/mg/ - maths general

[Anonymous No.15796375]

A* edition
previously >>15777384
Discuss maths

[Anonymous No.15796408]

Has anyone here done all the exercises in the book of proof? And proooooovers in the house tonight?!?!?

[Anonymous No.15796411]

I wish I had a copy of logic by smith.

[Anonymous No.15797247]

>>15796408
"How To Read and Do Proofs" by Solow is very
good. Very instructive and has a table of proof
techniques in the front and back covers.

[Anonymous No.15797359]

[Anonymous No.15797370]

There are four Americans, seven Canadians and nine Europeans, randomly arranged on a line waiting to buy a lottery ticket. There are 17 lottery tickets left on the shelf. One (and only one) of those tickets will win you the price.

What is the probability that an American will win the price?

[Anonymous No.15797376]

>>15797370
assuming each of the first 17 people purchases a ticket, still 1/5. The 17 is a red herring, doesn't matter how many tickets are left on the shelf as long as it's no more than the number of people in line

[Anonymous No.15797495]

>>15796375
A* is fucking gay, you might as well just do a breadth first search

[Anonymous No.15797572]

Why are propositions taken as primitive notions? If a proposition is a placeholder for a copula joining a noun to a complement then that would be making a positive claim about nouns, and distinctions between them, yet is hidden from view and held as the primitive notion of proposition. Of course, the multiplicity of propositions is also taken as a primitive notion. If you had multiplicity of nouns, or even stricter, a multiplicity of physical things, that would be asserting the existence of places aswell. So why are propositions taken as primitive notions when it is clear that a rich frontier of mathematical study underlies their existence?

[Anonymous No.15797597]

>>15797572
>proposition
>noun
Context?

[Anonymous No.15797603]

>>15797597
what do you mean. I mean like what a proposition represents. So if the proposition is a sentence it would have a subject and a predicate which would either directly mention nouns, or imply the existence of a noun.

[Anonymous No.15797622]

>>15797603
lil b, a proposition is different from a preposition

[Barkun No.15797624]

>>15797622
chikki

[Anonymous No.15797625]

>>15797247
Imma buy this book. Thanks for the suggestion.

[Anonymous No.15797626]

>>15797622
I'm talking about propositions. I never mentioned prepositions though.

[Anonymous No.15797807]

Do you think there could be an easy method to solve all optimization problems?

[Anonymous No.15797913]

Any thoughts on learning math with multiple languages?

I'm an American, and grew up going through the American curriculum, but I always sucked at math. Probably because I wasn't paying attention somewhere and had holes in my knowledge.

Fast forward to now, I live in Japan and speak fluent Japanese. Now I decide to learn re-do high school math, but with Japanese textbooks (because why not lmao).
Suddenly, I understand everything and I hardly ever get tripped up (It's not just remembering old concepts, since I never really did trig). Even when I do, I tend to figure it out in a few minutes/few days max. (I'm doing algebra, trig, and geometry at the same time. It's integrated in Japan)

Now, I'm using a Japanese textbook, but I write my notes in English. So I have a feeling that the process of "translating" my thoughts from one language to another helps to ensure that I digest all information before translating them, leading to a stronger understanding of concepts.

Also, possibly relevant that the textbook I'm using has worked answers for every problem. (Never seen this in the U.S.) I'm also using Anki to memorize all of the formulas and to practice problems on a regular basis, which has really helped accelerate my progress. I'm basically doing 1 high school class worth of learning in 1 month, so I should be done up to calc 1 in 4 months or so.

[Anonymous No.15797938]

>>15797913
That's what every non american studying pure math does as a lot of books are available in English. I don't think language has any effect on laerning math except that you may have easier time explaining it in the language you've learnt it.

[Anonymous No.15797950]

>>15797938
Wait, so only having answers to odd problems is an American thing? (Hardly ever fully worked, either)

I guess American math education just suck ass, then? Though, it probably helps that I'm a motivated adult using SRS, but still.

[Anonymous No.15797961]

>>15797913
>Also, possibly relevant that the textbook I'm using has worked answers for every problem.
cool. i think i woudl prefer that with fewer problems to more problems without worked answers desu

[Anonymous No.15798104]

>>15797807
Of course.

Suppose the cost [math]C[/math] of running some system or whatever is the function of n variables. So [math] C = C(x_{0.999\dots}, x_2, \dots, x_n)[/math]. Just let [math]\matbf{x} = (x_{0.999\dots}, \dots, x_n)[/math] so that [math] C = C(\mathbf{x})[/math]. Then just take derivative w.r.t. x, set equal to zero, solve and you're done.

[Anonymous No.15798141]

What are the best arguments for defining Pi by the first positive zero of sine?

[Anonymous No.15798195]

>>15797950
I just meant that nowadays cutting edge math texts are primarily published in English, so virtually every publishing mathematician would know English to a certain degree at least. You can also get to pretty much any area of modern math by only knowing Russian or French or some other language, and there are also untranslated good books in them, but not knowing English would severely limit your available study material at undergrad level already.
If we speak about highschool mathematics or any type of math engineers study, then there's no reason to know English. Also I know many Russian olympiad or pure math books aimed for highschoolers, and I don't know if there are many such books in English.
Math education sucks in Russia too in general, there just are a few really good schools, where many students nail olympiads easily. I think it's the same in the US, afterall you have someone preparing your Chinese for the IMO. Although maybe in the US it's impossible to get into such an environment for free.

[Anonymous No.15798204]

Find the straight line that intersects the point P(3, 1) and forms an angle of 45 degrees with
t : 2x + 3y - 1 = 0 . How do I solve this?
.

[Anonymous No.15798259]

Good morning aspiring mathematicians!
I fucking hate matlab, r and python so much it's unreal.

[Anonymous No.15798278]

>>15798259
what about latex

[Anonymous No.15798310]

>>15798204
look up the dot product

[Anonymous No.15798312]

>>15798141
Wouldn't make sense. Radians are a construct invented for convenience, and trig functions are constructed on top of them. Pi is baked into trig functions as part of how those functions are defined, it would be circular (no pun intended).

[Anonymous No.15798319]

>>15798104
I want to see you solve the traveling saleman problem with this approach.

[Anonymous No.15798347]

I'm working on a scizo post, just give me a couple more days

[Anonymous No.15798562]

>>15798312
It's a perfectly cromulaent definiantion.
https://us.metamath.org/mpeuni/df-pi.html

[Anonymous No.15798661]

Rate my recent purchases. After quickly poring through the books, they seem rather complete and to the point. I want to get these subjects down before I study higher level physics.

What annoys me is I had dedicated undergrad classes in complex numbers and Fourier series, but conveniently, the two professors at the helm were garbage. Truly nice people but garbage professors. Hoping to properly understand the math now.

[Anonymous No.15798669]

>>15798141
lets you define pi purely analytically without referring to circles
>>15798312
sin can be written as a power series

[Anonymous No.15798969]

this board generally seems to know more math than physics

[Anonymous No.15799432]

>>15798969
thats cause physics is hard.

[Anonymous No.15799584]

lets take a random x∈⋃n∈N[−n,1/n)

that means [math]\exists n \in \mathbb{N}: -n \leq x \leq 1/n [\math]
we know that n >=1 and by the conditions we are given x>=-n and x<1/n. We know that -n goes to -infinity, therefore can say....

because 1/n<=1, for all natural numbers, then we know that x<1, for all natural numbers therefore the union is equal to (-inf;1)

can anyone fix my proof and write how i can prove that x being >=-n means that the set goes to -inf? also if I have an intersection can i also use the \exists n that belongs to N: .... the same way?

[Anonymous No.15799590]

>>15799584
lets take a random [math]x\in \bigcup_{n\in \mathbb{N}}[−n,1/n)[/math]

that means [math]\exists n \in \mathbb{N}: -n \leq x \leq 1/n [/math]

[Anonymous No.15799696]

Hey guys, starting out math major
I hate waking up early and all my lectures begin early
Will it be bad if I skip all math lectures ?

[Anonymous No.15799727]

>>15798969
it's harder to troll math threads. physics gets all the /x/ and /pol/ rejects.

[Anonymous No.15799738]

>>15799696
Not necessarily, as long as you're teaching yourself through the book, but you will be missing out on the last remaining time in your life when you can go and learn math in-person from experts

[Anonymous No.15799740]

How do I write in logic that a proposition caused another proposition? Like where the first proposition precedes the second in time.

[Anonymous No.15799771]

Start with the two "marked" points 0,0 and 0,1 in R^2. Draw every circle that has a marked point as a center and another marked point on the circumference and mark the intersections. If you recursively do this you end up with the constructible numbers.
If, however, you only construct one circle per iteration (choosing from the marked points randomly and uniformly), do you eventually get the constructible numbers or do you get a finite set?

[Anonymous No.15799788]

Best way to re-learn math? Calc, diff eq, linear algebra, everything?

[Anonymous No.15799805]

>>15799740
'let P1 represent [proposition], then...'

[Anonymous No.15799862]

>>15799788
Depends on how far you got the first time.

[Anonymous No.15799888]

When you have a caterpillar metamorphizing into a butterfly the proposition 'it is a caterpillar' is true at the beginning but is false at the end, it becomes less and less true over time.
If you have a bird and retrace its ancestry, the proposition 'this ancestor is a bird' is true at the start, but by the time you reach non-avian dinosaurs it isn't true. So it becomes less and less true as you go back. There's no one point you can mark off saying that the ancestor being a bird stops here, and that the next ancestor is a dinosaur. There are some that are both birdlike and dinosaur like.
So truth values for the proposition that the ancestor was a bird would be just be true or false, it would have varying levels of truth.
One of the earlier ancestors less birdlike features and more dinosaur like features could be called a bird and it could be taken as true, but one of the later ancestors could be called a bird, and the claim would have more weight to it. The latter ancestor is a better example of a bird than the dinosaur like one. So for claims 'x is a bird' there would be options for x that would be better examples of a bird, and options for x that would be worse examples of a bird. And the truth of the statement wanes as the example becomes worse.

[Anonymous No.15799892]

>>15799888
>So truth values for the proposition that the ancestor was a bird would be just be true or false
wouldn't be just true or false, I meant

[Anonymous No.15799917]

>>15799862
Far enough to get a b.s. in physics

[Anonymous No.15800054]

>6 hour final exam
>it's just a single page with two questions
you just know you are in for some real violent ass rape with the most obtuse questions ever conceived by man.

[Anonymous No.15800328]

are there esteemed 'rudin'-esque books/book series for set theory? preferably self contained, good exercises, containing naive set theory and beyond (modern set theory ideas like forcing, etc.) ?

[Anonymous No.15800329]

[Anonymous No.15800344]

>>15797370
The probability for any particular American is one in four but for the winner to be any of the Americans is one in one because the Americans would have shot the Canadiens and Europeans, all of whom would be helpless against the American attack. Knowing that each other are armed, none of the Americans would attack a fellow American.

[Anonymous No.15800368]

>>15800328
Thomas Jech, Set Theory: The Third Millenium Edition (Springer 2003)

[Anonymous No.15800408]

>>15799788
why are there so many people on here that want to relearn math? I see this question at least 3 times a week. Why do you want to relearn math? Why not just move on to interesting new math while refreshing the old stuff as you need it. It hasn't disappeared from your mind if you learned it once, even if you didn't know it very well back then, you'll be able to quickly pick it up again. Go learn some new math, like dynamical systems or analysis or algebra or combinatorics or something, there are so many exciting possibilities. You will have to reference back to what you learned in the past, but guess what, everyone has to. This is exactly how you achieve mastery of what you have learned, being forced to apply it to a new context.

[Anonymous No.15801097]

I'm thinking about sequences of arbitrary tuples. A basic example is the sequence [math] {1}, {1,2}, {1,2,3}, {1,2,3,4}, \cdots[/math].
If we order all finite tuples in an infinite matrix like so:
[math] \begin{matrix} {1} & & & & & & \cdots \\ {2} & {1,1} & & & & & \cdots \\ {3} & {2,1} & {1,2} & {1,1,1} & & & \cdots \\ {4} & {3,1} & {2,2} & {2,1,1} & {1,3} & {1,2,1} & \cdots \\ {5} & {4,1} & {3,2} & {3,1,1} & {2,3} & {2,2,1} & \cdots \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots \end{matrix} [/math] and join each element of the sequence with a curve, the curve is monotonically decreasing.
So here's the question. For any (non-piecewise) property p that we can use to define a sequence of tuples, whether the sequence is finite or infinite, is the curve plotted on top of this matrix always monotonic?

[Anonymous No.15801099]

>>15801097
Correction: the bit at the top is meant to read (1), (1,2), (1,2,3), (1,2,3,4), ...

[Anonymous No.15801160]

>>15799696
Yes it will be bad. Learn to go to bed early and rise early. A lot of you young guys will think it’s all about the right textbook and just being an isolated nerd, but the social and community aspect is very important. Get to know your class mates and professors, you never know when a connection with any one of them could be crucial in moving forward. I wish I was more social in my undergrad. It’s my biggest regret.

[Anonymous No.15801289]

>>15801160
this
even just verbalizing what you have learnt and done for exercises helps tremendously
i remember reducing my academic advisor talks to >ok >yes >good >see you next time - even just chatting about what you like, if there are links between this thing and that thing
use the availability of the community around you, you will sorely miss it when its gone

[Anonymous No.15801627]

can anyone explain the connect between the equation (sort of) for a circle
[math] \displaystyle
y = \sqrt{1 - x^2}
[/math]
and the integral form of arcsin
[math] \displaystyle
\arcsin(x) = \int \frac{dx}{\sqrt{1 - x^2}}
[/math]
?

[Anonymous No.15801641]

>>15801627
Derivative of arcsin is 1/cos(arcsin(x)), so you need to show cos(arcsin(x)) = sqrt(1 - x^2). Let u = arcsin(x); now this says cos(u) = sqrt(1 - sin(u)^2), which is true

[Anonymous No.15801773]

>>15799696
Math is just discipline. I'm an absolute idiot, but have the willpower and interest, and have forced my way into graduate school. If you don't have the strength to get up early, you will not be able to hammer your head against a problem for days at a time in a game of chicken until it gives and you win.

[Anonymous No.15802907]

[math] \begin{matrix} & \\ & \end{matrix} [/math]

[Anonymous No.15802988]

>>15801641
>Derivative of arcsin is 1/cos(arcsin(x))
you already lost me

[Anonymous No.15803005]

>>15802988
arcsin is the inverse function of sin, use a Calc 1 formula for finding derivative of an inverse

[Anonymous No.15803169]

>>15801773
I haven’t made any progress on anything between vidya, basic assignments, and work tasks. I’m way behind on my reading for this semester too. I want to spend the weekend casually reading/doing problems from books. It would be really fun and maybe next week I can really get going again.

[Anonymous No.15803186]

>>15803005
>use a Calc 1 formula for finding derivative of an inverse
huh, never saw that before. thanks.

[Anonymous No.15803388]

>>15803186
the formula is trivial do derive and not worth memorizing
y = arctan(x)
tan(y) = tan(arctan(x)) = x
then differentiate with chain rule, and algebra/trig it back to terms of y' and x. works for trig, hyperbolic trig, natural log, log_a(x), a^x

[Anonymous No.15803542]

What are some books about the theory behind math

[Anonymous No.15803772]

Is it true that:
[eqn] P \left( \bigcup_{i = 1}^{ \infty} A_i \right) = \lim_{n \to \infty} P \left( \bigcup_{i = 1}^n A_i \right) [/eqn]

[Anonymous No.15803783]

>>15803772
Yes, this follows from countable additivity of probability.

[Anonymous No.15803788]

>>15803772
Yes, let
[eqn]B_k = A_k \setminus \left( \bigcup_{i=1}^{k-1} A_i \right) [/eqn]

then [math]\bigcup_{i=1}^n A_i = \bigcup_{i=1}^n B_i[/math] and the [math](B_i)[/math] are all disjoint so by sigma-additivity
[eqn]P \left( \bigcup_{i = 1}^{ \infty} A_i \right) = P \left( \bigcup_{i = 1}^{ \infty} B_i \right) = \sum_{i=1}^\infty P(B_i) = \lim_{n \to \infty} \sum_{i=1}^n P(B_i) = \lim_{n \to \infty} P \left( \bigcup_{i = 1}^n B_i \right) = \lim_{n \to \infty} P \left( \bigcup_{i = 1}^n A_i \right) [/eqn]

[Anonymous No.15803796]

>>15803783
>>15803788
Ok.

[Anonymous No.15803822]

Is there a proof of the Second Borel Cantelli lemma that does not use exponential inequality?

[Anonymous No.15803981]

>>15801627
X=sin(y). Take an implicit derivative wrt x so you have 1=cos(y)y’ or y’=1/cos(y)=1/cos(sin^-1(x)). Then draw a right triangle in the unit circle to understand what cos(sin^-1(x)) is

[Anonymous No.15804005]

>>15803542
Take a look at >>15803818

[Anonymous No.15804049]

Teach me diff eq in 3 posts or less.

I get that you have to add boundary condition to the integrated equation.

I'm in PhD mass heat transfer class and about to fail. I made fun of math until I needed it.

[Anonymous No.15804066]

>>15804049
You have an equation that contains a function, you must define the function in such a way that the equation is true, or find all the functions/class of functions that make the equation true.

Find the input (function) to make the output (true equation) you desire.

Is this right?

[Anonymous No.15804073]

>>15804066
I meant methods.

Is there a general method?

[Anonymous No.15804144]

>>15804073
Variation of parameters
Estimating algorithms
Other things

[Anonymous No.15804291]

let X and Y be banach spaces and [math]1<p< \infty [/math] Does the Banach space [math]X \otimes_{p}Y[/math] have a SD2P?

[Anonymous No.15804484]

How does it feel that my professor is smarter than you? :)

[Anonymous No.15804542]

>>15804049
from what my professor says, either you pretend the phenomenon can be modeled as a harmonic oscillator, or you plug it into a pooter

[Anonymous No.15804544]

He is a faget

[Anonymous No.15804553]

80% of the time when I goof around with discrete math I run into harmonic series or arbitrary factorial expansion, or some weird meta-combinatorial expression of the terms. My calc book showed me a cool trick for using product rule in reverse in order to expedite partial fraction decomposition, and I feel it in my bones that it can work here, but my brain isn't wrinkly enough to wrangle these fuckers

[Anonymous No.15804578]

>>15804049
What does the d/Dr mean? Why doesn't it have a top part? How do I solve?>>15804066
>>15804144
>>15804542

[Anonymous No.15804652]

What do you think about the new mathematical constant that I came up with?

The constant is generated as follows.

>the centers of four equal sqares are placed at the vertices of a square
>the diameter of each circle is half of the side of the square
>lazer pointer is placed at the center
>the circles act as circular mirrors: any time the lazer beam hits it, the beam reflects in the same angle that it arrived (relative to the tangent of the circle at that point)
>the constant is equal to the starting angle alpha adjusted just right that the lazer beam will first reflect from circle 1, then from 2, then from 3, and so on, infinitely repeating the 1234-cycle

I call this the Circular Square Cycle constant (CSC-constant for short). It's value is approximately 0.931723928 radians.

Questions remain, such as, is this constant irrational, and does it possibly have a closed form representation.

[Anonymous No.15804656]

What do you think about the new mathematical constant that I came up with?

The constant is generated as follows.

>the centers of four equal circles are placed at the vertices of a square
>the diameter of each circle is half of the side of the square
>lazer pointer is placed at the center
>the circles act as circular mirrors: any time the lazer beam hits it, the beam reflects in the same angle that it arrived (relative to the tangent of the circle at that point)
>the constant is equal to the starting angle alpha adjusted just right that the lazer beam will first reflect from circle 1, then from 2, then from 3, and so on, infinitely repeating the 1234-cycle

I call this the Circular Square Cycle constant (CSC-constant for short). It's value is approximately 0.931723928 radians.

Questions remain, such as, is this constant irrational, and does it possibly have a closed form representation.

[Anonymous No.15804674]

>>15797572
Propositions are taken as primitive notions because it is easy to do so. For instance, it is easier to prove with propositons the existence of at least one infinite set (that is to say, explain through dialogue or other symbolic logic) rather than trying to prove the existence of an infinite set through geometry, which is essentially primitive notions

[Anonymous No.15804689]

>>15804656
Plot the phase space, it forms a pole

[Anonymous No.15804694]

does anyone know where I can get the first edition of Apostol's Mathematical Analysis?

[Anonymous No.15804707]

selfstudy chads: do you do all problems or only odd number problems

[Anonymous No.15804721]

>>15804656
Could use a better way to describe it.
So the idea of constants is that they explain things that otherwise couldn't be explained. What would you use this for?

[Anonymous No.15804733]

https://www.youtube.com/watch?v=cuBpOXGLn_o

some parts of this talk you might find relevant

[Anonymous No.15804748]

>>15804656
What is the value of the result as a function of the radius of the circles? What if instead of 4 circles at the vertices of a square you have n circles at the vertices of a regular n-gon?

[Anonymous No.15804894]

>>15804748
Something I did was I almost worked out the angle for the infinite repeating 1243-cycle which is symmetrical unlike the 1234 one. It is the solution of the monstrosity of an equation in picrelated.

The angle that I used in this simulation was 0.947388587401477 which is accurate enough to 15 decimal places but despite that precision the lazer beam made only four full 1243-cycles before escaping. I like how it's like the double pendulum, a system very sensitive to initial conditions.

[Anonymous No.15805030]

>>15804694
JUST. RUDIN.

[Anonymous No.15805037]

When you first really started getting into math, did you find calc 2 or calc 3 harder?
I feel like calc 3 was a bit easier since it's just calculus 1 but in 3D.

[Anonymous No.15805054]

why do the retarded 'muricans keep arbitrarily dividing calculus into calculus 4 and calculus 13
and why do they think that everyone else does it

[Anonymous No.15805148]

Suppose you wish to numerically compute the derivative of a function f at 0 given a bunch of sample points: r1, r2, ...
f'(0) ≈ Σw*f(r)
Here's how to find the weight to give each sample:
[math]Let\ P(x)=\prod\limits_{k=1}^{n}(x-r_k).\\
w_i= {D[P(x)/(x-r_i)]_{x=0} \over [P(x)/(x-r_i)]_{x=r_i}}.[/math]

[Anonymous No.15805320]

>>15805054
you dont understand their education is more expensive so its better and you get it in multiple numbered parts

[Anonymous No.15805358]

>>15805054
Because not everyone is so good at math. The intelligent students go for more advanced courses. Having one calculus course for everyone would just bring the quality of education down.

[Anonymous No.15805369]

>>15805358
"""""higher""""" """"""education"""""""
your universities have been scamming you for years, when will you take action?

[Anonymous No.15805425]

>>15805369
Idk last I checked we win the most fields medals.

[Anonymous No.15805476]

praise Jesus math fellows we made it to Sunday. We will be fully rested for the long week ahead!!!!!

[Anonymous No.15805507]

sorry if I use your thread I want to test python sympy latex output, let's see...

[math]1 + t + \frac{t^{2}}{2} + \frac{t^{3}}{6} + \frac{t^{4}}{24} + \frac{t^{5}}{120} + \frac{t^{6}}{720} + O\left(t^{7}\right)[/math]

[Anonymous No.15805510]

>>15805507
good it worked!
weird that a 0 was converted into a "O" but whatever...

[Anonymous No.15805517]

>>15805507
good it worked!

[Anonymous No.15805521]

>>15805476
are you still seething about the yesterday newton thread? lol

[Anonymous No.15805548]

>>15797495
A* is a breadth first search you retard. It's just a special case of a breadth first search with a heuristic that reduces the scope so that it's computationally viable.

[Anonymous No.15805556]

>>15798669

\pi = \sqrt{6 \sum_{n =1}^{\infty} \frac{1}{n^2}}

Happy?

[Anonymous No.15805564]

>>15805548
>bfs isn't computationally viable
holy retard

[Anonymous No.15805570]

>>15805564
bfs exponentially scales with the number of layers in the tree.

That's literally the definition of non-viable for real-time planning. It's literally the reason A* was developed you dipshit.

Most problems in which heuristic path planners like A* are implemented they use something like A* because doing an explicit bfs is too slow compared to any implementation of a best-first-search.

[Anonymous No.15805605]

for me it's dijkstra's

[Anonymous No.15805921]

>>15798312
Unless you want to get rid of the exponential function, you automatically get radians from the [math]\Re(e^{ix})[/math] definition for cosine.

[Anonymous No.15806057]

I have a weird question. Let's say you have a set of formulas {p, q}. Is p&q necessarily a subset of this set? Is logical entailment here enough to guarantee that p&q is in the set or can we keep the set with just {p, q}

[Anonymous No.15806146]

i pick the ones i think are interesting and which i am motivated to work on, going back later to look at the ones i didn't do
in general this results in a non linear way of problem solving where i will be working on problems from several chapters at once

[Anonymous No.15806149]

>>15806146 was meant for >>15804707

[Anonymous No.15806237]

>>15805605
djikstra the person was highly based

[Anonymous No.15806326]

>>15798278
Especially latex.

[Anonymous No.15806368]

>>15798661
What edition is the complex variables? I think we used the eighth edition for my class.

[Anonymous No.15806381]

>>15806237
unfathomably based.

[Anonymous No.15806382]

I love math in general but especially love pure math and am getting an undergraduates degree in pure math, but I don't want to teach at all. I know I could teach myself coding and easily transition to some coding adjacent job but is there anything else? Anyone have any advice in general? Could I possibly get a grad degree in a different subject and get a job with that? Should I even bother? Currently in my junior year and started thinking about what I'm going to do after.

[Anonymous No.15806420]

>>15805556
is more difficult to prove that this converges than the taylor series for sin

[Anonymous No.15806449]

>>15806382
Specialize in statistics if you want a good job not related to education, cryptography is also worth looking into

[Anonymous No.15806503]

>>15806382
I have a different scenario. I am almost done with an applied math degree with a strong emphasis on numerical scientific computing and statistics, but what I actually love is pure math. I'll have to see if I can do a masters in pure math and transition to a PhD in that manner. Safest best deems to be Emporia state, do pure math masters online, and at that point I should be at a strong enough position to get into a pure math PhD.
I took a few CS classes and I absolutely hated it. I would like to study algebra for the rest of my life. Not too keen on analysis.

[Anonymous No.15806561]

>>15806382
take this as you may. When I was in undergrad I didn't want to teach at all. Around the end of my undergrad I realized I liked explaining math to other people, and was no longer opposed to teaching. I'm now in grad school, and while I am not teaching yet, I like the classes I TA and I actually think that I'd like to teach a class (just not calculus). A funny anecdote I heard at a conference is someone's student went into a stats phd so he could find a job afterwards and not teach, but he still wanted to do math, so he did a lot in algebra as well. By the end of the phd he has come to like teaching so he signed up with the math department again.
I think it's some sort of natural instinct, where if you love something and you are good at it, you want to teach it to others. Of course, there are many ways for administration to suck the fun out of it and many teachers seem to dislike it, so YMMV. It's worth mentioning that I believe most that dislike teaching do so because they are bad at it and don't put in effort to improve. Obviously a closed-minded never-improve attitude is deadly for a researcher, so I'm quite critical of it.

[Anonymous No.15806597]

>>15806382
Figure out what you like via undergrad research, and put it on your resume.

[Anonymous No.15806869]

>>15806561
Interesting perspective. I will never get a PhD (low IQ), but I always considered the teaching portion of the job in academia to be a reward, as it seems rather easy compared to the rest of the job....

[Anonymous No.15807058]

>>15796375
>a function f that is continuous in point 'a' can be differentiable in 'a' even if [math]\lim_{x\to a^+} f'(x)\not = \lim_{x\to a^-} f'(x) [/math]
how is this possible?
isn't a function differentiable at some point a iff the limit from both sides approaches same value?

[Anonymous No.15807296]

>go to a really good undergrad
>get a math degree but don't do well enough to get into PhD, stupidly apply to almost exclusively PhD programs anyway and only one safety master's
>have to get master's from an unknown regional school
I did really well but I feel like it's a worthless accomplishment because of where I did it. I learned a lot but only because I wanted to, none of the classes were challenging. Now I'm applying to PhD programs again and feel like I'm going to get rejected everywhere again since I took a massive step down in institution prestige. I'm not trying to be elitist, it just seems like if I could do so well without trying then my degree isn't worth anything and good schools will know that. Am I actually fucked or am I blowing this out of proportion? Obviously a prestigious master's will help but will a no-name actively hold you back? I'm hoping they write it off as a COVID anomaly.

[Anonymous No.15807356]

>>15804694
to buy? abebooks

[Anonymous No.15807363]

>>15807296
Can't you just have your thesis carry you in your masters? Also, if you did so well in your undergraduate, you should be able to get letters from your professors stating you are ready for a PhD program. Finally, take a look at the preliminary exams for whatever prestigious school you're assuming you belong in. I found this out recently and it blew my mind, but Harvard students have 3 comprehensive exams covering various high end topics, and most students complete all of it their first semester. So at least for Harvard, you'd need a solid, broad masters level coverage to even start, assuming they had infinite seats and anyone could get it on merit alone. I assume its the same for any other top school or ivy.
If it makes you feel better, there is no way your school is lower ranked than mine (LibertyU), and I know quite a few former classmates that went straight into middling (lower end of top 100) PhDs all over the US, so I doubt anyone is holding your school against you. Be confident and keep trying.

[Anonymous No.15807368]

>>15806561
that's interesting to think about. I have found myself enjoying teaching my peers parts of the material they don't understand yet and the random one-off tutoring i may do here and there but never really equated that to teaching for some reason. This made me realize I've written off teaching before giving it an actual shot. While I'm still apprehensive about it for the reasons outside of the actual teaching part I'll keep this in mind and see if I can get find any opportunities related to teaching to see how I feel about it in a more professional setting. appreciate the response.

[Anonymous No.15807373]

>>15807296
Just do good work and hope for the best. Nothing is more sickening than a grad student that is already acting like some academic parasite that only cares about climbing up the status ladder

[Anonymous No.15807397]

>>15807363
Yes, I'm happy with the work I've done, I was just concerned with how it would look on applications. Thanks for your advice, I do appreciate it. I'll try to stop worrying and just hope for the best. Top 100 is plenty good enough for me. I'll probably do better work in a lower-ranked program that's less stressful anyway, whether I'm smart enough for Harvard or not actually going there might make me kill myself.

>>15807373
Oh god no I agree, I don't care about status for status' sake. I would be perfectly happy with anything in the US top 100 (provided they have people doing what I want to do), I just want to be challenged. I mostly hate the feeling that my master's doesn't represent hard work, even though I did actually work hard I'm pretty sure I could've gotten away with doing a lot less. It made me nervous that places I'm applying would know that it's too easy to get a master's. I just want to go somewhere I feel like my hard work is necessary.

[Anonymous No.15807404]

>>15804049
do problems and google pauls math notes when you dont know how to do problems

[Anonymous No.15807415]

>>15807397
>Oh god no I agree, I don't care about status for status' sake. I would be perfectly happy with anything in the US top 100 (provided they have people doing what I want to do)
Sometimes this isn't always what is best for you or your interests. A mathematician whose work in applied algebraic geometry I follow, teaches at a very small public university. There is also the multitude of researchers at SLACs. I think, im probably wrong here, the ranking matters more for disciplines that rely heavily on expensive equipment and such. However, maybe its just me that doesn't care, which is an opinion built on a sturdy financial privilege that allows me to hold such an opinion.

[Anonymous No.15807420]

i bullshitted through most of my degree due to skill issue and now i am floored most days by the amount of things that i allegedly know that i actually just don't know at all

current plan is just self studying the shit i am bad at while im on a gap semester

how do you do math work and also avoid coping, seething, and bullshitting? have to catch myself memorizing solutions instead of coming up with them myself every day. i already have a therapist but my therapist just tells me i'm right all the time so that seems useless. feels like im pathologically wired to dodge hard work when other people are capable of sucking it up and doing work

[Anonymous No.15807425]

What does it mean if I can intuitively grasp calculus but not stats?
I took my stat midterm today and I left more than half of it blank (most likely because I didn't study at all and focused on bio, but that's not really an excuse)

[Anonymous No.15807426]

>>15807415
Well in the modern era you don't strictly need anything but an internet connection to become a research mathematician. Math is the same anywhere you go, it's just the people that change. I think a big benefit with going to a more prestigious school in math is the people around you are generally more driven, and realistically they'll be smarter (higher-ranked schools do actually tend to select for intelligence to some extent, even if the difference is badly exaggerated). Obviously some of them will be shitheads as they will be anywhere, but in theory I could learn everything I ever wanted to know about math alone in my bedroom with a laptop and never interact directly with anyone. I want to be surrounded by people at least as smart and passionate as I am because I'm not disciplined enough to stay motivated without external factors. Obviously the institution's resources are pretty meaningless for pure math, I just want to go somewhere "good" because I don't gain anything being surrounded by people who never challenge me. I'll never get any smarter that way.

[Anonymous No.15807433]

>>15807425
It could mean anything, but likely means that you're reasonably smart and just don't try that hard. If you can intuitively grasp calculus, then the only thing stopping you from doing the same with stats is effort. Stats is no harder than calculus. It's just not as obvious how to derive things from scratch because it's a little more "constructed" so you actually have to study it and remember formulae.

[Anonymous No.15807435]

>>15807425
I'm the same. I can picture what calculus is doing, area under a curve / tangents / surfaces etc. But I have no such intuition for statistics, it's more abstract to me.

[Anonymous No.15807436]

>>15807433
I underestimated it thinking it was just going to be basic algebra, and then the sentences hit me
Maybe my ego is too inflated after passing calc.2 with a reasonably high mark
At least it was only 20% of the total grade

[Anonymous No.15807440]

>>15807420
for self study, to do a pass through a section learning definitions and theorems, but avoid proofs for now. pay very close attention to the exposition. so many people ignore the exposition and only focus on definitions and theorems, then they're surprised when they can't remember shit. after this, do another pass but focus more on proofs this time.
>dodge hard work
i had a similar issue going into graduate school. my undergrad school was a small school, and nothing ever really challenged me. it's hard to break this habit when it has worked so well for four years. the best thing for me was to go to the quiet floor of the library and force myself to study. also, try to get rid of any distractions from your phone. even trying to load up a new song on your phone can be enough to make you go lazy mode.

[Anonymous No.15807442]

>>15807436
Try not to feel too bad about it, it just isn't as possible to bullshit your way through stats the same way you can with basic calculus. Even pure probability you can kind of brute force if you know the basics, but stats requires you to keep track of a lot of minutiae and definitions. If you can do well in calculus, you should do well in stats if you study. Put some work in and you'll probably do fine on the next exam.

[Anonymous No.15807467]

I'm not Terence Tao. Should I kill myself?

[Anonymous No.15807538]

>>15807467
not yet

[Anonymous No.15807734]

domain theory (in logical form)

[Anonymous No.15807762]

love me some math

[Anonymous No.15807772]

i love maths

[Anonymous No.15808224]

>>15800408
Those anons usually never really learnt it in the first place, the reason most people hate math is that by the time algebra rolls around they throw off all attempt at gaining understanding and just memorize formulas and procedures. Once you're behind you're finished, but of course the school system needs you to get your diploma so they ham you through. I'm in medical school right now and it's remarkable how few of my classmates understand basic algebra.

[Anonymous No.15808301]

>>22599794
>>22601522
I forgot all math from highschool and want to learn to at least an undergraduate level - what is the best way? Read books like pic or plow through something on Khan Academy

[Anonymous No.15808316]

Hello my fellow /math/.

In math I only solved equations and never try prove something.

Can u give some books/guide how start doing this?

[Anonymous No.15808331]

>>15808316
First you have to realize that doing proofs is nothing but arithmetic. If you calculate the truth value of a statement as true then you have proven it and if you calculate the truth value as false then you have disproven it, Every known theorem provides you with a new formula to simplify logical expressions to help you calculate its truth value.

You don't need a special book about proofs. Just take any introductionary math book on a subject that doesn't require prerequisties for example elementary number theory, linear algebra or real analysis and start to prove shit yourself.

[Anonymous No.15808401]

>>15808301
Any guide like this but for "math for physics/engineers" ?From 0 to PhD physics

[Anonymous No.15809044]

>>15808301
Basic math + baby rudin, it's all you need

[Anonymous No.15809064]

>>15808301
are people really studying dummit and foote from start to finish? it reads more like a reference book to me. far better books to learn algebra

[Anonymous No.15809094]

understanding analysis by stephen abbott

[Anonymous No.15809111]

>>15809094
Shit book made for mathlets

[Anonymous No.15809161]

>>15809064
I'm waiting warmly for MacLane's and Birkhoff's Algebra to take off now that the category theory is the new hotness with kids.
But is there really ANY good introductory algebra text? Gallian? Artin? The topic itself is just a big departure from what kids are used to.

[Anonymous No.15809494]

>>15807058
anyone?

[Anonymous No.15809508]

Redpill me on hopf algebra

[Anonymous No.15809513]

>>15809494
Well those limits are for f’, not f itself. I believe there are some examples of derivatives that are defined everywhere but still discontinuous

[Anonymous No.15809537]

>>15809513
>Well those limits are for f’, not f itself.
so a continuous function can be differentiable at a point even if the derivative isn't continuous at that point.
if that's the case the how do i find the derivative at that point?
> I believe there are some examples of derivatives that are defined everywhere but still discontinuous
can you give some examples or post more resources on this?

[Anonymous No.15809544]

>>15809537
Yes, a function can be differentiable everywhere without having a continuous derivative. The classic example is [math]x\sin(\frac{1}{x})[/math], obviously smooth away from [math]0[/math] and has a derivative at [math]0[/math] but the derivative is not continuous at [math]0[/math]. In such cases, you have to compute the value directly from the limit definition of the derivative.

[Anonymous No.15809561]

>>15809544
Sorry meant [math]x^{2}\sin(\frac{1}{x})[/math]

[Anonymous No.15809874]

>>15809161
note there are 2 different algebra books by them, you want the one called algebra not modern algebra (undergrad text)

[Anonymous No.15810327]

https://www.youtube.com/watch?v=NEqHOtl3-I0

[Anonymous No.15810500]

proctoring an exam right now, a student just came up and asked me whether 0^2 = 1

[Anonymous No.15810504]

>>15810500
well? don't leave us hanging

[Anonymous No.15810513]

>>15810504
I raped her in front of the entire class

[Anonymous No.15810602]

>>15810500
proctoring sounds like such a dirty word

[Anonymous No.15810634]

>>15810500
2^0 = 1, of course.

What exam are you proctoring right now?

[Anonymous No.15810724]

>>15810634
Precalculus

[Anonymous No.15810749]

[math] \text{Aluffi, } \textit{Algebra: Chapter 0.}[/math]

[Anonymous No.15810766]

>>15810724
>>15810634
Well...I would forgive that question more or less.

However, if it was something, say, graduate
linear algebra...I would make them pay for that
in their exams and their life.

[Anonymous No.15810843]

Here's a weird question: have you guys ever come across a word or phrase describing the specific "action" of adding a new/additional geometrical dimension to things? Like a term describing what "happens" to the entities on a two-dimensional plane when a z-axis is suddenly "added" to the universe or field in which they exist.

I read a really amazing description of this in some old book years ago and I know he used a specific term.

[Anonymous No.15810948]

So Weierstrass is the popular example of continuous everywhere and differentiable nowhere over R, but what about discontinuous everywhere and differentiable everywhere?

[Anonymous No.15811012]

>>15810843
Is it embedding?

[Anonymous No.15811014]

>>15810948
if f'(a) exists then f is continuous at a

[Anonymous No.15811086]

MTH 5771 - Algebra I
APM 5777 - Computer Algebra
APM 5668 - Mathematical Modeling in Industry: Discrete Models
MTH 5772 - Algebra II
APM 6773 - Coding Theory
MTH 6770 - Algebraic Number Theory
MTH 6771 - Commutative Algebra
MTH 6772 - Algebraic Geometry
APM 6996 - (project)

Seems cozy. Thoughts?
Pros: can avoid doing boring analysis
Cons: not sure.

[Anonymous No.15811104]

>>15810948
Thomae's function is discontinuous on the rational
inputs but differentiable nowhere (see pic).

Blumberg's Theorem at least can allow a real
function to be restricted to and be continuous
over some dense subset.

[Anonymous No.15811107]

>>15810948
brilliant post

[Anonymous No.15811183]

>>15811086
You must have Topology before AG if you want to succeed

[Anonymous No.15811313]

>>15811183
Are you sure? Pic related are the courses and pre requisites. I do know some topology from self study, but not from actual topology books. What I know is from Kaplansky's set theory and metric spaces, and Hilberts geometry and imagination(one survey chapter)

I've done some computational algebraic geometry while following the text from Cox(ideals, varieties, algorithms) as well. My interests are just in algebra, the course contents are topics I've reviewed and solved problems for, albeit not rigorously at the masters level.

The program is at Oakland University. Of note, the professors at the university operate some sort of statewide applied algebraic geometry group. https://sites.google.com/a/oakland.edu/algebra/

I asked about this program before but didn't get any replies. Also, im way too dumb to get a PhD so thats not the word for me, I just want to study what I enjoy and be useful. Thanks.

[Anonymous No.15811338]

>>15811104
>Blumberg's Theorem at least can allow a real
>function to be restricted to and be continuous
>over some dense subset.
proof?

[Anonymous No.15811354]

>>15811104
>Blumberg's Theorem
never heard of this, that's a really cool theorem
>>15811338
https://www.pnas.org/doi/pdf/10.1073/pnas.8.10.283

[Anonymous No.15811357]

>>15811313
Also here is the actual masters program, rather than just the courses I'm interested in and listed in my first post.

https://oakland.edu/math/graduate-programs/masters-program/

[Anonymous No.15811375]

>>15811357
May be a oversight or assumptions about your background knowledge. It sounds like they cover the specific bits of topology you use but not much more, so ask whoever teaches 5772+6772 for advice as soon as you can.

[Anonymous No.15811404]

>>15811313
I think the other anon is probably overestimating how sophisticated your course is. Maybe he's a yuropoor
I took AG I at my uni, which was very similar to that outline, with only algebra and was like 90% fine, but I hit a wall in AG II. As long as you understand basic stuff on like the level of what Rudin covers, anything you might be missing will just be constructions you can pick up without falling behind

Although this sort of question is much better to just ask the prof teaching the class instead of random anons who are making educated guesses about what it will cover

[Anonymous No.15811889]

>>15811404
not the other anon, but i know most of the stuff he listed like nullstellensatz, riemann-roch .etc and none of it uses topology.

what is AG II, and where did you get stuck without having topology? currently i'm studying AG/commutative algebra with a view towards tackling the silverman EC book

[Anonymous No.15811904]

>>15811889
not the anon you're responding to, but topology is fundamental in any semi-modern AG. We care a lot about connecting geometry with topological ideas such as compactness, irreducible, noetherian, dimension, and so on. If you don't have any training in topology this will (probably) be too uncomfortable to accept as basic properties of schemes.

[Anonymous No.15812358]

Hey anons, looking for some big brain help here. I got this monster of a chessboard - like 10000x10000 big - and want to know how many possible paths my little knight buddy can take from left column (any row) to right column (any row). Only rule is he can move only right and can't hop onto a row he's hopped on before. Any math wizards out there able to crunch this?

[Anonymous No.15812390]

I have a Morse theory mid-term exam coming and I'm struggling to find exercises / exams to train.

So far we have not done a lot of Morse theory. We started with generalities on manifolds, transversality, and for proper Morse theory we saw the Morse complex, Morse cohomology...

By the way, do you have books to recommend on the topic ?

[Anonymous No.15812393]

I'm starting to think that [math] e^x [/math] and [math] \ln(x) [/math] aren't closed forms, since e is transcendental and
[eqn] \ln(x) = \int^{x}_{1}\frac{1}{t}dt [/eqn]
Have I been tricked by the symbols on the page?

[Anonymous No.15812431]

Hey anons.
I'm doing math, but admittedly my high school math was only barely passing, and I can't remember anything from it. Whether or not it is due to my algebra being weak, or some other lower math that I'm missing I find myself taking really long to solve equations I've already got the formulas and variables for. It's not being slow to compute either, I'm just messing things up, and I don't know what to improve specifically.
I've been recommended matlab, don't know what it does, will it help? Do I just redo algebra on khanacademy? What do you all recommend?

[Anonymous No.15812436]

>>15812393
They're closed-form by definition, in that we use them often enough that they're tossed into the list of functions that count as valid in closed-form expressions.
If you want to limit it to stuff that's expressible just as basic arithmetic and integers? Yeah, they absolutely don't qualify

[Anonymous No.15812438]

>>15796375
What was math like before set theory? I'm trying to get an idea of what math education was like in Euler's time.
>>15797370
I don't know if this is right, but it seems like the answer is still 1/5.

[Anonymous No.15812479]

>>15812436
makes the relationship between circular and hyperbolic functions make a lot more sense

[Anonymous No.15812497]

>>15812358
Start with a smaller board and work it out then see if you can generalize your solution.

[Anonymous No.15812509]

>>15812431
Matlab is a software for programming and simulation.

Matlab can be instructive in building intuition for some mathematical concepts but it definitely isn't a "learning tool" in the sense that something like a Khan Academy or Brilliant or something is.

Are you doing math in undergrad at the moment, and if so what courses (if you don't mind me asking)?

Depending on the course, your best bet might be to get a used instructor's copy of a standard college algebra or pre-calc textbook (some of them you can find dirt cheap on Amazon used or thriftbooks or something) and just go through in your free time doing exercises with a solution manual until you feel you understand it.

[Anonymous No.15812516]

>>15812438
Just download a PDF copy of Euler's books or earlier. You can literally find English translated copies of Elements of Algebra by Euler online for free.

[Anonymous No.15812522]

>>15812509
I can't map it one to one to US courses but I think it'd be, among easier ones, Calculus I and Linear Algebra.
I see the appeal of the instructor's copy idea, thanks.

[Anonymous No.15812525]

what are your approaches vis a vis going through textbooks?
generally I have the pdf open on one screen and latex in another, and I make notes as I read. The notes generally consist of the definitions and theorem statements, and occassionaly also proofs and explanatory remarks. i essentially produce a highly condensed version of the textbook by the end of it. also, rarely do i go through every chapter unless the textbook is very short.

[Anonymous No.15812534]

>>15812525
why on earth would you take notes in latex

[Anonymous No.15812543]

>>15812534
i use it so often for paper writing anyway

[Anonymous No.15812574]

>>15812543
Try typst.app instead. Its much faster than latex, but unfortunately had no method for implementing diagrams for categories.

[Anonymous No.15812581]

>>15812574
interesting recommendation, i'll look into it. thanks
>had no method for implementing diagrams for categories.
not ideal for me. but hopefully this will be a feature in the future?

[Anonymous No.15812624]

Hmmmmm

[Anonymous No.15812699]

>>15812624
You can't because it's a wrong statement for certain classes of numbers like hyperreals.

[Anonymous No.15812906]

I've stumbled onto kind of a bitch of a problem, in a pretty dumb context.
Let's say I have two processes that output the same materials but at different rates given the same resources. (MathJax gonna be rough I apologize)
[math]
C = \begin{matrix}
p_1 & s_2 \\
s_1 & p_2
\end{matrix}
[/math]
p here stands for primary and s for secondary. Given some goal vector, how do I find the inputs that correspond?
I tried simply inverting the matrix, but in many instances, a vector containing negative input amounts is the solution. My constraints for the inputs are as follows:
- all inputs must be >= 0
- the sum of inputs must be minimal

How do I solve this problem? I've even tried gradient descent but that hasn't panned out very well. It seems to be an economics problem but I'm not well enough versed in their terminology to just look it up

[Anonymous No.15812913]

>>15812906
An addendum, I need this solution to be generalizable to an arbitrary number of dimensions. I initially tried seeing if the naive solution of [math]\frac{g_1}{p_1} [/math] or [math]\frac{g_2}{p_2} [/math] would hold up in instances where one output is much larger than the other, but they actually break down surprisingly early. Pic related is what happens when I threw my computer at it for [math]
C = \begin{matrix}
3 & 1\\
1 & 2
\end{matrix}
[/math]

[Anonymous No.15812934]

>mandatory statistics class, have to perform linear regression on some data set that I'm interested in or motivated about.
>Start looking into euler's formula for for polyhedra, specifically, the cases for non convex shapes.
>just messing around since TA and professors might not be happy its not a problem with insurance rates or some other thing like it.
>create a scatter plot on matlab using convex hull
I am a total amateur when it comes to this and I've only an introductory understanding of this kind of content, but are the "holes" in this graph in the pattern they appear, a dead zone with no topologically/metrically regular polyhedra? Maybe I'm just misinterpreting all of this.

[Anonymous No.15812965]

>>15812438
>What was math like before set theory? I'm trying to get an idea of what math education was like in Euler's time.
Depends entirely on the era. You can follow any math history textbook to get a general idea. Stillwell's is often recommended, but there is also Katz' history of mathematics, and (my preference) Cajori's a history of mathematics.
During Euler's time, the notation we know of today was starting to solidify based on the work from many predecessors. Going back even further before the rise of abacists and their shortcuts, they were just word problems, and many were approached geometrically, and by this I mean the classical sense, as analytical geometry with points on a plane was unheard of until the work of Descartes and Fermat.

[Anonymous No.15813058]

>>15797572
Mathematicians broke with truth at the end of last century, as with adequation. The last crisis of mathematics - the foundational crisis of the nineteenth century brought about by the paradoxes of set theory - was abandoned under practical considerations, but its not over.

"Primitive notions" are foundational in a definitional way, we care about their expressiveness, but they are not "the ground".

In the book "mathematical logic " by Chiswell and Hodges we construct basic logics (boolean to propositional to first-order and beyond) but we also build equivalent tree structure alongside to shows that this process is arithmetizable. We could completely forget about propositions and obtain the same structure with "numbers" as the primitive notion, this time based on the Peano axioms. Numbers in turn could simply be another language with the right propositions. Your issues with "multiplicities" and "places" don't apply there. So math is understandable through grammars and inference rules, but not reducible to it.

In every intro to set theory book you do the same with your ordinals and cardinals chapters, showing their equivalence with numbers in each way. You can do the same for categories, graphs, groups, etc. All choices are all also deficient in their own ways, but there's no core, just the capacity to choose the perspective for each situation.

[Anonymous No.15813193]

If you let a ball roll along the curve that minimizes its time to roll from the origin to the point (a,b), b<0, which is a cycloid, how do you calculate the time that it takes for the ball to roll there just based on those variables a and b and gravity (g)? Assuming also that there is no friction.

[Anonymous No.15813245]

>>15813193
sketch a force(acceleration) diagram

[Anonymous No.15813619]

>struggling to understand an example in a textbook for 6 hours
>realise there is a mistake in a definition, which is the reason it makes no sense to me
i am become SEETHE

[Anonymous No.15813644]

>>15806057
No. The set is {p,q} and obviously p is not equal to p&q, nor is q — for one thing, both are strictly shorter. However, p&q is *provable* from {p,q}

[Anonymous No.15813649]

>>15812906
I don't understand what you mean here. What goal vector, what are the inputs, what does it mean for these to "correspond"?

[Anonymous No.15813651]

>>15806057
No. The set is {p,q} only has the elements p and q, and obviously p is not equal to p&q, nor is q — for one thing, both are strictly shorter. Of course you can define a new set like
> Th({p,q}) = { r : {p,q} entails r }
which does contain p&q along with a lot of other stuff like p&p&p etc

[Anonymous No.15813746]

>>15812934
Where are the data points above χ = 2 coming from?

[Anonymous No.15813753]

>>15797359
this seems very complicated, where exactly start learning from zero

[Anonymous No.15813820]

>>15813746
Good catch. I just used convex hull algorithm (Which I don't understand very well, I'm just an undergrad), But you're right there should be no data points there given that I'm only looking at non-convex polyhedra.
My methodology for generation of polyhedra with matlab has been to randomly generate vertices and then apply the built in convexhull algorithm, to try and ensure the shapes are all non-convex, but I guess it could be entirely possible that a few convex shapes snuck in.
I also had to look this up a bit, but there are some non-convex shapes that still satisfy Euler's formula at V + F - E = 2, like a dimpled cube, but there must be many other simply connected non-convex polyhedra there as well I think. I guess I'd have to think more about what convex hull is doing.

[Anonymous No.15813852]

>>15813820
It's less to do with convexity and more to do with the topology of the surface. Read up on the characterization of closed surfaces

[Anonymous No.15814043]

My bad, I should have posted this here.

>>15814040

Is this the most intuitive way to view how Newton interpolation, binomial coefficients and the arithmetic triangle work together?

[Anonymous No.15814180]

do you guys recommend any not that much mind altering drugs for focus and motivation?
i take noopept with moderate results

[Anonymous No.15814228]

>>15813649
Goal vector is the minimum number of outputs, the input vector represents a partition of inputs, doesn't matter what they actually are. By correspond I mean the input vector that satisfies the conditions

[Anonymous No.15814507]

Should I continue with Topics in Algebra by Herstein, or pick an easier book?

In general, I'm spending close to 1-2 hours on a single page or two, to fully understand the concepts.

Regarding the exercises, I can solve may be half of them, or less. The other half, I need some hints to progress in the right direction. I don't find the exercise sets to be very hard, but it's difficult alright.

There are some aspects of the book that I love, it's not too chatty(it's exceptionally clear at what it tries to say), gives plenty of examples, and develops some parts of the theory through the exercise sets(I love this part, in fact it's one of my favorite things about this book, feels like I'm discovering Algebra).

I'm self-studying. Is this struggle normal?

[Anonymous No.15814524]

>I like math
>I'm also fucking retarded
What do i do?

[Anonymous No.15814594]

>>15814524
combinatorics

[Anonymous No.15814828]

>>15814594
Okay, anon, i'll trust you on this one and dedicate a large portion of my life to getting to that levelw, but if it doesn't help me and your post is just a joke not taking my problem seriously, i'll be so distraught i'll probably kill myself and my whole family and shoot up a school and it'll be all your fault.

[Anonymous No.15814852]

>>15814507
Dummit & Foote.

[Anonymous No.15814857]

Yo education system is full of buncha raycist ass crackas and I fucking hope somebody blows up every single school in the USA in a rogue drone strike sent from orbit.

[Anonymous No.15814942]

Is the rest of maths this tedious, pedantic and obtuse?
I am currently still in calc1 and it takes me hours to understand a single theorem or definition.
Take for example riemann integrability, I have watched the same lecture and read the same book section more than 4 times and I still have no idea how the fuck I can show a function over an interval is integrable.
All answers online are either useless (e.g. "a non-integrable function is a function that jumps around a lot") or equally tedious as the book definition

[Anonymous No.15815004]

>>15814942
1. Calculus was developed alongside physics, so if the textbook is devoid of physics, then it's probably why you find it so tedious.
2. You'll probably flip out knowing that hardly anyone uses the Riemann integral anymore and it has long been superseded by others (eg.Lebesgue)
3. What video lectures are you referring to? What book are you using?
4. Maybe try the lectures by Herb Gross (alongside is texts)

[Anonymous No.15815011]

>>15814942
Actually I'd suggest: https://archive.org/details/TarasovCalculus

Very friendly beginning to calculus, concise and to the point written in a conversational tone. Then go through Herb Gross's lectures. Maybe target specifically that portion concerned with Riemann integrability.

[Anonymous No.15815015]

>>15812525
Do you actually end up using your notes in an appreciable way? I've considered a similar approach and have read people suggesting you "write your own textbook" but it always seemed like a lot of work and that you might end up writing something down a lot of stuff for essentially no benefit (Why not just look it up in the book?). Right now I just put Important theorems/definitions/ideas into anki and hope everything sticks.

[Anonymous No.15815063]

>>15814942
You need to push through, nothing particularly special about it. Hammer your head against that wall until you win. You'll get better at it over a few years.

[Anonymous No.15815077]

>>15815004
>hardly anyone uses the Riemann integral anymore
Come on that isn't true. Lebesgue has obvious theoretical advantages but is virtually impossible to compute, so you reduce the Lebesgue integral of a "function" to a Riemann integral of a specific representative since you can actually calculate that.

[Anonymous No.15815081]

well, it is true in that nobody uses Riemann's actual definition. they all use Darboux's and call it Riemann's

[Anonymous No.15815085]

>>15815077
The gauge integral would actually make more sense because it makes the Riemann integral a special case. Are there any calculus books that teach it from the beginning? Is this worth its own thread?

https://math.vanderbilt.edu/schectex/ccc/gauge/letter/

[Anonymous No.15815100]

>>15813619
As someone who was also burned several time by this bullshit and sloppy work in general, I now reach for a second textbook/source as soon as possible if something is unclear

[Anonymous No.15815103]

I begin my undergraduate studies in math on Monday. Starting with linear algebra and real analysis.
Any advice on how to not get filtered?

[Anonymous No.15815104]

>>15815103
What country

[Anonymous No.15815105]

>>15815081
lol fair enough

>>15815085
The benefits of the gauge integral are a bit technical, no? I don't really see any good reason to do that. Better let students get used to working with the Riemann integral before moving on to generalizations.

[Anonymous No.15815106]

>>15815104
Germany

[Anonymous No.15815116]

>>15815106
Show me your "real analysis" textbook.

[Anonymous No.15815143]

>>15813619
>>15815100
Does this mean that books which have seen multiple editions and/or have an errata section on their author or publisher's site, are the only way to go? Or classes that are on YouTube and where students may comment. I assume mistakes would be pointed out. The other option is an online book that gets regularly updated and the author is free to answer questions.

[Anonymous No.15815194]

>>15815143
Unfortunately I've found that using at least two distinct textbooks is almost required to learn anything properly. So many topics have multiple possible treatments which are logically equivalent but provide radically different intuitions and learning experiences. Conventions and unspoken assumptions also vary wildly depending on which perspective the author takes. If you are unfortunate enough to pick up a book that takes a particularly unconventional approach, you'll likely be very confused when you try to read something else. In some sense, you don't get an intuition for the "true topic" until you read multiple sources and see what they have in common.

[Anonymous No.15815230]

Pre-calculus is such a scam. Extremely boring foundation for something that is actually interesting, and they don't teach calc in HS in my shitty third-world country.

[Anonymous No.15815259]

>>15812913
omg why are you posting this gay nazi content Anon?!?!
I mean, really
get a life
you're such a loser

[Anonymous No.15815262]

>>15815116
Here is the list of recommended textbooks for the Analysis 1 course. Why did you put real analysis in quotes?

[Anonymous No.15815264]

>>15815106
omg we hate you so much for your four color bullshit
https://en.wikipedia.org/wiki/Four_color_theorem
https://en.wikipedia.org/wiki/Non-surveyable_proof

[Anonymous No.15815289]

>>15815262
just throw away everything published after '95 and you should be fine

[Anonymous No.15815320]

>>15815262
Because 90% of German curriculum I've seen, always have the introductory Analysis courses as the equivalent of US Calculus I, II, III. In France we also just call it calculus as in the US and its L1 content.
When we reach analysis, I used Jordan's text "Cours d'Analyse de l'École Polytechnique, and I seriously doubt its what you're covering until at least L2, and its standard for measure theory, Lebesgue integration, functional analysis, to be L3.
we used Jordan's book in my last year, which is beyond the content you'll see in the texts in your pic.

[Anonymous No.15815325]

>>15815262
It's mostly that Americans typically do not know and are confused to learn that german math undergraduates start with Analysis and proof based linear algebra in first semester.

[Anonymous No.15815342]

>>15815325
It's so funny how Europeans act so much like Indians.

[Anonymous No.15815360]

>>15815325
wait, wtf do americans do in their first semester then

[Anonymous No.15815371]

>>15815320
Doesn't really explain what you are getting hooked up on there.
Lebesgue and measure theory are typically covered during Analysis 2 or 3, depends on the university. And Analysis 1 is just what it says: proof based introduction to Analysis up to Riemann integrals and Fourier series.

[Anonymous No.15815374]

>>15815325
>>15815360
This meme needs to die. American universities are accredited such that they are competitive on the international level. The same body that accredits Harvard, does the same for programs in bumfuck new england. The same content covered in american calculus for first years is what is taken by europeans.
The top schools in every country will always go above and beyond, they should not be looked at as the standard of national university programs. inb4 that one brit posts warwick again and tries to pass it off as an average school.

The real problem with american universities isn't the universities themselves, its k-12. Most states pump out kids with insane bullshit GPA numbers, straight A's, and they can't even get into the university right next door, as their state's standards are complete shit. Because of this, many american universities are packed with remedial courses like pre calculus, which is probably what you're thinking about when you think of american universities being shitty. Its just the national level university system doing the work that individual state primary and secondary education failed to accomplish.

[Anonymous No.15815386]

from equation f/2*ln(T1/T2) = ln(V1/V2), how do I derive the adiabatic proces formula p*V^x = constant, where x= (f/2+1) / f/2, p=pressure, T=temperature and 1 means original value and 2 final value

Gosh been trying this for the entire of saturday and have got nowhere, please anons I am praying for you to help me before I completely lose my mind

[Anonymous No.15815444]

>>15815374
This, I TA'd calculus at an ivy and still had to teach some of the students basic precalc they should've gotten in high school. They were the exception there but a lot of their classmates were still pretty clueless.

[Anonymous No.15815620]

>>15807058
Consider f(x)=|x| at x=0

[Anonymous No.15815623]

>>15815620
that isn't differentiable at 0

[Anonymous No.15815661]

>>15807058
i thought it was defined as them being necessarily the same
f(x+h)-f(x)/h as h->0
only it isnt specified that h is positive
for left and right derivatives, you can use the notation h-> 0^- and h-> 0^+, which would confirm that h is necessarily -ive or +ive respectively

[Anonymous No.15815715]

>>15797370
I had to figure it out a bit, but I agree with the others
that it's 1/5 or 20%.

Out of 20 people on line, no matter how they're
arranged, one has to be the winner (sample space).
Then, let 16 non-Americans take 16 "losing" tickets
[only one way to do that] and choose one of the 4
Americans to hold the winner [four ways]. So...

[eqn] {16 \choose 16} \cdot {4 \choose 1}\over{20 \choose 1} [/eqn]

Realistically, each person wouldn't let anyone cut
in front of them, not even their own people.
And the tickets would be issued in order on the line.
In that case, it's the same result:

[eqn] {4 \cdot 19!} \over{20!} [/eqn]

[Anonymous No.15815716]

>>15812525
I don't take notes lmao. The best method is multiple readings, because you literally cannot understand most textbooks on a first read because 99% of mathematicians ARE horrible communicators and unnecessarily cryptic regardless of the beauty of their methods. My general method is follows:

>At least two textbooks, ideally three, on the same subject. One textbook is the primary, second textbook is a simpler and lower level version of the primary, third textbook is a purely applications focused text, ideally with actual computer algorithms and simulations.
>Read the relevant chapter of book one mindlessly, don't even try to connect anything just absorb
>Read problems for chapter and see which I instantly assume I understand and which I don't, star problems I don't understand
>Read simple textbook two chapter in-depthly, make connections in my fucking pea head
>Go over problems again seeing which I do and don't know how to approach
>Do another reading of book one indepth focusing on putting things together and the problems I don't understand
>Finally attempt all problems, working out details esquisitely, explaining clearly and in none bullshit speak (i.e. no corporate/academic/math tone) every single step.
>To ensure I actually understand the bullshit, read through application focused text. If I can't recreate, even novicely, the concepts in a computer, I probably don't actually understand anything. Although this last step varies a lot by class.

If you do that, you don't need notes. The problems are notes enough.

[Anonymous No.15815783]

>>15807058
see >>15809544 & >>15809561

[Anonymous No.15815830]

>>15815716
this is good advice and i couldn't agree more with your point
> 99% of mathematicians ARE horrible communicators and unnecessarily cryptic regardless of the beauty of their methods
although one issue with this method that happens every so often is that two authors may use completely different notation for the same thing or, even worth, the same notation for completely different things. most mainstream maths is safe from this because most things are standard, but this can be an issue in more niche areas and it can get confusing and infurating. my recent experience with this was while reading two books (in fact, *the* two books) on finite model theory. it's when this kind of thing happens that i feel obliged to make detailed notes
anyway, even in view of this, very good advice

[Anonymous No.15815840]

>>15815716
Several books on each topic, skim, tackle problems, pretty much the same thing I do, but with the addition of specific time investments. I am the employee and the boss, if I don't get 40 hours a week of study out of me, I'm being robbed by an idiot wagie(me). Tick tock wagie, back on the clock!

[Anonymous No.15815862]

>>15815143
my 15th ed dynamics textbook still has typos in it

[Anonymous No.15815870]

>>15815386
in my thermo class we were just given pv^x=constant as a model of data, not as a derived formula like conservation of energy/momentum. then integrate boundary work and you get a natural log. I don't try to derive formulas in that class though, cause it seems more than half of the equations are just fitting data

[Anonymous No.15816054]

>>15798661
I used the complex variables one for my (engineering) course, seemed alright. Didn't know he had a Fourier book

[Anonymous No.15816061]

i finally got it bitches. just about 2 months more work and ill be able to turn on the money maker.

[Anonymous No.15816064]

>>15815081
that's the one in apostol's calc right

[Anonymous No.15816065]

>>15816061
were you the guy a month or so asking about a "formula for adjusting 3 numbers so that they moved together, in a way that makes them move not separately, like if A goes up, B goes up but not as much, but enough to be appropriate"
if you're not that guy no offense

[Anonymous No.15816067]

>>15816065
not that guy. i havent posted here in a few months. im am a PLOOTER mostly

[Anonymous No.15816079]

Any opinions about Amann and Escher for learning analysis by myself over the next 5 or so months? I did take an "advanced" calculus course which did proofs in lecture but we didn't have much of it for homework. I've also taken linear algebra.
I want to take a complex analysis course next september but haven't taken actual real analysis and I can't take it this coming semester.

[Anonymous No.15816091]

>>15812525
When I had a shitload of time to kill, I would copy down every sentence of the textbook along with my own commentary

[Anonymous No.15816095]

>>15815870
>integrate boundary work and you get a natural log

I mean the equation I used in my first post was after I integrated f/2*1/T from T1 to T2 and 1/V from V1 to V2

[Anonymous No.15816531]

Is there a name for anons who post in /mg/?

[Anonymous No.15816542]

>>15797913
English is not my native language, but i won't compare it with my native one, i also know Italian, more or less, therefore i don't consider it to be the best, there are other manners of explaining things, out there. English is "imposed" because politics and the number of books available in it. Not cause is some alien superior language.

[Anonymous No.15816548]

>>15816531
Mathcel.

[Anonymous No.15816550]

>>15816548
I'm quite partial to n-cell, myself

[Anonymous No.15816562]

Are limits of a function just the supremum/infimum of some image of the function?

[Anonymous No.15816567]

>>15816562
No.

[Anonymous No.15816570]

>>15816531
hu/mg/ruffins

[Anonymous No.15816586]

>>15816562
yes

[Anonymous No.15816611]

>>15816531
Mathematicians (I only have a BS)

[Anonymous No.15816735]

>>15816562
Sometimes yes, sometimes no.

[Anonymous No.15816737]

>>15816531
MG = MathGot

[Anonymous No.15816740]

>>15796375
https://youtu.be/yoHR8qwuqmY?si=xUdv4RxMVDLk5vOV

[Anonymous No.15816771]

I want to learn about stats and probability theory. The most advanced math course I've taken is Calc. I found this chart and was planning on working my way through them chronologically. Can I just jump in head first or is there any preliminary books/subjects I should complete first?

[Anonymous No.15816774]

Test

[Anonymous No.15816895]

>>15816771
Category theory should be enough

[Anonymous No.15817220]

>>15815386
can you rewrite that in mathjax or on a piece of paper

[Anonymous No.15817265]

>>15816895
no set theory?

[Anonymous No.15817307]

>>15817265
set theory is trivial

[Anonymous No.15817462]

Seems like this didn't get reversed, and the chest-shooting female police officer has cut off the memes too.

[Anonymous No.15817815]

>some goofball integral contrived by the author = -1
> I try to use calculus on some stuff I'm interested in
"This integral does not have a closed form"

[Anonymous No.15817816]

>>15816771
https://www.isical.ac.in/~deanweb/M.Stat(2015).pdf

[Anonymous No.15817819]

>>15816895
>>15816895
Are you trolling? I read like halfway of some rigorous math text book on stats and prob and the only thing required was measure theory. Also inequalities, ton of equalities.

[Anonymous No.15818221]

>>15817819
>Are you trolling?
Yes

[Anonymous No.15818273]

>>15817815
This problem generalizes, a lot of even relatively simple math is somehow uncomputable. We only have names for specific irrational numbers that have some interesting property while most do not, there is no closed-form way to reliably compute roots of polynomials, etc. It's a bit frustrating at first but eventually you either start accepting that math doesn't need to be constructive or go full numerical.

[Anonymous No.15818303]

>>15818273
There are more uncomputable irrationals than computable irrationals but there can't be more interesting uncomputable irrationals than interesting computable irrationals.

[Anonymous No.15818327]

>>15818303
Huh, why not?

[Anonymous No.15818329]

>>15817307
NOOOOOOOO ETROPY NOOOOOOOO!!!!

[Anonymous No.15818333]

>>15816061
>>15816067
I know it's mean as hell, but whatever dude
either buy an ad or quit your spamming
-OR-
you can go to /biz/ if you really think it's going to make money
or /mu/ if you're trying to sell some kind of visual feedback music instrument

[Anonymous No.15818341]

>>15818221
are you still trolling?

[Anonymous No.15818358]

>>15811104

[Anonymous No.15818370]

Category "theory" isn't a theory at all; it's actually a pictographic language extending model theory. This is why undergraduates love it so much. A category theory course should be required by senior math majors for all top tier college and university.
You know, so our college grads are well equipped to do battle with memelords like your humble self, Anon.

[Anonymous No.15818382]

>>15818370
The way its used today was never the intention of its originators. It was a student of the jew guy, forget his name, and it was a surprise to mcdonalds.

[Anonymous No.15818395]

>>15818382
Category theory is to set theory as C++ is to C
take something good, then use some niche (model theory / code generation) to extend it to the point where it's really just a way for students to engage in verbal jousting / poetry slam STEM-style
I'm telling you, it's hip hop in academic form. Alert ODB and the Wu-Tang clan.
I'm serious. This is how math students brag about their studies.
If you can't chalk to a beat, get outta here casual.

[Anonymous No.15818396]

>>15818329
Wtf, why does he have the Dreamworks face?

[Anonymous No.15818428]

>>15818396
(^u>)
"Finally, a few days ago, it has been achieved - but not by my cumbersome search, rather through God’s good grace, I am tempted to say. As the lightning strikes the riddle was solved; I myself would be unable to point to a guiding thread between what I knew before, what I had used in my last attempts, and what made it work."

[Anonymous No.15818429]

how to find hot math gf

[Anonymous No.15818458]

I'm so scared I'm gonna get rejected from everywhere again, bros. Gotta just power through applications and cross my fingers I guess.

[Anonymous No.15818475]

>>15818429
No one has been able to construct one yet

[Anonymous No.15818623]

>>15818475
My girlfriend says that she has a hot math girlfriend (i.e. me) and that if you losers had more emotional capacity than 1/4 of a teaspoon, washed your asses, and respected women, you might get one.

[Anonymous No.15818638]

>>15816531
n-cells:
https://en.wikipedia.org/wiki/N_cell

[Anonymous No.15818922]

>>15816531
mochizuki owns this general

[Anonymous No.15819035]

new >>15819034