useful) ref books

(pic related, I really struggled trying to prove that the sum of all angles in pic related is 180 degrees)

I visited my grandmother today after her appointment with a doctor. We discussed for hours, and the topics were war, the rotting effects of liberalism and globalism, and category theory.

It was interesting to hear her tell how she would have moved troops along the Eastern front. She then started asking me why the Rocket man is so aggressive, and I compared juche to sogun sasang explaining how that affects things. We then ended up discussing how all the LGBTQFT acceptance is nothing but mentally ill people normalizing mentally ill people, and how American rot is destroying the West. Using this perspective, I made her understand why I would never set my foot on the lost continent.

Then she told me to explain my master's thesis to her, and I did. I motivated Mitchell's embedding theorem by explaining what manifolds are, and then telling how a similar situation can be seen in abelian categories if one has sufficient imagination. I explained how the local concretization puts flesh on the bones of the abstract underlying skeleton. She understood it well enough to call it important stuff. Thanks granny 92 yo!

/blog

Anyone who calls math "important stuff" missed the point of it.

P.S. I am a research mathematician.

I don't remember asking for your opinion.

P.S. I am the backbone of these threads.

It's clearly important for anyone studying it.

This!

Neumann's Separation Lemma: Let [math]G[/math] be a permutation group acting on an infinite set, [math]\Omega[/math] with no finite orbits. Then for any finite subsets, [math]\Gamma[/math] and [math]\Delta[/math] of [math]\Omega[/math] ,there exists a permutation [math]g\in G[/math] for which [math]\Gamma^{g}\cap \Delta = \emptyset [/math]

can someone explain this

Write out what it means to take the Laplace transform of a function, and then T H I N K.

what does sgn(T) refer to, when T is a normal operator on a Hilbert space?

beautiful math incoming:
en.wikipedia.org/wiki/Linear_map

Pre-calculus: Stitz & Zeager (stitz-zeager.com/), Axler (Precalculus: A Prelude to Calculus) or Stillwell (Numbers and Geometry)
All three are pretty rigorous and I would argue Stitz & Zeager is best one of them but is rather lengthy so you might be better off with Apostol. (Also you could unironically use Lang's Basic Mathematics... While not recommended it's still doable as a precalculus book)

Calculus:
Rigorous; Spivak, Lang or Apostol
Intuitive/Introductory; Stewart
Go with Stewart only if you plan on becoming an engineer or only do mathematics because it's mandatory

The laplacian is a linear application under holonome constraint

Is it wrong that I automatically dismiss a maths book if the author is a woman?

Change my view, lads. What maths books with female authors are worth reading?

>Is it wrong that I automatically dismiss a maths book if the author is a woman?
There are female authors? How did I not know this, spivak BTFO

The definitive work on computable structure theory was written Julia Knight. Also the article in the handbook of recursive mathematics on Pure and Computable model theory was written by Valentina Harizanov.

>I really struggled trying to prove that the sum of all angles in pic related is 180 degrees

Out of curiosity what was the correct way to prove it? I'd do something like drawing parallel lines (pic related) not sure if it's a valid proof though.

Wait? That Spivak guy is a woman?

My prof wrote a pretty good book on rigorous geometry. Check out Mark Solomonovich's Geometry.
He does everything as the Euclideans do but with good explanation and examples and drawings

In general, reading mathematics written by a human female is not worth it. There are some exceptions.
>What maths books with female authors are worth reading?
Topos annelés et schémas relatifs.

>rigorous geometry
what do you mean?

Anything by Claire Voisin, in particular "Hodge Theory and Complex Algebraic Geometry"

so your opinion of the ontological status of mathematical objects is neither that they are realized by computation, that they have independent, objective existence, nor that they are fundamentally mind-internal. What *do* you think, then?

I took real analysis and immediately switched to app math major

I have no idea how you guys do proofs. I just have no idea where to take them once I get started.

Ex prove sqrt(2) isnt rational. i know now you do contradiction but i have no idea how whoever came up with that chose proof by contradiction. and once you get to the part p^2 = 2 * p^2 idk how the fuck you knew that implies p/q is even (i know how, i just didnt think to look for it) which contradicts something earlier

you people are fuckin crazy

>they are fundamentally mind-internal
This does not uniquely determine "intuitionism" or "platonism".

No, it's not wrong since most of them are garbage. Forget the whole "maths" part, it applies for all books.

Not even a women hater, just being honest here.

it's entirely a matter of practice. i once felt exactly the way you do

So what's your position?

>I took real analysis and immediately switched to app math major
This makes no sense. Real analysis is a part of and is actually exclusively studied by "app math majors" and engineers.

i know
but i took it as an indicator that i would blow at further theory courses so i resigned myself to codemonkey

The thing I quoted would be the closest to my position. Although this discussion is hardly relevant to a mathematics thread.

are you trying to imply that R is not an extremely important object in massive swathes of mathematics

>theory courses
What the hell is a "theory course"?

>an extremely important object in massive swathes of mathematics
In what sense?

It takes practise like everything else, eventually you'll get the feel for it and you can often guess what kind of proof would probably be efficient for whatever you're trying to prove. Obviously most things can be proven in multiple different ways too, sometimes a certain approach is just easier and/or more elegant than the others. Also, coming up with a new proof for some new problem often takes long.

>tfw when you see everyone that struggles with probability

>tfw struggled with probability but still aced that shit after ramping up the effort

Can't relate to meeting people who study probability (aka engineers) on a regular basis.

are you fucking serious
- almost anything topological is gonna involve R at some point or another
- C is built on R and is pretty fucking important in algebra
- I hope I don't have to tell you that the zeta function, which is C -> C, is extremely significant in number theory

>not going balls deep in probability theory
Do you hate fun and comfy

What kind of demented notion of fun and comfy do you have?

>not majoring in mathematical engineering
Do you hate money?

The only comfier area/course I have studied is complex analysis desu
t. too brainlet for abstract algebra

>not majoring in mathematical statistics
Do you hate money?

low-level abstract algebra is not harder than complex analysis

>not majoring in applied mathematical actuarial science
Do you hate money?

>low-level abstract algebra
What do you mean specifically?

Didnt stop me from being too stupid to really understand sylows theorems while also almost acing complex analysis
>tfw actually taking a course in insurance mathematics
300k starting

stuff like elementary group theory

what do you mean by "really understand"

Reliably solving questions on tests where you need to use sylows theorems is my definition of "really understand", but it probably had to do more with a shaky foundation of abstract algebra to begin with

you do realize this is a thread on Veeky Forums, nothing worth putting on a resume, bub

I care little for such petty things.

rate my proof

better:
if (p/q)^2 is an integer, then the prime factors of q^2 are subsumed in p^2; but since squaring only doubles the multiplicity of each factor, this means that the prime factors of q are subsumed in p, in which case p/q is an integer. therefore, rational square roots of integers are always integral, but no integer is a square root of 2.

>that retarded [math]\times[/math] symbol instead of [math]\blacksquare[/math]
It's trash.

You need to state that p and q are integers. and that K is an integer. Other than that, it's fine if a bit clunky.

Nobody cares bitch
>

That's not a proof.

>You need to state that p and q are integers.
This is clear from the definition of [math]\mathbb{Q}[/math].

Well he let q^2=K which works for proving rad2 is irrational. But if he had to prove rad3 is irrational, he wouldve had to let q^2 = 2k/3 which wouldve violated q being an integer.

So I guess I more said that to get him to think about that.

Exactly. I'm almost sure that using an equivalence of the 5th postulate you can draw the parallels, and using an equivalence of the 4th postulate the angles are equal

THANKS

If anyone else ITT has something I'd be very grateful, my grades depend on this

How would you formulate equivalence classes under a fuzzy logic system?

Define p and q as integers with q not 0. Also state that p and q have no common divisors except 1, or you could say their gcd is 1 instead. You should include an argument why 2 divides p^2 implies 2 divides p. It's because if a prime k divides a product ab, then it must divide a or b. I wouldn't set K and J, it makes it harder to read and it's obvious that if p and q are integers then so are p^2 and q^2.
>an even number divided by an even number is even
This is not true, consider 2 divided by 2, giving 1 which is not even. It's true for 4q^2 though since any even number divided by a smaller even number is even and q^2 must be greater than or equal to 1. This is also why it is valid to say that 2q^2/2 is even thus q^2 is even, since q^2 is greater than or equal to 1, so 2q^2 is greater than or equal to 2.
A cleaner argument for q being even is that since 2 divides p, 4 divides p^2, thus p^2=4k=2q^2 thus 2k=q^2 and 2 divides q^2. Thus by the same argument 2 divides q.

>you can get away from any set if you translate it enough
Wow amazing.
What are its properties? I've never seen it defined even in Von Neumann's book on QM.
Neither is any level of abstract algebra.
Sorry but you won't be able to get into our topology club with that trash.

Everything is proven from the ground up, starting with undefined notions (axioms we believe to be true but cannot prove, such as the existence of planes, points, and lines), the existence of isometries, then proving things one step at a time and using old proofs to prove new ones and so on. Nothing is taken for granted and everything must have solid logic and come from the given/built theories. It's the same as most math courses with proofs, but many geometry books/classes take certain things for granted and use wrong notions.

Actually the proof isn't correct since an even number divided by an even isn't guaranteed to be even. Any number with a single factor of 2 in its prime factorization is odd when divided by 2. So you need to use the argument that 2|p implies 4|p^2 then use that to get 2|q^2.

>normies get out of my group

Refer to that's where your kind belongs.

Forget it, that book isn't really helpful to me. Fuck.

The whole idea of linear systems is that I can find a basis spanning the set of solutions under addition, since if [math]g[/math] is a solution and [math]f[/math] is a solution, [math]f+g[/math]

I've wondered if there are non-linear systems where you can form a basis under a different operation.

For example, if [math]f[/math] is a solution, and [math]g[/math] is a solution [math]O(f,g)[/math] is a solution where [math]O[/math] is some operator. In the case of linear systems it would just be [math]O(f,g)=f+g[/math].

You could do something sort of like Fourier series for non-linear systems except it wouldn't be a series, it'd be iteration of the operator [math]O[/math]

Is this the right order of math? If not fix it.

Counting to 100
Addition
Addition of Large Numbers
Subtraction
Subtraction of Large Numbers
Multiplication
Division
Probability
Geometry
Pre-algebra
Algebra 1
Algebra 2
Trigonometry
Statistics
Pre-calculus
Calculus I
Calculus II
Calculus III

whats after calc 3?

my uni offers a phd in engineering math
is it a meme? what kind of job would it be useful for?

Linear algebra
Ordinary differential equations
Partial differential equations
Real analysis
Abstract algebra
Complex analysis

...

Attached: IMG_20180310_221350.jpg (4160x2336, 2.39M)

If you don't understand what I did here: , I just transported the alpha line to the intersection of the beta line and L1, then the alpha+beta line to the intersection of the gamma line and L1, etc

Well, the first thing you'd realise that it would be extremely hard to prove it in any other way, considering the definition of irrational - ie: a number that is NOT rational.

I've never touched group theory or lie algebras before. I just want a cursory understanding so I can try and understand what this one paper is saying when they bring them up in a proof, whats a fairly easy and quick resource for this? I don't need it to be especially rigorous.

Be honest: will you ever lose your virginity?

In Atiyah's K-theory page 6 (cimat.mx/~luis/seminarios/Teoria-K/Atiyah_K_theory_Advanced.pdf), he defines a covariant functor of one variable [math]T[/math] from finite dimensional vector spaces to finite dimensional vector spaces to be continuous if the map [math]T:\hom(V,W)\to \hom(T(V),T(W))[/math] is continuous (with the usual topology of hom being that of [math]\mathbb R^n[/math]). Then he develops some theory and claims this works too for functors of more than one variable, although he doesn't give an explicit definition of continuiity in this case. What I think a possible definition could be is (eg, 2 variables):

[math]T[/math] is continuous if the map [math]T:(\hom(V_1,W_1),\hom(V_2,W_2))\to\hom(T(V_1,W_1),T(V_2,W_2))[/math]

Does this look right?

Actually I think a better definition is continuity of the map [eqn]T:(\hom(V_1,W_1),\hom(V_2,W_2))\to\hom(T(V_1),T(W_1)\times\hom(T(V_2),T(W_2))[/eqn]