/mg/

[Anonymous No.12619163]

Math, generally
>dream scheme theme
Talk maths

Das alte: >>12605538

[Anonymous No.12619170]

Barnabas#3715

[Anonymous No.12619184]

>>12617523
Help

[Anonymous No.12619186]

>>12619184
Whats an algebraic projective curve

[Anonymous No.12619197]

>>12617206
>>12617460
thanks anon, was feeling a little discouraged reading gnedenko's probability theory because i started it without finishing spivak's calculus and i didn't realize i'd need calculus for probability (dumb i know). seems like i just need to keep getting my hands dirty to get some confidence and maturity.

[Anonymous No.12619251]

>das alte
Who is your favourite Der Alte and why is he Leo Kress?

>>12619197
Roughly, what you are supposed to do is to always get your hands dirty on one level. When you are all covered in mud, blood, pee and poo, that is when you move to the next level where you no longer play with stuff like "prove that the limit of 1/n is 0" etc., but instead you prove properties of limits. Then you are, once again covered by filth after your struggle, and then you climb up to the next level where you can use what you did before as things that are well known. You are supposed to feel dumb. When you no longer feel dumb, you need to take the step to the next thing and feel like an idiot once more. Fear not, that is how you get the maturity. I mean, kids are happy while adults are bitter and depressed. Maturity is obtained through pain and suffering.

[Anonymous No.12619291]

>>12619251
>Who is your favourite Der Alte and why is he Leo Kress?
Nichst sicher who das ist

[Anonymous No.12619422]

Hey /mg/ as a study into STEM graduate numbers I've been looking into why education policy is the way it is in certain countries and I've come up against issues with understanding economics. I don't understand the effects of bond yields, the comparative effects of projected demographic changes in foreign countries or what the effect of any central bank decisions are, and these kinds of things keep coming up in my reading. This community helped me a surprising amount through my masters in algebraic geometry so I'd like to see if you have any recommendations for macroeconomics that aren't reddit-tier.

[Anonymous No.12619460]

>>12619422
If it helps I've almost finished reading Mankiw's Principles of Economics

[Anonymous No.12619504]

>>12619251
yeah, i realized i wasted lots of time essentially reviewing what i was already proficient in over and over, because i thought i should have a ridiculous level of apprehension, something like 99%, in order to claim i truly understand something. all that time was wasted. now, if i think i have better than 50% chance of finishing a certain textbook i'll move onto something harder. and i am now learning much faster and more interesting things.

[Anonymous No.12619517]

>>12619422
>>12619460

my suggestion, following >>12619504, would be to dive straight into a quantitative, graduate level macroeconomics text, and drill through until you encounter a problem where you clearly lack some prerequisite necessary to thorough understanding, and then find some again difficult text that will elaborate that prerequisite, finish said prerequisite and then dive back into the higher level text again. i have wasted much time in studying economics by reviewing the basics over and over again. don't make the same mistake. if you aren't understanding then you aren't challenging yourself enough.

[Anonymous No.12619629]

>>12619186
That K is an algebraically closed field. Consider the projective plane IP2 over K, this is the set of equivalence classes (a : b : c) of points (a, b, c) in K3 \ {(0, 0, 0)} under the relation P ~ Q iff there is a t in K\{0} with P = tQ. Projective spaces are where things go well and whole for algebraic varieties.
An algebraic curve is a special type of algebraic variety (it's in IP2 rather than IP^{n+1} and has dimension 1), it is the subset of IP2 of common zeros of a homogenous polynomial in K[X, Y, Z]. You need homogeneity in other to make sense call a projective point a zero of each polynomial. For example, [math]C = \{ (x:y:z) \in \mathbb{P}^2 ;\ y^2 = 4x^3 - g_2x^2 - g_3\}[/math] for [math]g_2, g_3 \in \mathbb{Q},\ g_2^3 - 27g_3^2\ne 0[/math] is a special type of curve, an elliptic curve (in Weierstrass' form).

[Anonymous No.12619637]

>>12619186
That K is an algebraically closed field. Consider the projective plane IP^2 over K, this is the set of equivalence classes (a : b : c) of points (a, b, c) in K^3 \ {(0, 0, 0)} under the relation P ~ Q iff there is a t in K\{0} with P = tQ. Projective spaces are where things go well and whole for algebraic varieties.
An algebraic curve is a special type of algebraic variety (it's in IP^2 rather than IP^{n+1} and has dimension 1), it is the subset of IP^2 of common zeros of a homogenous polynomial in K[X, Y, Z]. You need homogeneity in other to make sense call a projective point a zero of each polynomial. For example, [math]C = \{ (x:y:z) \in \mathbb{P}^2 ;\ y^2 = 4x^3 - g_2x - g_3\}[/math] for [math]g_2, g_3 \in \mathbb{Q},\ g_2^3 - 27g_3^2\ne 0[/math] is a special type of curve, an elliptic curve (in Weierstrass' form).

[Anonymous No.12619788]

>>12619184
Your question is equivalent to asking if a function is regular as long as it has no poles (in an affine variety). This my be the definition of a regular function, but if you think of [math]k[\overline{C}][/math] as defined by a quotient such as [math]k[X_1,...,X_n]/I(\overline{C})[/math] then you just need to use theorem I.3.2.a) of Hartshorne to remember that a function over [math]\overline{C}[/math] is in [math]k[\overline{C}][/math] iff it is regular at all points.

[Anonymous No.12619871]

>>12619163
How important is Calc 3 material for Partial Differential Equations? I took the course 2 years ago so I remember jack shit about vector fields or plane geometry, but I remember partial derivatives really well.

Is it worth retaking or can I get through PDE only with ODE knowledge?

[Anonymous No.12619916]

>>12619788
Thanks for answering anon, I'm having to grasp as much of algebraic curves as I can in a short amount of time, so that's why I'm sucking good information from wherever I can.
Good to know it works as it is intuitive, what I was thinking was that if the g* had a common zero (would have to be of not greater order than f*), then taking representants for both f* and g* in the polynomial ring, say F and G, I'd have a factor H of G having that same zero and dividing F, such that F/H, G/H would be polynomials but now G/H doesn't vanish. Is that what is going on? It looks harder to prove than with polynomials in just one or two variables.

[Anonymous No.12620078]

>>12618380
^ This anon was saying Aluffi is inadequate (learning abstract algebra) for its lack of exercises. What would then be a good supplement to read alongside Aluffi? Pinter was mentioned - would Aluffi + Pinter be good?

[Anonymous No.12620167]

I'm trying to understand bayesian thinking like the less wrong squad.
Let [math]H = [/math] holocaust happened and [math]I = [/math] illegal to research holocaust. Then assuming [math]P(I | \lnot H) > P(I | H)[/math], which seems very reasonable we have,
[eqn]
P(\lnot H | I) = \frac{P(I | \lnot H) P(\lnot H)}{P(I | \lnot H) P(\lnot H) + P(I | H) P(H)} = \frac{P(\lnot H)}{P(\lnot H) + \frac{P(I | H)}{P(I | \lnot H)}P(H)} > \frac{P(\lnot H)}{P(\lnot H) + P(H)} = P(\lnot H)
[/eqn]
Thus we have to update our prior probability to something higher. Is this correct application of bayesian thinking?
In this situation I do think the prior [math]P(\lnot H)[/math] will be very small initially and the fraction [math]P(I | \lnot H) / P(I | H)[/math] to not be very large, thus we update from small to small, but higher.

[Anonymous No.12620186]

Elsewhere on /sci/:
>Goldbach and twin primes ask about primes, which is one family of number theory questions.
>Collatz asks a question about dynamical systems over [math]\mathbb{Z}[/math], which is closer to a question about the mandelbrot set or some other shit than anything about the primes. Dynamical systems in general are unsolvable without some kind of new paradigm we don't have yet, like how questions about polynomials weren't answerable before discovering group theory.
A genie comes to you and offers you the choice between the math community magically developing a new theory that solves most questions about primes or magically developing a new theory that solves most questions about iterated systems.
Which would you pick?

[Anonymous No.12620347]

>>12620186
i'd say the prime problems, i find them more aesthetic

[Anonymous No.12620502]

How would I go about proving something is an ordered set? I'm trying to solve problem 9 in ch1 of rudin's analysis, but I am not sure what to prove since he already defined the order (as per the definition of an ordered set which is simply a set S where an order is defined).

[Anonymous No.12620542]

>>12620078
It has exercises, just the first section on sets has few exercises, most sections have about 15 exercises. Dummit & Foote would be another one to look at, it has a ton of exercises, most are fairly routine though.

[Anonymous No.12620578]

>>12620502
Post the problem.

>>12620186
Goldbach. I like it more than Collatz.

[Anonymous No.12620597]

https://www.youtube.com/watch?v=ljdUHWVg2AY
>math major
>says he was on the pure math track
>hardly any algebra
>hardly any analysis
>all books physics majors use for their math
>no advanced subjects whatsoever
what the fuck kind of math degree is this?

[Anonymous No.12620600]

>>12620578
>Suppose [math]z = a + bi[, w = c + di/math]. Define [math]z<w[/math] if [math]a<c[/math], and also if [math]a=c[/math] but [math]b<d[/math].

I need to then prove that this turns the set of all complex numbers into an ordered set. I'm guessing I need to verify this is a valid order, but I'm not quite sure how to do that aside from maybe checking [math]z<w \implies w-z > 0[/math]

[Anonymous No.12620633]

>>12620597
is that EE thot in the comments who said she took all these classes in her degree bullshitting or is EE that math intensive?

[Anonymous No.12620636]

>>12620600
So, you need to show the following things:
(R) [math]z \le z[/math] for all [math]z \in \mathbb{C}[/math]. This is reflexivity.
(T) If [math]z_1 \le z_2, z_2 \le z_3[/math], then [math]z_1 \le z_3[/math]. This is transitivity.
(AS) If [math]z \le w, w\le z[/math], then [math]z = w[/math]. This is antisymmetry.
If the set satisfies (R) and (T), you have a preordering. If the preordering satisfies (AS), it is a partial ordering.

>>12619291
https://www.imdb.com/title/tt0075474/

[Anonymous No.12620647]

>>12620633
No idea about EE, I have a math degree and didn't use a single one of these books, wouldn't surprise me though they're all books aimed at physicists or engineers.

[Anonymous No.12620658]

>>12620542
Thanks

[Anonymous No.12620660]

>>12620647
What books did you use? I got a degree in applied math with statistics at a top 30 american school, and there is a lot of overlap. Replace the physics books with fourier analysis and numerical analysis and thats roughly what my degree looked like.

[Anonymous No.12620713]

>>12620660
This guy said it was pure math not applied.
I used Rudin (principles) and Folland for real analysis, Dummit & Foote for algebra. Atiyah Macdonald for commutative algebra. Serre for representation theory. Munkres for topology, Hatcher for Algebraic Topology. I also took differential geometry and a few other things too.

[Anonymous No.12620758]

>>12620633
Doesn't look that outlandish I think, and my Uni is far from top tier. Shit gets weird in the EE realm
>>12620597
Looks a bit lacking. Compare to say https://www.youtube.com/watch?v=fG7ZKdKTo6E

[Anonymous No.12621071]

PhD student here. I have been hanging around for almost 2 years without any paper.
How bad am I?

[Anonymous No.12621205]

>>12620186
Iterated systems, then reduce questions about primes to questions about the sieves that generate them.

[Anonymous No.12621295]

>>12619916
I don't have a full proof using only manipulation on polynomials.

Also I believe a great textbook to wrap your head around algebraic curves js Fulton's Algebraic Curves.

It takes its time and is very hands on.

[Anonymous No.12621323]

I'm a self taught software engineer making six figures but I'm getting quite bored of my job so I decided to start learning game dev and machine learning and my god I forgot how much of a brainlet I was. I literally forgot to even substract more than 2 digit numbers. I'm re-learning pretty much everything I was supposed to learn in school regarding maths. Aparently calculus is very prominent in AI and game development, but I was completely lost on the subject so I went back to algebra and trigonometry, but seeing as I can't do basic operations I need a refresher on arithmetics first. Hope it doesn't take more than a year. I feel so dumb watching Khanacademy videos about basic operations because the guy explaining is talking as if I were 8 years old.

[Anonymous No.12621332]

>>12621071
get a famous jury on your thesis to compensate

[Anonymous No.12621336]

>>12620502
>an order is defined)
you ave to prove the order he defined is indeed an order

[Anonymous No.12621341]

>>12619163
>theory of finite dimensional white safe space edition

[Anonymous No.12621433]

>>12621071
If you're applied you could get the hang of meta analyses and write some papers applying newer techniques that e.g. less mathematically inclined research fields would be slower to pick up, which you being a professional mathematician in training should find relatively trivial? Also, can't you just publish parts of your research towards your final thesis, and/or maybe try writing a survey paper?

What is your approach when it comes to research?

[Anonymous No.12621513]

>>12619422
In Humanism, the dream of the atheists is that people must get an education approved by the bourgeois ruling class, like the bourgeois did 100 years ago. this is why nowadays the middle class adapts the bourgeois mores.
This is because in atheism, people are
-a citizen
-an employee
-a consumer

Their dream was that people with a high education will be good citizen, and good citizen are people who keep embracing the Human Rights generations after generations.


Financing all those public servants training children into liking Humanism costs a fortune, just like welfare, and since humanists cant into supply and demand, they dont understand why making all people having a hi education will devalue their degrees.

Then you have to look at how the secular humanist public servants get money. You have to understand that in humanism, a public servant does not produce work, hence nobody gives them money as a trade against their ''work''. his only source of money is taking money from the plebs and contracting a debt in the name of the plebs (not in his name lol). In the humanist republic, public servants are not in competition. In this republic, competition is only for the private sector. This is why when you do a bank transfer in different currencies, the bankers tax you by 1 or 2 %, but the public servants tax you at 30% or more of your income. When competition is introduced in the bureaucracy, the bureaucrats start seething, like it happens with Ireland being a tax haven inside Europe, and the bourgeois leftist starts to talk about ''social dumping'' to feel righteous as if their care about the plebs.

[Anonymous No.12621515]

>>12621513

It turns out there are a few ways to get rich,
-invade a country
-Currency Devaluation
-taking money by force from the citizen
-creating a debt in the name of the citizen

In humanism taking territories and riches from other people who are in appearance just as humanist as you reflects poorly on the presidency, so they cant do that. Atheists only kill people if those people are depicted as barbarians in the atheist media. Now that 99% of all the 200 countries have embraced the atheist democracy, atheists have cut off this method to get rich.


Now the debt. The humanist bureaucrat is happy to issue bonds in the name of the plebs, since the bureaucrats will pay up the coupon with the money he takes from the plebs.


The devaluation is pretty neat, but it doesnt work well for a solid reputation on the international scale. Devaluation has only one purpose: to decrease the nominal value of the public debt created by the bureaucrats. The debt is expressed in the new currency and it cost less (on paper).


Devaluation doesn't work when their is a unique currency for many countries, like the euro in europe. This is why all the cockroach in Germany and the tax heaven that are the Netherlands keep telling other countries to reduce their debt, because now devaluation is impossible. This is another moronic idea by the humanist. And as usual the cognitive dissonance of the atheist keeps creating problem.
For instance the bugman called the dutch gets lots of money by being a tax heaven, so the other countries get less money from the taxes, then the dutch gets very rich, and then whines that poor countries dont have enough money and yet should not issue too much bonds.

[Anonymous No.12621530]

>>12621515
The natural way to reduce the burden of the nominal value of the debt is inflation, but with the helicopter money and so on, inflation is killed by the atheist bureaucrat. At least the yield of the bonds are very low so money is free of charge.
Then it is a matter of political choice of what to do with this free money. Since the atheist is a bugman addicted to drug and sex, coomsumin is the what the atheist population wants, so the debt goes into monthly checks or higher salary for the bureaucrat bugman. The atheists who want to feel smug say the debt should go to ''infrastructure'' and ''investment for the nation'' ie bureaucrats should crate a plan like in communism to build roads and what not.
now for the bond yield and the atheist central bank. You have to understand that at the beginning of Humanism 200 years ago, the atheists were infatuated with the bourgeois bureaucrats being wise and guiding the plebs towards a better future (and since atheists are hedonists, a better future means just better material conditions, like cars, central heating, fresh water and no stigmata associated to sex and being an hedonists in general) and knowing what they have do to. This is why atheists call their period the ''enlightenment'' and the ''belle epoque''. It turns out that bureaucrats, bourgeois or not, are utter morons, just like the rest of the plebs, who are fucked as soon as the technological progress stagnates, ie like has been since the 90s. Human rights are just a disguise, a narrative made up by the bourgeois to normalize hedonism and feel righteous at the same time. Like when they turn to their priests in academia to say that bonobos have orgies all the time, so it's okay and in agreement with nature that humans have orgies too. Atheists are not sex addicts, they just act according to their human nature, hence no fault and it's normal and no punishment should be given for this.

[Anonymous No.12621536]

>>12621530


Now that atheists feel they cant coom bigger than their parents, they feel that ''atheist democracy is under threat'' and they are desperate to find ways where they can keep cooming while still feeling like they are on the right side of history, ie better than ''religious barbarians''. It is very important for the atheism that atheism is not perceived as a religion. religions is always seen as barbarian and anti-progress (ie anti technology), anti GDP, anti human rights.


So the central bank is here to control inflation. Officially it is its goal. Of course ''officially'' in atheism is meaningless, it's just ''according to the current rules made up by the atheist ruling class'' and if the bourgeois hates the effects of their democratic rules, they change their democratic rules to get the effect they want.

What matters about inflation is the qty of money and its velocity. It turns out with all the QE money make the plebs buy 4k TV, there is a lot of money printed, but the velocity is not there yet, especially with the lock downs, since people dont spend much.
This is why people are scared that with so much printed money, as soon as people will spend it en mass, there will be inflation and too high inflation is a major problem, but inflation around 2--5 % is super nice for the bourgeois bureaucrats who can pay up the bonds contracted in the name of the plebs. A lack of competition created also inflation, since competition is deflationary and competition favors technological progress and technological progress is also deflationary (iphone of 2019 is cheaper than the iphone of 2020)

[Anonymous No.12621544]

>>12621536

Now for the bond yields, the central bank, ie the bureaucrats (normally a public bankers it not always a bureaucrats, but they really for all intent and purpose) keeps telling in their public speeches that they are the ones in charge and that the free bond market is their slave, not their master. This is keeping the 200 year old dream of the humanist that in the atheist republic, the humanist public servants are in charge of the private sector and the opposite.
SO regularly the public servants of the central bank will talk about what rates they will give and hope that the plebs believe them. It turns out that in the atheist democracy, it is really bankers who dictate what the rates will be, especially in the long term. This is all about the ''yield curve'', ie what is the yield, over time and for different maturity of the bonds, of the public debt created by the bureaucrats.

For instance, when the yield curve suddenly changes, the bureaucrats have to quickly make a public appearance to say they that this change is made by them, and not by the free market.

Lots of people, from schizos to bugmen, talk about the yield curve so just go there
https://www.alhambrainvestments.com/download/2369/
https://seekingalpha.com/article/4392983-interest-rates-and-yield-curve-control-part-4
https://seekingalpha.com/article/4274830-inverted-yield-curve-is-to-revert
https://seekingalpha.com/article/4253682-of-slopes-and-flops-yield-curve-inversion
https://seekingalpha.com/article/4293622-why-yield-curve-inversion-suggest-recession


Before you take a class in voodoo ''economics'' you should take a coruse in finance. It's like taking a logic class before doing maths. It helps a lot for seeing who talks rubbish or not.

[Anonymous No.12621547]

Economics of Money and Banking
https://www.coursera.org/learn/money-banking


This document contains redacted course notes of the second part of the course Economics of Money and Banking by Professor Perry G. Mehrling of Columbia University in the United States that is available on Coursera.org. This course explains the basics behind money and banking that are essential in understanding the financial system. According to Professor Mehrling, the financial system is about balancing flexibility and discipline.

Professor Mehrling builds on his own background in the history of monetary economics and financial economics. He sees himself in the American tradition of monetary thought that is based on the tradition of British central banking thought. Each generation had to rethink the underlying issues for themselves in order to make sense of the conditions of their own time. The current challenge is to work out the implications of financial globalisation for money, banking and central banking.

https://www.naturalmoney.org/moneyandbanking-02.html

[Anonymous No.12621549]

The Economics of Money & Banking

The last three or four decades have seen a remarkable evolution in the institutions that comprise the modern monetary system. The financial crisis of 2007-2009 is a wakeup call that we need a similar evolution in the analytical apparatus and theories that we use to understand that system. Produced and sponsored by the Institute for New Economic Thinking, this course is an attempt to begin the process of new economic thinking by reviving and updating some forgotten traditions in monetary thought that have become newly relevant.

Three features of the new system are central.

Most important, the intertwining of previously separate capital markets and money markets has produced a system with new dynamics as well as new vulnerabilities. The financial crisis revealed those vulnerabilities for all to see. The result was two years of desperate innovation by central banking authorities as they tried first this, and then that, in an effort to stem the collapse.

Second, the global character of the crisis has revealed the global character of the system, which is something new in postwar history but not at all new from a longer time perspective. Central bank cooperation was key to stemming the collapse, and the details of that cooperation hint at the outlines of an emerging new international monetary order.

Third, absolutely central to the crisis was the operation of key derivative contracts, most importantly credit default swaps and foreign exchange swaps. Modern money cannot be understood separately from modern finance, nor can modern monetary theory be constructed separately from modern financial theory. That's the reason this course places dealers, in both capital markets and money markets, at the very center of the picture, as profit-seeking suppliers of market liquidity to the new system of market-based credit.
Perry G. Mehrling


https://www.ineteconomics.org/education/courses/the-economics-of-money-banking

[Anonymous No.12621551]

>>12621549
YouTube links to download with jdownloader

https://www.youtube.com/playlist?list=PLmtuEaMvhDZbmfO7rtVLBGJ4Eu_iFBtSU The Four Prices of Money

https://www.youtube.com/playlist?list=PLmtuEaMvhDZbVJfl0Se-1eQncA_2ZB4bs The Natural Hierarchy of Money

https://www.youtube.com/playlist?list=PLmtuEaMvhDZZyyAkEniNUMTTnlJj6qiKW Money and the State: Domestic

https://www.youtube.com/playlist?list=PLmtuEaMvhDZYfVv95KDQWd8-7UrJCJ9Pm The Money View, Macro and Micro

"https://www.youtube.com/playlist?list=PLmtuEaMvhDZZh6zLsntFVt3UIgQ3VqvVv The Central Bank as a Clearinghouse

https://www.youtube.com/playlist?list=PLmtuEaMvhDZapRsqgacn0gLLO-5zQkcwU Federal Funds, Final Settlement

https://www.youtube.com/playlist?list=PLmtuEaMvhDZZJrTj6tyB41ollE3V9ICDZ Repos, Postponing Settlement

https://www.youtube.com/playlist?list=PLmtuEaMvhDZZ0iHoJmCN30Qm0PgyiD4c9 Eurodollars, Parallel Settlement

https://www.youtube.com/playlist?list=PLmtuEaMvhDZYdsq2xV-XMH_BktZzORjM2 The World that Bagehot Knew

https://www.youtube.com/playlist?list=PLmtuEaMvhDZa6t0f1aooC1QzPJmupu1Lg Dealers and Liquid Security Markets

https://www.youtube.com/playlist?list=PLmtuEaMvhDZYlJeLypSZ5px_JnVHgFmOq Banks and the Market for Liquidity

https://www.youtube.com/playlist?list=PLmtuEaMvhDZaBnW0RhzOOk6FO91MdsSEc Lender/Dealer of Last Resort

https://www.youtube.com/playlist?list=PLmtuEaMvhDZa7lHhyQgkwSIhFy9VRF3my Chartalism, Metallism and Key Currencies

https://www.youtube.com/playlist?list=PLmtuEaMvhDZZT848wo0fKzpjMm0FcOTv2: Money and the State: International

https://www.youtube.com/playlist?list=PLmtuEaMvhDZZfzK2aL4YHCgJDHIvicnkZ: Banks and Global Liquidity

https://www.youtube.com/playlist?list=PLmtuEaMvhDZaxgF-8EmoGUox54zLH6PC6 Foreign Exchange

https://www.youtube.com/playlist?list=PLmtuEaMvhDZYoo6ou5q3LQBC34hqw1A_G Direct and Indirect Finance
https://www.youtube.com/playlist?list=PLmtuEaMvhDZZk--VcZIQCbki7JiVt4-hF Forwards and Futures

[Anonymous No.12621553]

>>12621551

https://www.youtube.com/playlist?list=PLmtuEaMvhDZb_WqDkpWLvzOmROPXf8bzL Interest Rate Swaps<

https://www.youtube.com/playlist?list=PLmtuEaMvhDZYv1g1Yp_AE5gFqJ7Ny80Hc Credit Default Swaps

https://www.youtube.com/playlist?list=PLmtuEaMvhDZYl_kIW7KgBDCBNoUraW8zU Central Banking for Shadow Banking

https://www.youtube.com/playlist?list=PLmtuEaMvhDZYAHtKBvxC7dL-eL8apCOGD Touching the Elephant: Three Views

[Anonymous No.12621571]

imagine being a farmer under Biden

[Anonymous No.12621612]

>>12621571
>faps to traps (trans women)
>can't stop posting about trans women
rent-free

[Anonymous No.12621634]

>>12621571
What is said in this image isn't true, executive orders about 'equality' only apply to agencies under executive control. What sports is the executive branch in charge of? Do they even run the national teams?

[Anonymous No.12621646]

>>12621612
Traps are men who pass as women, but still refer to themselves as males. Trans are people who actively pretend to be a diferent sex.

[Anonymous No.12621681]

>>12621071
If you are Euro, you don't necessarily need to worry. My supervisor always says that publishing anything during the first two years is an achievement of its own.

[Anonymous No.12621690]

>>12621323
What's your discord?

[Anonymous No.12621691]

>>12621323
openstax.org/subjects/math

[Anonymous No.12621755]

>>12621323
You don't need videos, at this level they will slow you down and you don't need extra explanations. Just get a good book and read the rules, sit and do a bunch of exercises. The rules are simple. This is what I did when I had to take a placement test for mathematics when I'd been away from school for a while. Took me a couple months to get up to trigonometry and pass the test to take a calculus course.

[Anonymous No.12621795]

>>12620597
This is infuriating. Most of these are physics books or 'math for engineers'. Why does a pure math major read that Steward book? What university doesn't use Rudin for undergrad analysis 1? Why no Munkres? Why no D&F or Artin for algebra? Why no Stein & Shakarchi for complex variables? What the fuck is 'Abstract Mathematics'? Why a book on statistics instead of probability theory? Why no electives?

You'd have to be actually autistic to find this program enjoyable. Thank christ I didn't see this video in high school otherwise I wouldn't have pursued math any further.

I actually understand now why there's this meme that undergrads need to take 6+ grad level courses. At reputable institutions it's definitely not necessary. But if you're at this shithole you're better off skipping to PhD courses starting the first semester.

[Anonymous No.12621812]

>>12621795
That's what I was thinking, I fell over when I heard this was the 'pure mathematics' track. You make a good point, the audience for this video is future mathematics students and it would make me not interested as well. I'd think, great just more plugging into formulas and shit.

[Anonymous No.12621861]

>>12621812
>I'd think, great just more plugging into formulas and shit.
It's kind of a big problem with the way math departments are set up as well, or at least my university.

An engineer may take (all plug and chug, non-proof based) 4 semesters of calculus, linear algebra, ODEs, PDEs, complex variables, and think they have a good sense of what undergraduate mathematics is like. This is 8 courses after all, and yet none of them is remotely rigorous or (at least to me) interesting. Moreover none of these courses (or at least the non-honors variants) will be ever taken by serious math majors.

You basically have to self-select into studying higher mathematics from the get go (i.e. by taking something like Harvard's math 25 or 55 sequences) or else you're doomed to 4 years of monotony.

[Anonymous No.12621917]

Why are french math and physics books so kino anons? I wish my french was better so I could further read some of their books.

[Anonymous No.12621967]

>>12621917
If you know any French at all you should be able to pick up reading math quickly. Just start with a book with an English translation and read the English and French side by side.

Do you have any particular books in mind?

[Anonymous No.12621978]

>>12621967
I'm thinking of Laurent Schwartz Cours D'Analyse since it is pretty similar to Tao and Zorich.

[Anonymous No.12622003]

guys...
i want to fuck a girl or a tranny or even a feminine boy will do...

[Anonymous No.12622029]

>>12622003
>tfw you will never drag algebra tranny to bed from her flaxen hair and fuck her boipucci so hard she switches to analysis

[Anonymous No.12622033]

>>12622029
There was one in my complex analysis class, wonder if that happened. Everything was fine until speaking... ugh. Now a PhD candidate at Cornell.

[Anonymous No.12622103]

>>12622033
it sort of ruins the mood when you hear a baritone voice.

[Anonymous No.12622135]

which college intro class is easier to pass: linear algebra or differential equations ?

[Anonymous No.12622155]

>>12622029
Yes, you are correct. You won't be doing that to me.

>>12622135
Linear algebra. Everything is so straightforward on the conceptual level that the hardest thing is to actually do matrix multiplication by hand.

[Anonymous No.12622220]

>>12622155
>>12622155
>hardest thing is to actually do matrix multiplication by hand.
for a university course? surely thats prereq

[Anonymous No.12622250]

>>12622220
We had that on our first year linear algebra course. Not like a million exercises on it, but it was new to most of us. It wasn't, but maybe is now, part of the HS curriculum.

[Anonymous No.12622465]

>>12622029
fuck bro... this hurts...

[Anonymous No.12622536]

>>12622250
did it at least go into span, bases, eigenvalues and finding inverses using row/column operations

[Anonymous No.12622621]

>>12622465
That hair thing would hurt more.

>>12622536
Of course. Spaces, spans, bases, eigenvalues, inverses, determinants, systems of equations and their solutions, linear maps, base changes, inner products etc., but also the basics of matrices.

[Anonymous No.12622642]

Did the pandemic made you go out and approach more colleagues online? From other universities? Did you change your mind about remote collaboration? How different/worse than doing it in person is it?

>>12619197
>seems like i just need to keep getting my hands dirty to get some confidence and maturity
Based.
The truth is, if you're not overwhelmingly certain that you don't have enough to do it and that you're not being significantly psychologically biased against yourself, then worrying about potential is a waste of time. It's better to take the pragmatic approach (I don't like telling myself lies that intelligence is unreal or that everything will be ok either, but I guess some people do well with this) try to set good goals with serious deadlines, some to push yourself but not so much critical (you gotta be adaptable with those, it's like making yourself believe they're mandatory and critical until the deadline and then you switch gears and just follow the if-then-else you planned), and some that are endgame scenarios. Try your best until the end, if it doesn't work you simply go to plan B.

>>12620186
Primes for the win.

>>12617474
Cool. I just wanted to make clear I don't see myself getting as far as him (to be honest it's far from my priority, which is be paid to study and contribute on what I most enjoy), even though you probably just mentally bumped into a general comparison between you and him and commented that.
Ah, I watched it. Or sort of, I put in the background. I liked, though not so much because I felt a bit of an unwelcoming vibe. You know when girls lump together and associate the group and their acitivities to their gender, distancing from the opposing one, etc? Same thing often happens with boys doing 'boys stuff' too. But maybe it was just impression, I'd listen to another.
The russian mathematician said some things we talked about, like also having an identity that isn't tied to mathematics, knowing that you have a place outside of it.

[Anonymous No.12622723]

>>12621646
>t. under 13
Everyone but you knows >>12621612
meant "traps"

[Anonymous No.12622731]

>>12621691
I looked there, and it has no math just school arithmetic

[Anonymous No.12623302]

>be a level 2 newbie asking questions about newbie stuff and get a bunch of attention from others and a few people calling you a brainlet or trolling with even more stupid answers
>be a level 20 newbie asking newbie questions on graduate level subjects and get ignored by most anons who can answer, with a few answering sometimes but essentially almost just saying "why are you asking such a trivial thing? kys"

Yeah I know how to learn math by now, but no one get the time to learn everything they want in a confined amount of time.
Funny to think how we lose possibilities/opportunities/resources when we climb higher.

[Anonymous No.12623450]

Guys
Why is Calc 1 easier than PreCalc?

[Anonymous No.12623464]

>>12623450
In calc 1 you learn all the tools that would've made precalc easy.
Remember doing precalc with calculus knowledge I learned online and was able to complete tests and assignments easily and very quickly. The teacher was initially angry but eventually she stopped complaining.

[Anonymous No.12623486]

>>12623464
So I can just find integrals and make the teacher eat shit?

[Anonymous No.12623539]

>>12623302
Actually interesting questions are a whole different can of worms, but barely anyone enjoys answering "explain this" questions. It's usually either kindness, showing off or boredom.

[Anonymous No.12624335]

>>12622642
>my priority, which is be paid to study and contribute on what I most enjoy
I like your priority. With your comments on the video, I think I'll just skip it altogether. There should be a new one next Friday.
>Did the pandemic made you go out and approach more colleagues online?
It only made me return here.
>From other universities?
None of you seems to be from mine.
>Did you change your mind about remote collaboration? How different/worse than doing it in person is it?
With an unstable connection and the limitations of webcamming instead of doing stuff on blackboard in the same room, I think it is worse. It doesn't affect the actual content of the discussions, but it makes the performance awful.

[Anonymous No.12624661]

Anyone doing research in coding/information theory? Strongly leaning that direction for my graduate work, wondering if anyone has regrets. I'm interested in neural decoding in brain-machine interfaces.

[Anonymous No.12624675]

>>12621549
you posted this in the mathematical finance thread too, thanks. i'm enjoying it thoroughly

[Anonymous No.12624885]

>>12621553
>>12621551
>>12621549
>>12621547
>>12621544
>>12621536
>>12621530
>>12621515
>>12621513
Nice that you are into ecnoomics but this is a bit spammy. Pls put it in a picture or pastebin next time.

[Anonymous No.12625405]

Hey everyone, I'm facing a kinda tough decision right now. I'm a math major enrolled in a class called "logic" in uni, which is turning out to be way more interesting and in depth than i expected. picrel is a screencap from the text.

but this class puts me at 21 credit hours, and i frankly do not care about it as much as my self-study material (combinatorics, nonstandard calculus). should i drop it? the professor says it will "make us better at proofs"...

has anyone taken a class that covers material like this? was it game-changing? should i stick with it despite calculus III and a topology intro?

[Anonymous No.12625437]

>>12624661
Aspiring arithmetic geometer here, I'm strongly considering exploring applications of the maths I know, as a research interest.
For now I'm focusing more on cryptography, but I have noticed algebraic geometry codes as well and I will try to learn about them at some point.

[Anonymous No.12625522]

Zorich or Amann Escher's Analysis? I like Rudin but I want to see the other author's point of view in Analysis.

[Anonymous No.12625983]

>>12625405
what makes you better at proofs is just really the first chapters of any logic textbook, ie about FOL and also doing proof constructively, ie all the stuff about predicative maths. Advanced logic doesnt make you good at proofs for maths, but only at proofs in advanced logic.

[Anonymous No.12626008]

>>12625983
also adopting Sequent calculus, instead of hilbert's crap

[Anonymous No.12626021]

>>12625983
Can you suggest a good logic textbook?

[Anonymous No.12626317]

Gonna study maths for the first time this year.
I'm a bit behind on my assignments, lolz.

[Anonymous No.12626348]

>>12625522
I only know about Zorich, it's a great book. It covers all the same material as Rudin's principles of mathematical analysis plus more with volume II (the new edition has an appendix on the Riemann–Stieltjes integral). It has a lot of applications and such though as well, not sure if that's what you're looking for.

[Anonymous No.12626445]

>>12625983
thanks for the advice. i suspected as much. i have already taken two separate classes on logic, actually, so i think that i should drop the class.

[Anonymous No.12626587]

>>12619163
How many right angles are in the OP image?

[Anonymous No.12626594]

>>12619163
You forgot to write "maths general"

[Anonymous No.12626600]

>>12626587
Who cares

[Anonymous No.12626604]

>>12626600
t. Combinatoricist

[Anonymous No.12627052]

Pic related is a puzzle for mg

https://www.youtube.com/watch?v=yppnIO3hZrQ

>>12620167
I dont think you need Bayesian thinking to see that this is true, that if something is hidden then there must be some controversy, and controversy increases likelihood of lies. But cool math anyway, got me to look at the theorem for once

[Anonymous No.12627076]

>>12626594
No I didnt

>>12620186
I would go with iterated systems/Collatz. Primes are beyond our comprehension and to understand them to soon would blow our minds. Iterated systems seem closer to sanity, and we would know how to use them better.

Also the anons saying that understanding iterated systems would be like inventing calculus, I dunno enough to say surely, but before calculus we at least had the method of exhaustion. Iterated systems are more like power sets that branch out into confusion.

[Anonymous No.12627082]

>>12627052
Important hint: The top left drawing was composed of 4 penstrokes

[Anonymous No.12627083]

>>12626587
100

[Anonymous No.12627232]

>>>/lit/17379390

I made a related puzzle for lit. Is mg smart enough?

[Anonymous No.12627412]

Holy shit. The positive series as I proved earlier bumps it op a notch, and the alternating series seems to bump it down a notch. Weird hax in the space of numerical operators.

[Anonymous No.12627462]

>>12627412
Proov:

Take 1/n, you just need one more unit on the denominator. N times the bot, n times the top, subtract one from the top. Wouldve been 1/n but now you get 1 extra fit, seen if youd have stract from denom too. Oscillates over under just by 1 number to infinity.

[Anonymous No.12627609]

1/7 : 6/49 : 43/343 : 300/2401

Over under but how to prove it works (/? It feels intuitive but I cant figure how prove

[Anonymous No.12627667]

>>12627609
i'll think about it if you write down clearly what you want to do

[Anonymous No.12627686]

>>12627667
Trying to show that the alternating sum of 1/n to its powers equals 1/n+1

[Anonymous No.12627719]

>>12621795
The *vast* fucking majority of them. God, sometimes I can't handle the autism in this place.

[Anonymous No.12628006]

how many math classes should i be taking a semester? i'm in a logic class, calculus three, a class on metric space topology, but i'm probably gonna drop the logic class. should i think replacing it with something else?

[Anonymous No.12628032]

(these are not my only classes obv, those are just the math classes)

[Anonymous No.12628422]

>>12628006
It depends. If you're still in calculus 3 then maybe try to get some other distribution requirements out of the way, rather than add on a more trivial math course.

I saved up most of my elective slots until I was done with the algebra and analysis sequences. This worked out nicely since I was then able to fit in a bunch of cool courses during my last several semesters.

[Anonymous No.12628905]

How did Ramanujan come up with crazy identities like this?

[Anonymous No.12628930]

>>12627719
So you're saying the vast majority of pure math students never study the material covered by Rudin or D&F, etc?

[Anonymous No.12628959]

Stupid undergrad question:
I'm struggling with a proof about approximating x^x with series (I have the formula and can verify it, but can't construct a good proof) and I'm convinced that I don't understand what an infinite series really is. Is there some kind of way to classify different series based on the types of terms they contain? Such as all the series for which the terms are polynomials, the series for which the terms are nested logarithms and so on and consider facts about such sets of series.

[Anonymous No.12629170]

>>12628905
Scizophrenia

[Anonymous No.12629232]

>>12628905
feminine chaos

[Anonymous No.12629273]

History and outline of Gleason's proof
Gleason in 1959

In 1932, John von Neumann also managed to derive the Born rule in his textbook Mathematische Grundlagen der Quantenmechanik [Mathematical Foundations of Quantum Mechanics]. However, the assumptions on which von Neumann built his proof were rather strong and eventually regarded to not be well-motivated.[14] Specifically, von Neumann assumed that the probability function must be linear on all observables, commuting or non-commuting. His proof was derided by John Bell as "not merely false but foolish!".[15][16] Gleason, on the other hand, did not assume linearity, but merely additivity for commuting projectors together with noncontextuality, assumptions seen as better motivated and more physically meaningful.[16][17]

By the late 1940s, George Mackey had grown interested in the mathematical foundations of quantum physics, wondering in particular whether the Born rule was the only possible rule for calculating probabilities in a theory that represented measurements as orthonormal bases on a Hilbert space.[18][19] Mackey discussed this problem with Irving Segal at the University of Chicago, who in turn raised it with Richard Kadison, then a graduate student. Kadison showed that for 2-dimensional Hilbert spaces there exists a probability measure that does not correspond to quantum states and the Born rule. Gleason's result implies that this only happens in dimension 2.[19]

[Anonymous No.12629275]

Gleason's original proof proceeds in three stages.[20]:§2 In Gleason's terminology, a frame function is a real-valued function f {\displaystyle f} f on the unit sphere of a Hilbert space such that

∑ i f ( x i ) = 1 {\displaystyle \sum _{i}f(x_{i})=1} {\displaystyle \sum _{i}f(x_{i})=1}

whenever the vectors x i {\displaystyle x_{i}} x_{i} comprise an orthonormal basis. A noncontextual probability assignment as defined in the previous section is equivalent to a frame function.[b] Any such measure that can be written in the standard way, that is, by applying the Born rule to a quantum state, is termed a regular frame function. Gleason derives a sequence of lemmas concerning when a frame function is necessarily regular, culminating in the final theorem. First, he establishes that every continuous frame function on the Hilbert space R 3 {\displaystyle \mathbb {R} ^{3}} \mathbb {R} ^{3} is regular. This step makes use of the theory of spherical harmonics. Then, he proves that frame functions on R 3 {\displaystyle \mathbb {R} ^{3}} \mathbb {R} ^{3} have to be continuous, which establishes the theorem for the special case of R 3 {\displaystyle \mathbb {R} ^{3}} \mathbb {R} ^{3}. This step is regarded as the most difficult of the proof.[21][22] Finally, he shows that the general problem can be reduced to this special case. Gleason credits one lemma used in this last stage of the proof to his doctoral student Richard Palais.[1]:fn 3

Robin Lyth Hudson described Gleason's theorem as "celebrated and notoriously difficult".[23] Cooke, Keane and Moran later produced a proof that is longer than Gleason's but requires fewer prerequisites.[21]

[Anonymous No.12629277]

reminder that QM relies on 2 theorems
-gleason'sthereom
-the spectral theorem

all those theorems have constructive versions so QM is constructive.

[Anonymous No.12629284]

Gleason's theorem highlights a number of fundamental issues in quantum measurement theory. As Fuchs argues, the theorem "is an extremely powerful result", because "it indicates the extent to which the Born probability rule and even the state-space structure of density operators are dependent upon the theory's other postulates". In consequence, quantum theory is "a tighter package than one might have first thought".[24]:94–95 Various approaches to rederiving the quantum formalism from alternative axioms have, accordingly, employed Gleason's theorem as a key step, bridging the gap between the structure of Hilbert space and the Born rule.[3][12]:§2[25][26]:§1.4

[Anonymous No.12629288]

Moreover, the theorem is historically significant for the role it played in ruling out the possibility of hidden variables in quantum mechanics. A hidden-variable theory that is deterministic implies that the probability of a given outcome is always either 0 or 1. For example, a Stern–Gerlach measurement on a spin-1 atom will report that the atom's angular momentum along the chosen axis is one of three possible values, which can be designated − {\displaystyle -} -, 0 {\displaystyle 0} {\displaystyle 0} and + {\displaystyle +} +. In a deterministic hidden-variable theory, there exists an underlying physical property that fixes the result found in the measurement. Conditional on the value of the underlying physical property, any given outcome (for example, a result of + {\displaystyle +} +) must be either impossible or guaranteed. But Gleason's theorem implies that there can be no such deterministic probability measure. The mapping u ⟨ ρ u , u ⟩ {\displaystyle u\to \langle \rho u,u\rangle } {\displaystyle u\to \langle \rho u,u\rangle } is continuous on the unit sphere of the Hilbert space for any density operator ρ {\displaystyle \rho } \rho . Since this unit sphere is connected, no continuous probability measure on it can be deterministic.[26]:§1.3 Gleason's theorem therefore suggests that quantum theory represents a deep and fundamental departure from the classical intuition that uncertainty is due to ignorance about hidden degrees of freedom.[27] More specifically, Gleason's theorem rules out hidden-variable models that are "noncontextual". Any hidden-variable model for quantum mechanics must, in order to avoid the implications of Gleason's theorem, involve hidden variables that are not properties belonging to the measured system alone but also dependent upon the external context in which the measurement is made. This type of dependence is often seen as contrived or undesirable; in some settings, it is inconsistent with special relativity.[27][28]

[Anonymous No.12629293]

Gleason's theorem motivated later work by John Bell, Ernst Specker and Simon Kochen that led to the result often called the Kochen–Specker theorem, which likewise shows that noncontextual hidden-variable models are incompatible with quantum mechanics. As noted above, Gleason's theorem shows that there is no probability measure over the rays of a Hilbert space that only takes the values 0 and 1 (as long as the dimension of that space exceeds 2). The Kochen–Specker theorem refines this statement by constructing a specific finite subset of rays on which no such probability measure can be defined.[27][30] The fact that such a finite subset of rays must exist follows from Gleason's theorem by way of a logical compactness argument, but this method does not construct the desired set explicitly.[20]:§1 In the related no-hidden-variables result known as Bell's theorem, the assumption that the hidden-variable theory is noncontextual instead is replaced by the assumption that it is local. The same sets of rays used in Kochen–Specker constructions can also be employed to derive Bell-type proofs.[27][31][32]

Pitowsky uses Gleason's theorem to argue that quantum mechanics represents a new theory of probability, one in which the structure of the space of possible events is modified from the classical, Boolean algebra thereof. He regards this as analogous to the way that special relativity modifies the kinematics of Newtonian mechanics.[4][5]

The Gleason and Kochen–Specker theorems have been cited in support of various philosophies, including perspectivism, constructive empiricism and agential realism.[33][34][35]

[Anonymous No.12629294]

Gleason's theorem finds application in quantum logic, which makes heavy use of lattice theory. Quantum logic treats the outcome of a quantum measurement as a logical proposition and studies the relationships and structures formed by these logical propositions. They are organized into a lattice, in which the distributive law, valid in classical logic, is weakened, to reflect the fact that in quantum physics, not all pairs of quantities can be measured simultaneously.[36] The representation theorem in quantum logic shows that such a lattice is isomorphic to the lattice of subspaces of a vector space with a scalar product.[5]:§2 Using Solèr's theorem, the field K over which the vector space is defined can be proven, with additional hypotheses, to be either the real numbers, complex numbers, or the quaternions, as is needed for Gleason's theorem to hold.[12]:§3[37][38]

By invoking Gleason's theorem, the form of a probability function on lattice elements can be restricted. Assuming that the mapping from lattice elements to probabilities is noncontextual, Gleason's theorem establishes that it must be expressible with the Born rule.

[Anonymous No.12629299]

Gleason originally proved the theorem assuming that the measurements applied to the system are of the von Neumann type, i.e., that each possible measurement corresponds to an orthonormal basis of the Hilbert space. Later, Busch[39] and independently Caves et al.[24]:116[40] proved an analogous result for a more general class of measurements, known as positive-operator-valued measures (POVMs). The set of all POVMs includes the set of von Neumann measurements, and so the assumptions of this theorem are significantly stronger than Gleason's. This made the proof of this result simpler than Gleason's, and the conclusions stronger. Unlike the original theorem of Gleason, the generalized version using POVMs also applies to the case of a single qubit.[41][42] Assuming noncontextuality for POVMs is, however, controversial, as POVMs are not fundamental, and some authors defend that noncontextuality should be assumed only for the underlying von Neumann measurements.[43] Gleason's theorem, in its original version, does not hold if the Hilbert space is defined over the rational numbers, i.e., if the components of vectors in the Hilbert space are restricted to be rational numbers, or complex numbers with rational parts. However, when the set of allowed measurements is the set of all POVMs, the theorem holds.[40]:§3.D

The original proof by Gleason was not constructive: one of the ideas on which it depends is the fact that every continuous function defined on a compact space attains its minimum. Because one cannot in all cases explicitly show where the minimum occurs, a proof that relies upon this principle will not be a constructive proof. However, the theorem can be reformulated in such a way that a constructive proof can be found.[20][44]

[Anonymous No.12629317]

>>12628905
this one is actually pretty simple, it's based on a similar continued fraction for tan/cot

[Anonymous No.12629320]

I see the wind, oh I see the trees. Everything is clear in my heart

[Anonymous No.12629327]

A concept of voyage through time has been puzzlingmodern physicists for a long time. Einstein’s general the-ory of relativity allows the existence of closed timelikecurves (CTCs) [1, 2], where an object could travel backin time and interact with a former version of itself.The possible existence of CTCs points to a variety oflogical paradoxes, such as famous grandfather paradox[3]. However, such paradoxes can be efficiently eliminatedin quantum theory. One of the models that does so wasproposed by Deutsch [4]. His model of CTC (D-CTC)operates within the density matrix formalism to describethe states of the two registers involved: a chronology-respecting (CR) system and a CTC chronology-violating(CV) quantum system, which interact with each otherviasome unitary operation. For any such unitary op-eration and state of the CR system, a self-consistencycondition [5] must be satisfied, where the state of theCV system prior to and after the interaction is set toremain the same. Such condition ensures the exclusionof the arising grandfather-like paradoxes, but also intro-duces a nonlinear evolution. This, in turn, gives rise topeculiar phenomena, e.g., violation of no-cloning theo-rem [6, 7], increasing entanglement with LOCC [8], anddistinguishing non-orthogonal quantum states [9] whichhas been experimentally simulated in [10]. In addition,there exist another unusual implications of this modelconcerning the possible enhancement of power of D-CTC-assisted computation, such as the equivalence of classicaland quantum computing or the ability to efficiently solveNP-complete and PSPACE-complete problems [11–13].


https://arxiv.org/abs/1711.08334

[Anonymous No.12629330]

Abstract: One out of many emerging implications from solutions of Einstein's general relativity equations are closed timelike curves (CTCs), which are trajectories through spacetime that allow for time travel to the past without exceeding the speed of light. Two main quantum models of computation with the use of CTCs were introduced by Deutsch (D-CTC) and by Bennett and Schumacher (P-CTC). Unlike the classical theory in which CTCs lead to logical paradoxes, the quantum D-CTC model provides a solution that is logically consistent due to the self-consistency condition imposed on the evolving system, whereas the quantum P-CTC model chooses such solution through post-selection. Both models are non-equivalent and imply nonstandard phenomena in the field of quantum computation and quantum mechanics. In this work we study the implications of these two models on the second law of thermodynamics - the fundamental principle which states that in an isolated system the entropy never decreases. In particular, we construct CTC-based quantum circuits which lead to decrease of entropy.

[Anonymous No.12629716]

What are the best public domain (old ones not new ones) math books? I was bored and thinking of typesetting some or revising them.

[Anonymous No.12629725]

>>12629716
this is a real classic
http://17centurymaths.com/contents/euler/introductiontoanalysisvolone/ch1vol1.pdf

[Anonymous No.12629944]

>>12629716
anything Dirac
anything von neumann
anything grothendieck
anything Ernst-Mach

[Anonymous No.12629948]

>>12629944
anything Max Born
anything de broglie

[Anonymous No.12629952]

>>12629948
anything clifford
anything onsager

[Anonymous No.12629990]

>>12629952
anything Euclid

[Anonymous No.12630171]

Mathematics seems to be obsessed with generalisation. Is it possible to generalise mathematics itself?

[Anonymous No.12630208]

>>12630171
of course, it's called mathematical logic

[Anonymous No.12630457]

>>12630171
>Mathematics seems to be obsessed with generalisation
because we have too many mediocre mathematicians, and writing papers of the type "we picked a thing and generalized it" is one of the easier things to do
of course what they don't tell you is that the generalisation is probably useless

[Anonymous No.12630487]

>>12630171
That only seems true from a surface level understanding of math, and many young mathematicians make the mistake of thinking that most general = best. History is filled with mathematicians who missed the solution to the problem they trying to solve because they chose the wrong formalism to tackle it. Good general theory does not search for the maximum generality but the right generality.

[Anonymous No.12630506]

>>12630171
>>12630457
http://girard.perso.math.cnrs.fr/mustard/article.html

[Anonymous No.12630536]

best algebra 1 textbook?

[Anonymous No.12630624]

>the thoughts start again
>going insane
>haven’t been the same after my sports head injury
>remember Gödel
>only think Gödel thoughts
>everything is okay
>cam down
Thank you Gödel. Saved my life.

[Anonymous No.12630647]

>>12630457
> In those times I was treating Petrovskii's words with some doubt, but now I am being more and more convinced of how right he was. A considerable part of the super-abstract activity comes down simply to industrialising shameless grabbing of discoveries from discoverers and then systematically assigning them to epigons-generalizers. Similarly to the fact that America does not carry Columbus's name, mathematical results are almost never called by the names of their discoverers.

[Anonymous No.12630673]

Why didn’t he publish his findings until Leibniz showed him what he himself had found?
I’ve gotten the explanation before that it was because it came to him from intuition and he didn’t have much analysis on why or how he came up with it. Is that right and makes sense?

[Anonymous No.12631036]

how do I learn to understand/conceptualize math problems? I just can't wrap my head around certain concepts

[Anonymous No.12631239]

>>12631036
Practice, practice, practice some more. At the heart of every math problem is some sort of arithmetic calculation. Experience will allow you to "see" or have a resonable expectation of what is/can be involved.

[Anonymous No.12631255]

What is a good book for discrete dynamical systems? E.g. for non-linear recursion equations, discretization, inverse of discretization.

[Anonymous No.12631281]

>>12623450
most of the stuff you learn in calc 1 isn't really that difficult. its just that most people fucking suck at algebra which causes them to do poorly in calc

[Anonymous No.12631691]

>>12630536
https://www.openstax.org

[Anonymous No.12632046]

>highly intelligent guy
>living in a sub-90IQ country
>all women are dumb and complete sluts
Must be nice being born in a first world country where all women are intelligent and you can easily find a math gf

[Anonymous No.12632070]

>>12630506
I initially thought this was about "mustard witches" and was left somewhat disappointed.

[Anonymous No.12632074]

>>12632046
>implying implications
>not keeping a harem of third-world mouthbreathing sluts

[Anonymous No.12632129]

>eCHT Research Seminar
>The electronic Computational Homotopy Theory Seminar is an online international research seminar. Topics include any part of homotopy theory that has a computational flavor, including but not limited to stable homotopy theory, unstable homotopy theory, chromatic homotopy theory, equivariant homotopy theory, motivic homotopy theory, and K-theory.
>In the 2020-2021 academic year, the seminar will meet about once per month. The format is two 45-minute talks separated by a 30-minute coffee break. The seminar meets on Thursdays at 10:15am-12:15pm in Detroit (Eastern Time).
And so on. Starts this week. https://s.wayne.edu/echt/echt-research-seminar/

>>12632046
>obtain \mathgf
>get outperformed by \mathgf
>become an empty shell and eventually get dumped by \mathgf
or alternatively
>get \mathbf
>get outperformed by \mathbf
>get overly dramatic about it and drive your \mathbf away
No inbreeding, senhor.

[Anonymous No.12632338]

>>12632046
kek anon
thanks for the laugh

[Anonymous No.12632655]

Not sure if I understood all that is to understand here.
The central matrix is [math]\gamma[/math], call the left one [math]\delta[/math] and call the result [math]\eta = \begin{bmatrix} -i & 0 \\ 0 & i\end{bmatrix}[/math].
Then the action of [math]\eta[/math] is multiplication by [math]-1[/math], so it's rotation by 180º about the origin. So I guess the idea of what [math]\delta[/math] is, is having an action close to the mapping [math]\tau\mapsto \tau - i[/math] so that rotation about [math]i[/math] translates to rotation about the origin and then we go back near [math]i[/math] with [math]\delta^{-1}[/math].
But [math]\delta(\tau) = (\tau - i)/(1+i)[/math] is weirder than simply subtracting [math]i[/math], and [math]\delta^{-1}(\tau) = -i(\tau+1)/(\tau-1)[/math] is even weirder. I find way simpler to just think of [math]\gamma(\tau) = -1/\tau[/math] geometrically or substitute the action of [math]\delta[/math] by the mapping [math]\tau\mapsto \tau - i[/math]. What is the point of this matrix? I don't get it.

[Anonymous No.12632798]

Do you guys even finish proof-based maths books? How long does it take you?

[Anonymous No.12632846]

Did you guys ever finish inside a cute girl (male)? How long did it take you?

[Anonymous No.12632881]

>>12632798
Hardly ever. I usually just pick results here and there and combine them to get some non-results because I forget some detail or misinterpret some claim. A chapter or two a day if I really start reading, double or triple the time if there are exercises and I try those.

[Anonymous No.12632898]

>>12632846
i can barely last 2 minutes

[Anonymous No.12633016]

>>12632798
I don't think anyone really does that in a university setting. Generally, students will use a textbook like Rudin or D&F as a reference, following the course notes and homework assignments (which likely include Qs from textbook). You can check out course websites to see how long it takes for them to teach students with a certain textbook.

[Anonymous No.12633218]

QM thread >>12633182

[Anonymous No.12633227]

Any books that go through special/general relativity with a mathematical mindset? Books like Carrol are a bit too physical for me, I know enough differential geometry to get by but it's the physics that hold me back.

[Anonymous No.12633242]

>>12632798
I hardly ever read the whole book. A big pet peeve of mine regarding introductory texts is that they frequently include material that isn't necessary for one's first look at a subject. I generally try to find a syllabus pdf for a course using the textbook and see what sections the professor focuses on.

Once you get to graduate level books you should never read the whole thing.

[Anonymous No.12633297]

how do you calculate this probability, knowing that

1. you have 8 coins
2. 7 are of equal weight
3. you weigh three against three

[Anonymous No.12633355]

>>12632881
>>12633016
>>12633242
Cope.
My uni is full of asians devouring books, from undergrad to graduate level. They won't necessarily finish all of them, but in quantity they do the equivalent of finishing many. And I can't say they do worse than others in general.

[Anonymous No.12633364]

>>12633355
>Cope.
Your post is cope
>My uni is full of asians devouring books, from undergrad to graduate level. They won't necessarily finish all of them, but in quantity they do the equivalent of finishing many.
Asians dont know how to learn properly
>And I can't say they do worse than others in general
But they don't do better in general, despite the massive timesink a textbook is

[Anonymous No.12633400]

>We choose positive integers [math]p,q[/math] s.t. [math]\mathrm{gcd} (p,q) = 1[/math].
Do you read "s.t." as "such that" or "so that"? Or do you choose one of them at random?

[Anonymous No.12633492]

>>12633400
Always read it as "such that".

[Anonymous No.12633512]

>>12633227
>Any books that go through special/general relativity with a mathematical mindset?
dirac's book i think, the one about black holes

[Anonymous No.12633518]

>>12633512
This one?
https://press.princeton.edu/books/paperback/9780691011462/general-theory-of-relativity

[Anonymous No.12633542]

>>12633492
I do the same as well. But I've just found out that the two are actually not interchangeable:
https://www.jmilne.org/math/words.html
For example, in
>(A) Choose an integer n>1 such that 2n is the sum of two primes
>(B) Choose an integer n>1 so that 2n is the sum of two primes
(A) implies the existence of a counterexample to Goldbach's conjecture, while (B) excludes this possibility.
(Though this inconsistency vanishes once both are formalized, as "such that" and "so that" are replaced by precise and unambiguous logical operators.)

[Anonymous No.12633569]

>>12621978
Do you have some pdfs? I'd say I'm B1 in French and I'd definitely like to learn both French and math at the same time

[Anonymous No.12633574]

are all numbers based off 1/2?

[Anonymous No.12633609]

what's the probabilty of rolling 2 dice 4 times, and every time one dice is never greater than the other by 2 ?

[Anonymous No.12633864]

>>12633569
Do you know about b-ok.cc? If you were asking specifically for Cours d'analyse, it's there.

[Anonymous No.12633886]

>>12619163
Are there any finitary scholars in this thread? What's your take on interval arithmetic for real analysis?

[Anonymous No.12633893]

Some representation stuff
>The Benson -- Symonds Invariant for Ordinary and Signed Permutation Modules
https://arxiv.org/pdf/2101.10612.pdf
You who wished for cat girls of your own, maybe this is a step closer to that
>Cyber Kittens, or Some First Steps Towards Categorical Cybernetics
https://arxiv.org/pdf/2101.10483.pdf
Idempotents and spectra of rings
>Characterizing lifting and finiteness of idempotents
https://arxiv.org/pdf/1806.03599.pdf
Maybe useful
>Software for doing computations in graded Lie algebras
https://arxiv.org/pdf/1708.05838.pdf

>>12633574
Sure. Given any rational number [math]\frac{p}{q}[/math], write [math]p = 2p\cdot \frac{1}{2}, q = 2q\cdot \frac{1}{2}[/math] to see that [math]\frac{p}{q} = \frac{2p}{2q} \cdot \frac{1}{2}[/math] to see that all rationals are based off 1/2. Then use your favourite way to get rel numbers from rationals and then add the imaginary unit to see that all complex numbers are based off 1/2.

>>12633355
I don't care.

[Anonymous No.12633918]

>>12633893
Oops, not [math]\frac{p}{q} = \frac{2p}{2q} \cdot \frac{1}{2}[/math] but [math]\frac{p}{q} = \frac{2p}{2q} \cdot \frac{\frac{1}{2} }{\frac{1}{2}}[/math]!

[Anonymous No.12633925]

>>12633893
begone succubus

[Anonymous No.12633931]

>>12633518
yeah i think it finishes with black holes

[Anonymous No.12633934]

>>12633925
>\succ ubus
It's Erzsébet Mathory to you. Bathing in the blood of undergrads to keep myself eternally under 24 years old.

[Anonymous No.12633938]

>>12633569
grothendieck essays are in french and people translate them in english

[Anonymous No.12633944]

Combien valent les manuscrits d’Alexandre Grothendieck ?

Gilles Rotillon, Professeur émérite de sciences économiques, Université de Paris-Nanterre
17/09/2017
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Alexandre Grothendieck est un des plus grands mathématiciens du 20ème siècle et à sa mort en 2014, après plus de vingt ans retiré du monde, on a trouvé chez lui 68 000 pages non publiées qui s’ajoutent aux 28 000 déjà répertoriées par le département de mathématiques de l’université de Montpellier et également non publiées. Ces pages font l’objet d’une demande d’évaluation de la part de ses héritiers, comme l’exige la loi, pour pouvoir déterminer les droits de succession qu’ils devront payer.

Comme il n’y a pas marché pour les écrits mathématiques, les références manquent pour qu’un expert puise proposer une évaluation, comme c’est souvent le cas pour les manuscrits littéraires, les lettres ou les tableaux. Et puis les experts en l’occurrence sont des mathématiciens dont toute la pratique s’appuie sur la discussion entre pairs des travaux en cours, disponibles sans contrainte sur des sites spécialisés comme arXiv.org, ce qui conduit « naturellement » à fixer un prix nul pour ce type d’écrits. Cette évaluation est aussi en accord avec la théorie économique, dans la mesure où les écrits en question ressortent de connaissances ayant le statut de biens publics.

[Anonymous No.12633950]

Alexandre Grothendieck a révolutionné l’algèbre et la géométrie dans son œuvre publiée, et on peut penser que les écrits nouveaux contiennent des pierres solides pour approfondir ces domaines de connaissance. La science avance en s’appuyant sur les travaux des anciens (les épaules de géants comme le disait Newton) et nul doute que les épaules de Grothendieck ne soient parmi les plus puissantes. Ne pas rendre publics ces textes pour que la communauté mathématique puisse s’en servir pour faire avancer sa science serait un crime intellectuel, car seule cette communauté a les compétences pour les apprécier à leur juste valeur qui ne se mesure pas en euros mais en une meilleure compréhension de son objet. Compte tenu de la nature de ces textes, on voit mal un collectionneur prêt à payer des fortunes pour avoir dans un coffre en Suisse ces manuscrits. Et qu’un mécène puisse se porter acquéreur pour en faire bénéficier la communauté mathématique créerait un précédent qui pourrait affecter à l’avenir toutes les productions scientifiques posthumes et donc le fonctionnement libre des échanges de connaissances. On peut comprendre que les héritiers soient frustrés d’une telle évaluation mais ils n’ont pas de droits de propriété intellectuelle sur ces textes, n’en étant pas les auteurs. Et s’il leur venait l’idée saugrenue d’interdire l’accès à cette production sous prétexte qu’ils sont les enfants d’un génie, ils ne feraient que manifester l’incompréhension de ce qui faisait justement le génie de leur père.

[Anonymous No.12633956]

Kant, écrivait dans Fondements de la métaphysique des mœurs[1] « Dans le règne des fins tout a un prix ou une dignité. Ce qui a un prix peut tout aussi bien être remplacé par quelque chose d’autre à titre d’équivalent. Au contraire, ce qui est supérieur à tout prix, ce qui par suite n’admet pas d’équivalent, c’est ce qui a une dignité ». Que la production mathématique d’Alexandre Grothendieck ait une dignité plutôt qu’un prix, c’est ce que nous risquons de découvrir à nos dépens si nous continuons à vouloir absolument lui en attribuer un autre que zéro.
[1] E. Kant, Fondements de la métaphysique des mœurs, trad. V. Delbos, Livre de poche, 1993.

[Anonymous No.12634245]

what in the name of fuck

[Anonymous No.12634276]

https://www.youtube.com/watch?v=loCBvaj4eSg
thoughts?

[Anonymous No.12634283]

>>12634276
atheists are dug addicts desperate to build a narrative about drugs being virtues

[Anonymous No.12634306]

>it took humanity 10 000 years to discover that shapes on a non flat surface are different than a flat surface
wtf??

[Anonymous No.12634324]

Will learning from an LA book like Hoffman & Kunze make me understand LA more for ML than a CSnigger who learned it from Strang? Or should I next read a Matrix Analysis text like Roger?

[Anonymous No.12634448]

>>12634306
only retards think that "writing down something in modern mathematical notation" equals "discovering"

[Anonymous No.12634492]

>>12633893
>Cyber Kittens, or Some First Steps Towards Categorical Cybernetics
https://www.strawpoll.me/42523191

[Anonymous No.12634558]

>>12633893
>>12634492
this is fucking garbage im seething right now fucking category kittens theory

[Anonymous No.12634568]

>>12619163
>Das alte:
I'm German but (or maybe because of it) I find this extremely annoying

[Anonymous No.12634616]

>>12634492
Voted No.

>>12634558
Why exactly? Are you sure you aren't taking this a bit too seriously?

[Anonymous No.12634630]

>>12619163
The sigma summation notation is to integration as the pi product notation is to _____?

[Anonymous No.12634639]

https://youtu.be/RTcXiutDxYY

should be nice

>>12634630
https://en.wikipedia.org/wiki/Product_integral

[Anonymous No.12634669]

>>12634616
because this kind of ""math"" is a joke
setting up 15 pages of notation in order not to do something, but only to orgasm over how nice the notation and definitions look
the math community is concentrating on meaningless garbage, day after day we come closer to gender studies level of retardedness
there are too many people going into phds and this is the result, this is absolute lowest of the low
i have more respect for the random person who tries to prove riemann hypothesis using basic calculus

[Anonymous No.12634744]

Please answer me this /mg/ honey. If not for the endangered tenured boomers coming in to give the same lecture on a broad undergrad topic like analysis for the 40th year, would this archetype of the platonist pure mathematician classicalist who only works on a blackboard be practically eliminated? That is, most researchers have at least something in their workflow ensuring that their results aren't complete made-up uncomputable undecidable fluff conjecture.

[Anonymous No.12634826]

>>12634639
Joel also runs an online the Oxford Set Theory Seminar channel, which are more set theory research talks.

[Anonymous No.12635063]

How much about ODEs / PDEs does one need to know to get into SDEs? I already have the probability / analysis background.

[Anonymous No.12635074]

>>12633569
>>12633938
Not a PDF but there are a lot of good talks between French mathematicians on YouTube, e.g. Serre and Alain Connes on the Serre-Grothendieck correspondance
https://www.youtube.com/watch?v=pOv-ygSynRI

[Anonymous No.12635083]

>>12631255
Wadefug no combinatorics Chads present?!? Please help a geometer out.

[Anonymous No.12635134]

>>12634324
go through numerical recipes in C or someshit.

[Anonymous No.12635256]

>>12633893
>Then use your favourite way to get rel numbers from rationals

Are you implying there is such a way?

[Anonymous No.12635396]

https://math.stackexchange.com/questions/2790034/for-simple-gamblers-ruin-fair-coin-flipping-how-does-one-derive-the-formulas
Why are we allowed here to make an equation
[eqn]\mathbb{E}[t]=p\cdot (n_1+n_2)+(1-p)\cdot 0[/eqn]
I don't get this whole thing about 'stopping time' and the notation [math]A_t[/math]. Why can we analyze expected value only when the game is finished? I mean, it's not guaranteed that at the time [math]t[/math] the game is finished; it is finished at the time [math]t[/math] with some probability. Why can we just make a leap and throw away all the non-ending states of the game and analyze the expected value assuming that the game is finished at the time [math]t[/math]

[Anonymous No.12635509]

>>12635396
Read chapter 4 in Durrett's probability book.

>Why can we analyze expected value only when the game is finished?
He isn't only analyzing expected value when game is finished, and in fact his equation (1) is saying exactly that the expected value at any turn is equal to starting balance.
>I mean, it's not guaranteed that at the time t the game is finished
That is exactly how t is defined, i.e. the time at which the game is finished. This is almost surely finite since at any state of the game A wins the game with 9 consecutive winning turns.
> it is finished at the time t with some probability.
Yes with probability 1
>Why can we just make a leap and throw away all the non-ending states of the game and analyze the expected value assuming that the game is finished at the time t
Nothing is being thrown away.

[Anonymous No.12635534]

>>12634669
I see. Have you ever read other applied CT papers. They are usually absolutely horrible. I tried reading one just to see what people think they can do with it on brains and then I found out I had a symmetric monoidal category enriched with probability spaces within my cranium. That is when the probability of me reading any more became 0.

>>12635256
Yes. Just copy whatever some first year textbook says. You know, lies have never been printed.

[Anonymous No.12635569]

>>12635509
>>12635396
I’ll also add bc I think this may be the real point of confusion: he’s implicitly considering the rv A_{min(n,t)}. From this we still have (1) for all n and then letting n tend towards infinity we get (2).

[Anonymous No.12635699]

Why do word problems like geometric applications of optimisation give me such trouble, but equations and stuff don't? I mean, English was one of my best subjects in school. Yet geometric problems in differentiation and integration eat my ass hard.

[Anonymous No.12635716]

>>12624335
>With your comments on the video, I think I'll just skip it altogether
It was more of a gut feeling than anything else, not a big deal. Just so you know. I think I'll take a look when it comes out.
>It only made me return here
What made you take off the first time? hanging out with irl friends/colleagues?

>>12628905
Shiva.

>>12630624
Careful with poisoned food.

>>12632129
Yeah I think most pairs of mathematicians wouldn't work as a couple because of that. Though in my experience, most of them marry someone from academia, sometimes even close to their area...

>>12632798
I finished one and more than 90% of another, both were undergrad books. I usually do the exercises, so it takes 2-7 or even more days per chapter. If I were immortal I'd finish many, but life is short.

>>12633355
I know some chinese guys who do this, they do quite well. But I think they could use their time even better.

>>12633574
You can use base 2 instead of decimals, every real number will be a laurent series with coefficients 0 or 1 evaluated on 1/2.

>>12634639
Are product integrals really useful or is it more of a curious thing like wheels?

[Anonymous No.12635864]

>>12635716
>Are product integrals really useful or is it more of a curious thing like wheels?
I think the latter

[Anonymous No.12635994]

>>12635716
>It was more of a gut feeling than anything else, not a big deal. Just so you know. I think I'll take a look when it comes out.
That should be soon enough.
>What made you take off the first time? hanging out with irl friends/colleagues?
I had no colleagues and hardly any friends. I guess I just started hating everyone in these threads and left, swore myself that I would never return here or to maths. A double failure on that.

[Anonymous No.12636188]

>>12635063
Not much, mostly you just need measure theory. The two books I have in the preface say that's the only assumed knowledge. If you've seen some ODEs/PDEs and have the analysis/probability background you'll be fine.

[Anonymous No.12636234]

What is the definition of a game? Not some subtype of games, but games in general. Are they just a function on topological spaces?

[Anonymous No.12636263]

Without arbitrarily restricting the input domain or making it piecewise in any way, how can modify an ordinary polynomial function so it's no longer entire?

[Anonymous No.12636326]

I really like this curve.
sin(sin(x) + cos(y)) = cos(sin(x y) + cos(y2))

[Anonymous No.12636334]

>>12636326
me too, how'd you find it?

[Anonymous No.12636343]

>>12619163
Bros im getting into deterministic and non determinist programming. Any book for getting into non deterministic linear and non linear prog?

[Anonymous No.12636344]

>>12634306
Tbf, I think it's not just "non flat surfaces," it's specifically things that are distinct from any deformation of a 2 dimensional plane. So if you did geometry on a cylinder it would be equivalently deformed into a plane, and Euclidean geometry would remain valid, but a sphere CANNOT be deformed into a plane, nor can a saddle, which is why they have a serious divergence with plane geometry. This is (I think) an essential question that motivates topology. I have to admit I'm shooting in the dark a bit here, I haven't done formal geometric reasoning in a solid three to four years and my degree has a focus on applied mathematics. Anyone care to comment?

I do like to imagine some Franco-Prussian era cavalryman trying to work through his copy of Euclid on the surface of his horse's saddle, endlessly frustrated because he keeps coming up with a triangle that has less than 180 degrees, which contradicts Euclid, but Euclid MUST be right and HE must be wrong, unaware that he's working with mathematics that could shake the foundations of academia. If only he knew...

[Anonymous No.12636358]

>>12636326
>Computation time exceeded

[Anonymous No.12636377]

>>12636334
I went poking around Google Images for "pretty-looking curves" and a related curve was a little ways down the search results. Thought I'd have a little fun modifying things and liked what I ended up with.

[Anonymous No.12636663]

What's a good introductory text to differential geometry?

[Anonymous No.12636671]

>>12635699
It gets worse when you ESL lecturer is writing your PDE questions.

[Anonymous No.12636685]

>>12636663
Depends on your background. Since you say introductory I'll suggest the standard do Carmo Differential Geometry of curves and surfaces. Or the one by Toponogov by the same name if you like russian books.
If you want slightly more advanced then Kuhnel's Differential Geometry: Curves - Surfaces - Manifolds is good.
Finally if you want an advanced intro consider:
Manifolds and Differential Geometry by Jeffrey Lee.

[Anonymous No.12636711]

>>12636663
Godinho & Natario's Riemannian Geometry book is basically a more modern version of do Carmo's book on the same topic with later chapters being focused on mathematical physics as an application. It also has solutions to problems which can be helpful if you're stuck. That said, I heavily recommend these lectures if you want to get into differential geometry, they're extremely good on their own and they're even better if you use them as a complement to your reading
https://www.youtube.com/watch?v=7G4SqIboeig&list=PLFeEvEPtX_0S6vxxiiNPrJbLu9aK1UVC_&index=1

[Anonymous No.12636761]

>>12636711
>>12636685
Thank you. My back ground is mathematic and physics, but I my confidence in how much of of multivariable, ODEs and PDEs I retained after doing papers in them isn't high, so am looking for a Diff geo book that just starts out basic and progresses from there.

Honestly the hardest part of mathematics for me as always been just understanding notation and understanding the question/problem. The actually theory, especially relating to physics as always been a piece of cake

[Anonymous No.12636825]

>>12632655
Where is the analytic number theory anon when I most need him? Please help me senpai

[Anonymous No.12636884]

bros i can't concentrate on math
everytime i open a textbook, i start thinking about hot trannies

[Anonymous No.12637048]

How do I make fun also can someone point me towards some good recources on fundamentals?

[Anonymous No.12637056]

>>12636663
>>12636663
>What's a good introductory text to differential geometry?
isham

[Anonymous No.12637057]

>>12637048
Instead of fundamentals, start studying exact functors between abelian categories, that is, the categories [math]\mathbf{ExFun} (\mathcal{A}, \mathcal{B})[/math]. You will suddenly understand what fun was when you realise you have lost it. What once was is no more.

[Anonymous No.12637364]

>>12637057
Useless anime poster. I'll go look for fundies.

[Anonymous No.12637375]

>>12634744
Please respond, I need to decide whether I should change majors or just apply to a better grad school.

[Anonymous No.12637429]

>>12632655
>>12636825
It all makes sense now. This is the first time (or maybe second) one of their exercises only makes sense after I read a bit further down after it gets cited in the text.
It's simply that the matrix's action maps the neighborhood *holomorphically* to a zero's one such that in the image the points get perfectly rotated by 180 degrees, not just approximately. And I guess the approximation is better as closer the points are, but I don't think I'll try to make this precise right now.
This matrix is important in this context because it's an ingredient to achieve the section's goal, it doesn't feel like random nonsense anymore.

[Anonymous No.12637467]

Can someone recommend me some resources on Fourier transforms, DCT and wavelet transforms? Brainlet here. I'm forced to take an image processing class.

[Anonymous No.12638582]

Is there any way to turn the expression a*10 + b into b*10 + a, using only arithmetic and not using a or b as variables?

>>12637467
Someone will do it if you post your question again without the anime girl. Newfags arent allowed to post anime girls.

[Anonymous No.12638610]

>>12638582
ye work in Z/9Z.

[Anonymous No.12638650]

>>12638610
Can you elaborate cause I havent studied fields much yet

[Anonymous No.12638723]

>>12638582
Not really. Consider for example [math]a = 2, b = 2[/math], with [math]10a + b = 22[/math] and [math]10b + a = 22[/math], and also [math]a = 1, b = 12[/math] with [math]10a + b = 22[/math] and [math]10b + a = 122[/math].
Clearly shows that [math]10b + a[/math] can't be recovered from [math]10a+b[/math].

[Anonymous No.12638728]

>>12638723
*[math]10b + a = 121[/math] on the last equation.

[Anonymous No.12638876]

>>12638723
I meant B is one digit sorry

[Anonymous No.12638883]

>>12638876
You're retarded, you know that right?

[Anonymous No.12639113]

>>12628930
No damn it, most American undergrads do not use Rudin.
mathdept.ucr.edu/sites/g/files/rcwecm1516/files/2019-11/209ABC_Syl.pdf
sites.science.oregonstate.edu/~ossiand/Mth412-512_2016Syllabus.pdf
math.unm.edu/~crisp/courses/math401/spring19/info.html
math.purdue.edu/~catlind/MA341/
Many such cases! I think Caltech, MIT, Princeton are among the rare exceptions to the rule. The same goes for Dummit and Foote. Those are *challenging* books for undergrads. Moreover, most professors don't go to the /sci/ wiki or reddit to pick textbooks.

[Anonymous No.12639204]

>>12639113
>>Moreover, most professors don't go to the /sci/ wiki or reddit to pick textbooks.
>"Bob, is that you? How's the job at Springer going?"
>[...]
>"So you'll pay us 10% commission if we use Springer books for classes? Say no more, I'll tell the lads we'll finally get a new pool table. I think we were all getting tired of using CUPs for everything."

[Anonymous No.12639250]

>>12639204
This is true. Count the number of Pearson Prentice-Hall logos in the youtube thumbnail from >>12620597
I've seen more Pearson-cucked math departments than Springer, though.

[Anonymous No.12639315]

>>12638883
Proof?

[Anonymous No.12639964]

>>12639113
you're picking mostly lower tier schools. I admit that the original question was whether 'most students use Rudin', but that most top institutions use it should tell you something.

For example, in addition to Caltech MIT and Princeton, we have:

Harvard
> http://people.math.harvard.edu/~tcollins/Math112.html
Chicago
> http://www.math.uchicago.edu/~eskin/math204/math204.html
Columbia
>http://www.math.columbia.edu/~drouot/MA.html
Berkley
> https://math.berkeley.edu/~vvdatar/m104f17.html

These are all syllabi for particular semesters, but from knowing students at most of these schools I'm confident in saying that Rudin is still that standard reference for undergrad analysis I.

[Anonymous No.12640252]

Has applied category been applied to anything actually useful?

[Anonymous No.12640267]

Has applied category theory ever done something that's actually useful?

[Anonymous No.12640287]

>>12640267
It’s turned a lot of young “men” into women for me to date.

[Anonymous No.12640375]

hey mg, biz here, ive been trying my hand at daytrading but im having a hard time figuring how to calculate my returns

i spend $100 at 30 shares per dollar and acquire 3000 shares

the price falls 10% to 33 share/dollar and i realize a loss, vacating 33% of my position, selling 1,000 shares for 30 dollars, and now hold 30 dollars and 2,000 shares

the price again falls by 10% to 36.3 shares per dollar and i spend my 30 dollars and acquire 1089 shares totaling 3089 shares

the price from here rises 16%, to 31 shares per dollar, how many shares can i sell to realize profit? if i sold 1000 shares, what percentage of my sale is loss vs gain?

how many shares can i sell if i wished to realize another loss, expecting another short term drop in price, but /without/ vacating my green position low? i want my 89 green shares in where they are at, to realize gain with tomorrow, but in the short term, the shares i purchased high are rotting, and i wish to vacate them

i want to vacate my high position and maintain my position low, if i sold 1200 shares, what percentage of those 1200 are red shares vs green? is it 1089 green and 111 red? or 89 green? those 1089 shares all saw a 16% increase, and that 16% was applied to 30% of my holdings.

this is a very simple example, and the complexity increases enormously with each transaction. i am familiar with coding, but id love some direction for resources for this type of automated accounting, as i dont know the vernacular

how can i know exactly, during all transaction histories, with all varying exchange rates, what portion of each of my holdings are currently accessible profits, and what portions are losses, and if i were to sell, lets say i bought high 10 times and low only 3... but each purchase represents a certain percentage of my total portfolio can u see my problem?

[Anonymous No.12640747]

>>12640375
>daytrading when you struggle with arithmetic

[Anonymous No.12640930]

Analytic number theory is fucking wild. How the fuck do these nerds come up with so many weird mind numbing identities?

[Anonymous No.12640945]

>>12619163

I'm having a basic bitch chess phase and I recently learned that Champion Emanuel Lasker made a substantive contribution to Commutative Algebra. Bourbaki even mention it in their historical notes. Neat.

[Anonymous No.12641019]

>>12640375
>high position
>low position
>green shares
>red shares
>maintain position
>vacate position

What the fuck is the point of using these dumb terms? Just multiply the shares by the price bro, then compare it to the baseline $100 bro. Profit.

If it adds up to a profit, sell.
If it doesn't, bad luck idiot - you lost the game.

This is literally the most basic aspect of trading: figuring out if you've made a profit: comparing the $ value of how much you had to the $ value you have now.

[Anonymous No.12641052]

>>12638582
In Z/9Z every number is written as a residue of "how much N is distant from the less distant multiple of 9". i. e. 10 = 1 mod 9 since the closer multiple of 9 to 10 is 9, the distance between 10 and 9 is 10-9=1. Another example take 321 the it is closer to 9*35 so 321-35*9 = 6 and 321 = 6 mod 9.
Your equation mapped to the ring Z/9Z becomes 10*a + b = a + b = a+10*b (mod 9).

Also you should be at least 14 to post on this board, how the heck don't you know about ideals, ring and quotient of a ring by an ideal?

[Anonymous No.12641066]

Is there any hope of continuing pure maths as a hobby post graduating? Anyone here that’s done it? If so, in what subjects?

It seems doable for easy material, but I worry that it’s impossible to progress in grad level material without full time study.

[Anonymous No.12641094]

>>12641066
>Is there any hope of continuing pure maths as a hobby post graduating? Anyone here that’s done it? If so, in what subjects?
http://spoirier.lautre.net/en/

[Anonymous No.12641119]

>>12641094
>set theory
>incel

Don’t know which is worse.

[Anonymous No.12641198]

>>12641119
>Don't know which is worse

How about category theory?

[Anonymous No.12641351]

>>12619871
Are you an engi?
Afaik you rather need analysis knowledge for pdes, rather than odes, although intuition always helps.
Look through fourier series and transforms, partial derivatives are given.

Knowing what a laplace operator is useful for the heat equation and such. But you don't need lots of vector calculus for it. If you get stuck on the lin alg side of the text you can always just review that.

[Anonymous No.12641364]

>>12633934
Its a fucking b

Holy shit you a retarded

[Anonymous No.12641388]

>>12641351
Not the guy you’re replying to but most undergraduate PDE courses are aimed at engineers and definitely don’t require real analysis. Rigorous PDE in the shape of something like Evans obviously needs basic analysis background.

[Anonymous No.12641404]

>>12641094
>that fucking website
What the actual fuck

[Anonymous No.12641432]

A geometer could like this:
>Nilpotent varieties in symmetric spaces and twisted affine Schubert varieties
https://arxiv.org/pdf/2101.11677.pdf
Gorenstein stuff
>On properly stratified Gorenstein algebras
https://arxiv.org/pdf/2101.11899.pdf
Someone may be interested in this
>Notes on diffeomorphism classes of the doubling Calabi-Yau threefolds
https://arxiv.org/pdf/2101.11841.pdf

>>12641364
I didn't realise we were in a bath general? I like rubber ducks.

>>12641119
Which is the cause and which is the effect?

[Anonymous No.12642061]

>>12620078
Moskowitz, Jacobson, Grillet, Rotman, Knapp, etc.

[Anonymous No.12642094]

>be early 30s
>probably lower end of midwit IQ (and OK with that)
>complete pic related, all exercises, try to
rewrite and generalize a lot of the main topics, and to recognize similarities in different fields
>found it fairly straight-forward once I got into the habit of actually thinking about the material

How far could someone like me get self-learning math? At what point am I likely to be filtered by the requirement for original thought, pattern-recognition, creativity, and other attributes that make people just better at math than others?

[Anonymous No.12642097]

Mathchads, I kneel.

[Anonymous No.12642271]

>>12642094
Who knows?
Go as far as you can, that's all you can do.
Good luck!

[Anonymous No.12642339]

What is the point of self-learning if you are never going to actually learn anything relevant? This is not to say that one should stop learning at all, but it is unlikely that one could ever reach the precipice of mathematics if one were educated in a field even parallel to it. The necessary feedback that one receives from a professor is lacking, and unless one proceeds with rigour, which is unlikely to be grasped by one who ventures alone, one will always have gaps in one's work. Even, if one were to proceed with rigour, it is unlikely that one could dedicate the same amount of time to the field. Mathtards like to posture how difficult their field is, but it is likely that if the majority of them had not picked the major, they would be incompetent in mathematics as well. Therefore, from now on, I will just cope like this.

[Anonymous No.12642359]

>>12642094
Try your hand at linear algebra, it's fun, useful, some of the material will be familiar, and linear transformations behave really nicely.
>>12642339
I think I don't get your point. In any case, it's just neat, and also you can learn stuff to >apply elssewhere

[Anonymous No.12642382]

>>12642359
tl;dr: mathematicians have feedback loops which allow them to succeed in mathematics, unlike self-learners. Even the most average of mathematicians is competent at mathematics solely because of these feedback loops. A person who never gets to experience such feedback will most likely reach a point at which he will be filtered which is not the case for a mathematician.

[Anonymous No.12642472]

>>12642339
>you need teachers to get good at X
you can say this about many things you know

[Anonymous No.12642474]

>>12642339
the invisible hand guides in all subjects

[Anonymous No.12642549]

>>12641066
Your willpower to study for the sake of studying decreases as you get older. Consider that you'll have very different priorities 10 years from now (career, marriage, kids, etc.).

[Anonymous No.12642618]

>>12642094
given that this is the quality of "lecture notes" from a uni in 2021, self-learning is the way to go and you can get very far with it with good habbits and good practice.

[Anonymous No.12642722]

https://www.ipetitions.com/petition/mathematics-is-not-redundant

[Anonymous No.12642865]

>>12642722
absolute clown world

[Anonymous No.12642884]

>>12642722
I don't understand how normogroids caught onto this. Someone must've ratted us out.

[Anonymous No.12643394]

>>12642865
>>12642884
Really sucks. The department was pretty run down already in the end of 2019 because of all sorts of MBA stuff draining all the uni funds. I'm not sure if Pirashvili is old enough to retire, but the rest of them definitely aren't and now isn't the optimal time to be unemployed.

[Anonymous No.12643596]

>>12641019
when you have many holdings at many different prices your holdings represent a certain percent of your total holdings, and those percentage holdings are related to a percentage of your total purchasing power at the time you acquired them, today, tomorrow. you also have to consider your current cash portions, and their current buying power compared to when you acquired the cash
the math on a single trade is easy, the math on 100 trades spread across many currencies and many different types of holdings and many exchange rates becomes substantially more difficult because of the sheer volume of variety
you think i’m an idiot because if i sold at 31 i’d be down a few percent compared to where i bought back, but you’re an idiot for even considering i was down at all when i somehow acquired more than i’d started with, because you see only
dollars. but for all you know if i’d exchanged into euros when i’d sold and the dollar ranked during that time i’d be up even more when i repurchased at 36 with a stronger currency
you assume a bad bet today is a bad bet tomorrow when i could take a bad bet yesterday and turn it to a good bet today
you’re like thats such a tiny percentage what’s the difference, accept your luck
it’s that i have acquired more time off my locked holdings from yesterday, and turned bad luck, which is only a measure of time, into good luck today
just because it’s over your head doesn’t mean it’s stupid and worthless you incorrigible niggers

[Anonymous No.12643773]

>>12643596
>my gambling lingo makes it more legitimate!

[Anonymous No.12643834]

>>12643773
>look mom im dabbing again

[Anonymous No.12643906]

>>12642722
This was attempted at the University of Rochester in the 1990s and the administration ultimately backed off. Best of luck Leicester anons.

[Anonymous No.12643986]

>>12642722
is there anything the sacred boomer/xoomer/zoomer combo can't destroy?

[Anonymous No.12644206]

>>12643906
Really? I had no idea, but that could explain why my supervisor worked in Rochester for such a short period (during the 90's exactly). I wonder if the British decision making ability is as good as that of their colonies. But yeah, good luck to everyone in Leicester!

>>12643986
Most likely not. Even trying to name anything would probably seem like a challenge to them, and then the said thing would be destroyed.

[Anonymous No.12644327]

>>12639113
I said the material covered by Rudin & D&F not those books specifically. One link you posted uses folland, which is more advanced than Rudin's principles.
If you look at the original video for a 'pure math' book list it's all physics & engineering related math books. No algebra or serious real analysis at all regardless of book.

[Anonymous No.12644603]

The \sum notation that /sci/'s mathjax supports is all inline: [math]\sum_{n=1}^{\infty}x[/math]. How do I fix it?

[Anonymous No.12644643]

I have been regularly posting in this general for almost a year and have a big folder of hoarded pdfs that I started collecting in May last year. You may be pleased to know that I've almost always restrained myself from posting about shit I'm unfamiliar with and starting shitty discussions about babby-tier stuff.
/mg/ how can I, a part-time forklift driver who dropped out of high school motivate myself to learn basic algebra?

[Anonymous No.12644649]

>>12644643
Close browser, open textbook, read, do problems. Are you retarded?

[Anonymous No.12644650]

>>12644643
rent-free

[Anonymous No.12644709]

>>12633400
There's also "subject to"

[Anonymous No.12644738]

>to prove A∨¬A one must already have proved A or ¬A
y/n?

[Anonymous No.12644776]

Does anybody know graph theory terminoloy that can help me search for what I'm looking for? I have a graph that can be cut into 2 subsets of nodes {a,b}, where any node in a can only reach another node in a on the original graph by moving such that the total number of moves is a multiple of 2, and the same for any node in b (example set with this property - the star of david with alternating node colors).
What's the name for graphs with this property for n subsets where all paths between members of a given subset have a length that is a multiple of n?

[Anonymous No.12644787]

>>12644776
2 - bipartite graph.
3 - tripartite graph.
In future, post in >>>/sci/sqt/ instead.

[Anonymous No.12644908]

>>12644603
\sum\limits or use \displaystyle (didn't test the latter here though, I prefer the former).

[Anonymous No.12644978]

>taking galois theory this semester
>professor is absolute shit
>grades the homework on completion. doesn't even give feedback
>hard exams
this is the end, isn't it?

[Anonymous No.12644985]

>>12644908
test
\sum\limits_{n=1}^{\infty}x should appear as: [math]\sum \limits_{n=1}^{\infty} x[/math].

[Anonymous No.12644990]

>>12644985
>enclosing \infty in curly braces
you nasty bitch.

[Anonymous No.12644997]

>>12644985
testing to see if /eqn tags work properly

[eqn]\sum_{n=1}^\infty x[/eqn]

[Anonymous No.12645020]

>>12642722
Tick tock, poor methematicians.

[Anonymous No.12645040]

>heh luckily i study math
>unlike those poor office slaves I wont have my job replaced by a machine
>realise that ai will solve mathematics...
how do i cope?

[Anonymous No.12645045]

>>12644990
[eqn]\sum\limits_{n=1}^{\hat{\infty}}x[/eqn]

[Anonymous No.12645072]

>>12644978
Doesn't matter, you can just learn it on your own if the course is trash

[Anonymous No.12645101]

>>12644978
My galois theory course was hard too, which is unfortunate because I really feel like I understood the material. However the professor decided to finish Galois theory in 4 weeks and then move on to algebraic number theory. The exams were the worst.

[Anonymous No.12645106]

I feel like an idiot, but it's been years since I went to college. I'm trying to generate a function to randomly generate a number [0,1] that weights 50% at 0 and inverse-logarithmically slides down to essentially 0 at 1. Can anyone help, or should I try to dig out my old notebooks?

[Anonymous No.12645159]

>>12645101
At least you learned some algebraic number theory, one of the most based subjects based.

[Anonymous No.12645166]

>>12645101
At least you learned some algebraic number theory, one of the most based subjects.

[Anonymous No.12645170]

>>12645159
Yes, I enjoy the material, but it makes for a very compressed course with way too much material for an undergrad. Plus the course notes were quite dense so I had difficulty because I just had general algebra books, at the start he never suggested we'd need a book on number fields and such.

[Anonymous No.12645226]

Can someone explain the proof of Balog Szemeredi Gowers to me? It's so technical it's basically impenetrable, my lecturer presented it as if he was reading straight from a book, he gave no insight into what's going on

[Anonymous No.12645230]

>>12645226
Holy shit that name is arcane

[Anonymous No.12645235]

I have something really special for the next mg edition guys, so excited!

[Anonymous No.12645239]

>>12645230
/mg/ has a combinatorics deficiency, it's basic junior stuff. Idk because I studied topology but the chads talk that stuff at a young age

[Anonymous No.12645246]

>>12645239
>BSG is basic junior stuff
kill yourself nigger faggot

[Anonymous No.12645268]

>>12644643
I am >>12642094, a fellow high-school dropout and NEET, now in early 30s who is now very motivated to learn mathematics. My suggestions are:

1. Forget the PDFs, get an actual physical book, and STICK TO IT. Don't switch between different books and fields; you will make progress in none of them.

2. Start from the beginning, and try and get out of the thinking that this basic material is for kids. This attitude will make you skip a lot of important fundamentals that will help you think for yourself. THIS IS WHAT HAS HINDERED ME THE MOST. I used to think 'well yeah obviously I know the product of two negative numbers is a positive number', but I didn't ever bother thinking about why that is the case.

3. Try and prove things based on what information you have been given. Recognize when later theorems have been built on theorems you have previously proved

4. Try and think about different ways of saying the same thing. For example, the number 123 is a positive integer, but also a polynomial

As for motivation? For me I just find it fun to be using my brain. Others seems to recommend thinking of it as a game where you level up. At the most basic level, you will realize that math isn't that hard, and that taking the time to learn it properly will put you above 90 % of your peers who can't be bothered to think in a logical, mathematical manner. And it will be a start to applying yourself and getting a better job (if that's what you want).

[Anonymous No.12645272]

>>12645271

[Anonymous No.12645277]

>>12645226
this is the first link i found in google
is this the thing?
http://schoen.home.amu.edu.pl/remark-B-S-G.pdf

[Anonymous No.12645279]

>>12645040
AI is currently trash at math and if it ever gets good the singularity is happening so I'm not really concerned.