[math]/\mathfrak{mg}/[/math]the King of mathematics editiontalk maths, formerly >>16135585
>>16160352[math]\mathfrak{first}[/math] for Emil Post
>>16160030Well, I think we're talking past each other a little bit. I'm also certain that the undergrad measure theory in my university is not taught to the same level of rigour as a proper graduate course. That's not what I was saying.I attached the table of contents of our lecture notes, iirc we went through chapters 1-5 and 8 in the measure theory course. This was 8 weeks, 8 contact hours per week.Comparing this to axler's book, we went through the equivalent of his chapters 2,3,5, and 7. There was also a course on functional analysis immediately following it which went through the equivalent of his chapters 6, 8, and 10.For the graduate probability courses: it's interesting. We have some masters courses just like yours, but in it we rushed through the measure theory in, say, 10 contact hours, to get to the probability, with the understanding it's been covered before.These three separate semester-long courses then cover roughly the same topics as yours, with (as far as I can tell) some extra also.At least, I recognize most of the topics in his overview as being treated in two of our courses (one on measure theoretic probability and one on stochastic (markov) processes). Then we also covered the stochastic calculus of semimartingales in a third semester.One very interesting aside is that there are essentially no examples or applications in these courses. I always thought that was a shame, and it's something I think american universities do better, because the applied courses don't actually require the theoretical ones as prerequisites, making it feel pointless to some.Relatedly, since you've some experience with teaching (in america, I assume, too?): I noticed it's a lot more common to have year-long courses, when that basically doesn't occur here. Do you think there is any particular reason behind it? Here, it's done to relieve the instructors somewhat, so they don't have the workload of teaching and grading for 6 months continuously.
One of the worst things mathematicians ever did was ceasing to be mindful of the fact that they were approximating when they were approximating, merely because the margin of error became infinitely small (infinitesimal). Something is only exact when no part of it or bit of it is wrong or inaccurate.
>>16160468The UC system is actually a good bit closer to a "European" model in that they do 4 10 week sessions in a year instead of 2 6 month semesters (as is more common in the US). As far as I'm aware Todd's classes on Probability Theory were intended to be fit into 3 consecutive 10 week blocks. I'm much more used to the "east coast" way of doing things in the US where we have 2 14-16 week semesters (length depends on location) and then 2 shorter sessions (a 10 week summer and 6 week winter) for optional and accelerated classes. It's funny that you bring up the year-long courses as an odd occurrence. I actually really like when they are able to do this because it allows for students to have a seamless development of a complicated topic (e.g., measure theoretic probability and stochastic processes) without a lot of turnover or breaks in between. When I've taught measure theoretic probability at US universities, if most of the students finished their measure theory course in the previous spring it makes it much easier to jump into properly probability oriented material in the fall semester. It all just kind of hinges on how your institution intends the "flow" of material to function (and whether anyone can actually follow that intended plan). I like the TOC for that course by the way. It does seem like a "hollowed out" version of a graduate measure course so I'm sure it was a good one. The more abstract and challenging details can be filled in later.One thing that is kind of surprising to me is how late you guys did normed spaces. At my university normed spaces pretty much immediately follow from integrability and the convergence theorems (because that's really all L^p is, the set of equivalence classes of p-integrable functions). We used L^p spaces as a gateway to signed and product measures. Lp is especially important for Radon-Nikodym as the p norm lets you easily define normalized Rad-Nik induced measures. Sorry for being cantankerous my Kraut friend.
I don't know much about algebraic topology. Is there a generalization of covering spaces to higher homotopy groups? I mean the following: The universal covering is defined to be simply connected. Does it make sense to talk about an n-connected covering where pi_n is trivial? Where can I read about this?
I have to take > 1 semester of diffential geometry Or> half a semester complex analysis> AND half a semester diff equationsThoughts? My favourite classes were topology and probability theory
>>16160352I have 1 day to study for AP Stats. I know nothing about stats at all. I just want to pass with a 3/5. Is it possible?
>>16160745Is the differential equations class just memorizing solutions or is there any theory?
>>16160352Who is he?>>16160790Can I complete this in one lifetime? I am 22 btw
>>16160790Someone edit this with pictures that aren't blurry
>>16160957>Who is he?Joshua King>Joshua King came to Cambridge from Hawkshead Grammar School. It was soon evident that the school had produced someone of importance. He became Senior Wrangler, and his reputation in Cambridge was immense. It was believed that nothing less than a second Newton had appeared. They expected his work as a mathematician to make an epoch in the science. At an early age he became president of Queens’; later, he was Lucasian Professor. He published nothing; in fact, he did no mathematical work. But as long as he kept his health, he was an active and prominent figure in Cambridge, and he maintained his enormous reputation. When he died, it was felt that the memory of such an extraordinary man should not be permitted to die out, and his papers should be published. So his papers were examined, and nothing whatever worth publishing was found.
We consider set of binary sequences [math]\gamma \in \{0,1\}^{\mathbb N}[/math].Let [math]A_n \subset \{0,1\}^{\mathbb N}[/math] be the set of sequences which among their first 2n entries have the same number of 0's and 1's.E.g. [math]A_3[/math] holds, among others, all sequences starting with0,1,0,1,1,0but not those starting with e.g. 1,1,0,1,1,01. What's [math]\dfrac{|A_n|}{2^{2n}}[/math] as a function of n, i.e. how many sequences have that type?2. Likewise, taking the union below n, what's [math]{|\bigcup_{k\le n}A_k|}/{2^{2n}}[/math]3. Taking the union of such set together, in the countable limit, what's the ratio [math]|\bigcup_{n\in{\mathbb n}} A_n|[/math] over [math]|\{0,1\}^{\mathbb N}|[/math]?(My motivation is that I want to find a countable collection of decidable/detachable subsets of sequences, such that the countable union isn't decidable anymore, and one where the canonical measure on them isn't trivial (0 or 1). I assume the value in 3 is strictly between 0 and 1, although I'm not sure.)
>>16161032As you have written it the [math]A_n[/math] all have uncountable infinite cardinalities.There are [math]{2n \choose n}[/math] possiblities for the first [math]2n[/math] entries and then [math]2^{\aleph_0}[/math] possibilites for the remaining entries.
>>16161075Yeah in the finite cases I mean to just take the sequences of length 2n and compare them with all possibilities of that length, 2^(2n).1 is probably easy (binomial (2n,n) you say?). The finite union case 2 is maybe more annoying to compute, as there will be overlaps I guess, but the value for 2 is not so interesting for me anyway.The meat is with 3. While all sequences will be 2^\alpeh, I wonder about the fraction of sequences that have a balanced initial segment of length 2m for _some_ m. I don't know if this is measure zero or it's compliment, or if there's a real between 0 and 1 for that ratio.
>>16160923Pretty theory heavy I think. It's a class for math majors in their last year of undergrad.
I'm studying for a test tomorrow and there is a question that is supposed to require a method that we haven't studied yet (generating functions).I've tried it solving the stuff we've covered already which is the inclusion exclusion principle but it seems quite hard.Find the number of integer solutions for the equation x1+x2+x3+x4=20 with x1, x2 even, x3, x4 odd, and x4 <= 3.So far I have:total of solutions with no restrictions:N = CR(4,20) = C(23,20) = 1771Next step for the I. E. P. would be to calculate number of integer solutions such that x1 is odd.The furthest I've gotten is that the number of solutions with that restriction is the same as the total number of solutions for 2*x1+1+x2+x3+x4=21 but I don't know how to find it.The final answer for the whole problem is 100.
>>16161383Just introduce new variablesx1 = 2 y1x2 = 2 y2x3 = 1 + 2 y3x4 = 1 + 2 y4Then you get rid of the odd/even restrictions.
>>16161405Thanks, that worked nicely.
does he know all of hatcher, munkres, kobayashi-nomizu, evans?
>>16161203Is it before or after Lebesgue integrals and Sobolev spaces? My assumption is that it's before because you're saying senior undergrads are taking it but you never know I guess.
Lol you people don't even know basic geometry
>>16160981Such humiliation on a Wikipedia page
https://www.msn.com/en-us/news/us/teens-come-up-with-answer-to-problem-that-stumped-math-world-for-centuries/ar-BB1lRSKJHey guys, TND tourist here. Did these ladies actually do it? It's old news but I guess its making the rounds again.
>>16161032for 3: consider a sequence of infinitely many coin-flips with p=1/2 of heads, ad translate it into a binary sequence. What is the probability that your sequence is never in A_n for any n? It is probability zero. Therefore the measure of that union is 1.The situation changes if you change the probability p. In your setting that would correspond to distorting the measure on your space, could be incompatible with what you’re asking (not sure)https://en.wikipedia.org/wiki/Random_walk#One-dimensional_random_walkhttps://en.wikipedia.org/wiki/Kolmogorov%27s_zero%E2%80%93one_law#Examples
>>16161869They did give a proof for the theorem but it's not a "problem that stumped the math world for centuries".
It seems to be at least not identical to other known proofs. There is, however, a visually similar known proof. Pic related. The main difference is that the old proof takes the original triangle and constructs more triangles inside of it, and the new proof takes the original triangle and constructs more triangles outside of it. If they got the idea from this older proof, they probably should say so. As for the trigonometry thing, it seems to be not quite true, but stuff like that normal in science reporting.
What is a manifold?I stopped studying math in high school.
>>16162263a second countable Hausdorff space that is locally like n-dimensional Euclidean space
Thoughts on Elements de Mathematique by Bourbaki?
>>16162282about as useful as principia mathematica
>>16162455Which is to say?
>>16162458pointless aim, with substandard propaedeutic value
>>16162470What are the best mathematics textbooks for all respective fields, then?
>>16162475there is no best, only whatever works for you
>>16161696Before
Do humans exist for the purpose of solving and finding new mathematics? (Pure)Or does math exist for the purpose of helping humans in the practical world? (Applied)
>>16162563neither
>>16162590Then in your opinion, what is the purpose of math, and the purpose of humans?
>>16162847Just say man instead of reddit human
>>16162882>>16162847>>16162563both underaged. sad
>>16163013Wrong
>>16162495Then you probably should be fine in terms of difficulty for the ODE/PDE course. I personally really like differential equations but a lot of people find them tedious, especially at an undergrad level.
>>16162563Man was made in God’s perfect image. Mathematics is Man’s quest to find the language to describe that image.
What skills do pure mathematicians have that physicists/engineers and the like don't? How much would the latter two benefit from having those skills?
>>16161383>>16161405>>16161515The test went very well. I still don't have the result, I'm not 100% sure on all the answers but I didn't completely blank on any of them.Now no more math tests for half a semester.
>>16163113Source on mathematics ever leading to any sort of natural language development? I'm no linguist, but this is news to me.
Since libgen sucks now can someone with access download these for me?https://www.tandfonline.com/doi/full/10.1080/00029890.2023.2266980https://www.tandfonline.com/doi/full/10.1080/00029890.2024.2279472https://www.tandfonline.com/doi/full/10.1080/00029890.2024.2294677https://www.tandfonline.com/doi/full/10.1080/00029890.2024.2305019https://www.tandfonline.com/doi/full/10.1080/00029890.2024.2313951
Query on the notation of summations:What's the consensus if I have, say, 2 conditions on the range of a summation? Example:[math]\sum_{\substack{x\in A,\\ 2\vert x,x\notin B}}x[/math]In this example, it's the "summation of all [math]x[/math] in [math]A[/math] such that [math]x[/math] is divisible by 2 and is not in [math]B[/math]". Is it considered "standard" to allocate the first line of the subscript of [math]\sum[/math] to the range and the 2nd line for the conditions on the range? That is, [math]\sum_{\substack{range\\conditions}}[/math].Using the example given above, is it then considered incorrect to write it as [math]\sum_{\substack{x\in A, 2\vert x,\\x\notin B}}x[/math]? In this case, the condition of it being divisible by both 2 and not in [math]B[/math] is split into two separate lines.Sorry for this weirdly specific question.
Just to clarify on >>16163634, the superscript of the summation is not used. It's all subscript, and the subscript has 2 lines.
If there isn't enough space to the side of an equation, is it alright to put the "because", i.e. [math]\because[/math] between a line of equation and the next? Like so= bla bla bla= bla bla bla= bla bla bla([math]\because[/math].....)= bla bla bla= bla bla bla
>>16163634You should put it directly below the sigma. Apparently you can use \displaystyle for that
>>16163865I already do that, the only reason it appears as though to the side is because of the formatting on /sci/. It's directly below the sigma in my LaTeX software.
Any good books to introduce me to graph theory?
>>16163866Then yeah, use as many lines as you want, since they won't be confused with a superscript that way.
>>16163168Damn, I got the answer sheet and it actually went very bad lol. Fuck me.
>>16161383>Find the number of integer solutions for the equation x1+x2+x3+x4=20 with x1, x2 even, x3, x4 odd, and x4 <= 3.>generating functionsImplied assumption is x_i >= 0 (since that gives the answer 100)f1=f2=1/(1-x^2) = 1+x^2+x^4+...f3=x/(1-x^2) = x+x^3+x^4+...f4=x+x^3Answer is the coefficient of x^20 in f1*f2*f3*f4. Use partial fractions.f1*f2*f3*f4 = x^2*(1+x^2)/(1-x^2)^3= 1/8 * (1/(x+1) - 3/(x+1)^2 + 2/(x+1)^3 - 1/(x-1) - 3/(x-1)^2 - 2/(x-1)^3)power series coefficient is 20th derivative of this evaluated at zero divided by 20!. 20th derivative is1/8 * (20! / (x+1)^21 - 3*21!/(x+1)^22 + (2*22!/2) * /(x+1)^23 - 20!/(x-1)^21 - 3*21!/(x-1)^22 - (2*22!/2)/(x-1)^23)Evaluate at zero and divide by 20! gives 1/8 * (1-3*21+2*21*22/2+1-3*21+2*21*22/2) = 100
For those of you that do math at a grad level, how do you get over constantly feeling like a retard? It's gratifying when you finally figure out some proof that you've been spending days on but it's brutal constantly feeling like it's never good enough.
>>16165355Feeling like a retard is part of the process. If you *don't* feel like a retard you aren't pushing yourself hard enough.
kurwa zmieniłem tę jebaną odpowiedź i nie będę miał 100 kurwaaaaa
>>16163209Do you know what hypotenuse means
>>16165359Thank you for the encouragement. I guess I am a retard, I'll just slowly become a retard that's moderately okay at measure and functional analysis.
Are there any good YouTube lectures for Measure Theory?
>>16166033As a fellow retard, I'll add that it can be worth it to skip a proof or two, at least for a while.Sure, it feels bad, but in the time you save you can learn plenty of different things that you _can_ figure out.I've found that, usually, when I come back to something later, I have lots of different ideas about the topic than I had initially.
>>16163209it is thought that Dynkin Diagrams would be of use in communicating with Aliens>>>16163634a notation that is common in some circles [math]\sum \{ij : 0 \leq i <j\leq 3\}[/math], which would evaluate to something like 11. an oddball notation is Einstein notation, check that shit out. but most people just play it by ear with superscripts and subscripts that make sense to them
>>16165355It's the same process as weight lifting. At first it's really heavy and you can barely do a rep but if you keep at it eventually you can do multiple reps and wonder why you ever had problems. When you make it through your first upper division course you will also gain a lot of confidence (say like intro algebra top or algebraic geometry, measure theory, whatever).
>>16163634>>16166122also check out Dijkstra notation. its strictly better but not worth trhe trouble of switching over
Could you guys tell me the formula to solve this?
>>16166144>On average 20%There is no way to answer this for sure without knowning the exact probability distribution. If it's possible that 100% of the water of a bucket will be lost then even 999 buckets could be low if you're unlucky.
>>16166144You lose 20% of the water you bring, which means you're left with 80%.You want 160 litres of water, so 160 should be 80% of the number of litres, and thus the number of buckets, that you gather.Hence [math]160=0.8b[/math]
>>16166154Thank you.
Best textbook to learn General relativity for mathematicians?
>>16166144what game?
>>16166169>Best textbook to learn General relativity for mathematicians?
>>16160030Hello, I'm not the anons you were replying to but thanks for the course recommendation. If one were to follow this probability course, is there any accompanying text that would be recommended along with it, like a set of lecture notes or something for reference and maybe exercises, or a separate exercise set?
>>16160352What to study for algebraic geometry
>>16166536commutative algebra, basic differential geometry.
>>16166487They use B.K. Driver's Probability Tools with Examples. Super rigorous and very "analysis forward" presentation of probability theory.I like it quite a lot as a "secondary" measure theoretic probability text after you've already gotten a good feel for things but it might not be the easiest as a first read introduction to the topic. There's a ton of exercises and the standard homework assignment list in the beginning of the book if I'm remembering correctly and it should be free through UC San Diego's website.
>>16165355Nobody I know spends more than a couple hours a day fiddling with a problem that you're making no progress onThere are many other things you can (and need to) do which you're actually capable of that you should always be able to give yourself a daily reminder that your brain isn't complete cottage cheese
>>16166129My post was because I just finished measure. I got a B+ (which was above average for my class) but I feel like I honestly didn't earn that grade even though in some sense I objectively did. I definitely learned a ton in that course but I'm not sure I'm much more confident in my proofs than I was prior because I'm just kind of a retard sometimes. It doesn't help that I'm not actually a math PhD and am instead doing a "math minor" for my EE PhD. It's kind of funny though. In some sense we have an advantage in EE because we have so much exposure to such advanced math so early, and as a result dealing with PDEs and complex analysis isn't that scary. We definitely don't focus on proofs though, and as a result I have a pretty underdeveloped skill set in that regard despite being in some sense more apt at the "computation" side of math than my math grad peers.
What to study for algebraic topology
Gaitsgory solved geometric langlands
>>16160352Condensed Proof of Riemann Hypothesis
Damn, y'all some high IQ niggas up in here.Well, I'll leave you to it.
>>16160352test
>>16160647It is a simple logical fact that [eqn] \forall \epsilon > 0 \quad | a - b| < \epsilon \iff a = b [/eqn]>But le heckin REALSIt's also true that [eqn] \forall n \in \mathbb N \quad | a - b| < 1/n \iff a = b [/eqn]
>>16164154Jungnickel for algorithmic graph theory.
>>16162263Something that looks like Euclidian space when you zoom into a small point. For example, you can draw longitudes and latitudes on a sphere, but if you consider a small portion of it , they will look like a grid i.e., the 2d Euclidean place. It's basically a fancy word for smooth shapes.
>>16166712jump right into hatcher if you're solid on point-set.
is the Khan academy statistics course any good?i'm starting a research gig soon and I literally can't remember how to do anything.
>>16166712tom Dieck, skip shartcher >>16167696
>>16167704What's your level of math background and how serious does your working knowledge of statistics need to be? You might just be better off slowly working through a PDF of one of the standard undergrad books. Sheldon Ross's Introduction to Probability and Statistics for Scientists and Engineers is free online and pretty good.
Can anyone give a comparison between Janich, Vector analysis, and Munkres, Analysis on manifolds?
Guys, I'm proud of myself.I was trying to cook up a formula for a matrix with given eigenvectors and eigenvalues similar to how lagrange interpolation is done and I basically rediscovered the hodge star operation.My whole motivation was to represent complex numbers as real 2x2 matrices (I'm trying to do quaternions too).[math]1 \sim \begin{bmatrix}1 & 0\\ 0 & 1 \end{bmatrix},\ i \sim \begin{bmatrix}sinh(t) & cosh(t)\alpha \\ -cosh(t)/\alpha & -sinh(t) \end{bmatrix}.[/math]
>>16168143Jänich = 4chanMunkres = Reddit
>>16168486Munkres, then.
>>16168764Wrong.
He won.
>>16168930IUTT truly is the ultimate expression of algebra. It so carefully walks the line between brilliance and pure schizo-babble that not even the most battle-hardened number theorists know what's real and what's just from not taking their meds.
RIP to the money man
>>16169230He won. Rest in peace king.
>>16169230>makes 30billion>dies from chain smoking
>>16169230I bet it was the VAXX
>>16169230His interview from Numberphile:https://www.youtube.com/watch?v=QNznD9hMEh0&t=0s
>>16166556>>16166536>algebric geometry>differential geometry
>>16169335Yeah? It's not necessary but having that knowledge beforehand helps with topics like smoothness and tangents. And there's a plenty of quality literature like Griffiths-Harris that assumes familiarity with differential geometry.
>Complex analysis>Prof claims the following without reference or proof>Almost all roots of polynomials with complex coefficients are complex.How does this work? R and C have the same measure
>>16169517R has measure 0 in C.
>>16169528How come?
I've been taking a online remedial mathematics course and I'm currently on long division. I feel like I need to start over because I rushed through the course and the course itself is quite lackluster. I've been passing the sections with flying colors but they only teach me how to follow one procedure and not how to gain number sense. The same exact problem plagues Khan academy so it isn't that good either.If I'm asked to show how to solve a basic arithmetic problem in multiple different ways I would flounder. Currently I haven't gained the ability to do mental arithmetic quickly which would hinder me later down the road if I proceed to more advanced math topics.Is there a book that can help me alleviate this issue?
>>16169549Openstax, these books in this order, they are all free to download from the Openstax website:Prealgebra 2e,Elementary algebra 2e,Intermediate algebra 2e,College algebra 2e
>>16169548What is the measure of R in R^2?
>>16169549Euclids elements
>>16169549This book would do it.
What do i need to know to make sure i score at least 30 on aleks math placement? Ive been out of school for years.
>>16166712Bredon's Topology and Geometry is vastly superior to both of the books that were recommended to you. Unlike tom Dieck, it focuses on geometry and not categorical troon shit, and unlike Hatcher its proofs are precise and rigorous.
>>16169296Or chain smoking made him 30 billion.https://youtu.be/95g9fgH1Qmct.Doctor of M.D. and Pure MathematicsI dont post in this thread because youre students trying to learn, not because I cant rek the place.
>>16170546>categorical troon shitobsessed
>>16170411>human calculator>obeseaparently this guy cant even do basic arithmetic
>>16160352Any functioning ways around chegg paywall?Is it even worth trying to bypass?
im averaging 5 pages a day of shilov's linear algebra. it seems to be filtering me hard. Is this normal? Any other books you guys can recommend?
>>161714095 pages is fine, but I don't like Shilov personally because he introduces determinants in the first chapter. I feel determinants don't really make much sense until you study analysis on manifolds. Personally, I prefer Halmos or Axler, but both need to be supplemented by a book that covers matrix algebra for a complete treatment.
>>16170411pure sthetics
>>16171256the shoemaker's son always goes barefoot>>16171409I only read Serge Lang in this subject, is Shilov a recommended read?
Do you guys use several different books to study one subject? I have Axler and Hoffman's linear algebra and I wonder if I should read them both or just focus on one of them.
>>16171511I have like 8 books on Probability Theory because they all cover different topics in the second half and with different emphasis.
>>16171547Probability is so stupid, something will either happen or it just won't. there's just no point worrying about it at all, much less dedicating several hours of study to it.
>>16171572Lol, this is a funny joke
>>16171572Incredible. This man might just be what we need to solve math once and for all.
>>16171511Considering how unconventional Axler is, it does make sense to complement it with some other book, but not really Hoffman & Kunze; something more applied instead. With something like Analysis, it's better to just use one book because how homogenous the treatments of the subject are.
>>16170546Why do troonies like category shit so much?
>>16171572Brainlet
>>16171572You should go buy thousands of lottery tickets. You either win or you dont so its 50/50
>>16171254Kys, Zero.
>>16171640Because it has a critical mass of like minded people to become a safe space. Or maybe just because it makes you buttmad.
>>16171663You missed my point. Whether I buy 1 lottery ticket or 1000 it’s all completely pointless because the probability to win is extremely small, what’s the point in knowing whether that extremely small probability is 0.000000001% or 0.000000002%? So why worry?
>>16171714Just think about it. You either win or you don't. That's 50/50.
>>16171714Do you actually want an answer as to why one would study probability theory or do you just want me to call you a retard? I don't mind either (or both).
>>16171717It’s not 50/50, but it’s a probability so small that you know you will never win, what’s the point in calculating it? What’s the point in knowing that if I buy two more tickets that probability will increase by 0.00000001%? There’s no fucking point, you know you’re not gonna win so why are you worrying so much about it?>>16171721I’ll tell you why people study probability theory and other stupid crap: because the entire academic world is based upon that. Do you think every physicist is researching the unknown phenomena from quantum mechanics or general relativity? No, most of them are studying an extremely obscure field just to have a job and funds. Do you think most mathematicians are trying to prove the millennium problems? No, instead they waste their time researching the “deep” intricacies of probability theory. The entire academic world is built upon this, people aren’t doing useful research, they aren’t moving their fields forward, they’re just trying to find an obscure subject so they can release dozens of papers on it every year and call themselves experts on that in the hopes that they will be hired by some good uni and raise their prestige. It’s pathetic.
>>16171737First day on /sci/?
>>16171737My brother in Christ, you are genuinely retarded beyond saving. Probability theory, Stochastic Processes and statistics are perhaps the most practical of all possible math disciplines for any applied science/engineering field. Probability theory literally forms the basis by which we analytically model experimental uncertainties. That's about as useful as it gets.
>>16171743That’s not what I’m talking about. The basics of probability theory are useful, but do you honestly believe engineers and physicists are reading papers on probability theory? No, there’s no useful research being done in it, there’s just people using it to get funds and prestige, there’s no point in learning anything about it beyond undergraduate stuff. And for the layman there’s not even a point in learning it at all. What does it matter for the average person whether or not the probability of winning the lottery will be 0.000001% higher if they buy two tickets? What does it matter for the engineer whether or not an extremely obscure theorem has been discovered in probability theory?
>>16171751> The basics of probability theory are useful, but do you honestly believe engineers and physicists are reading papers on probability theory? No, there’s no useful research being done in it, there’s just people using it to get funds and prestige, there’s no point in learning anything about it beyond undergraduate stuff.I'm an engineer who focuses primarily on non-linear state estimation and non-linear signal detection theory. Both of these topics are applied in the sense that the fundamentals of the probability distributions relate to radar/sonar, but they are both heavily reliant on some fairly in depth topics in probability theory. In particular large deviations theory is very relevant to signal detection and allows for the primary mechanism of analysis of error rate curves for correlated sample sequences (as you can't use the standard CLT constructions with correlated samples in the sum). Renewal theory and ergodic processes are also central to state estimation for a target moving in the presence of process and measurement noise. These are graduate level probability theory topics that have a lot of relevance to my engineering field.
>>16171737Correct, and also why we will never reach the stars. Getting grants to research more useless shit rather than researching shit that matters,
>>16171511Reading two books in parallel seems like a waste of time, but having several books is very usefulIf an explanation isn't clicking for you it's good to be able to go read a different one rather than bashing your head into itPlus different books will have different advanced/side topics, even if the core content is the same
>>16160790retarded memeslop
Good morning, happy mother’s day, God bless you, Jesus loves you.
>>16167474That's just an arbitrary statement one must, for themselves, accept as fact. If you cannot explain it rationally, perhaps it cannot be explained rationally. However, to accept what one has heard *merely* because one has heard it is irrational. Irrational application of mind is conducive to wrong viewpoints and thinking "true" that which is "untrue".
Here's a fun recreational maths problem I came up with.In picrel is an equilateral triangle whose vertices are at (-1,0), (1,0) and (0,sqrt(3)). Point is picked from inside and then shortest paths are drawn from that point to reach of the sides. Viviani's theorem says the sum of those lengths is eaqual to the height of the triangle.Find coordinates for the point such that the orange line is twice as long as the green line, and the blue line is twice as long as the orange line.
>>16172857>In picrel is an equilateral triangle whose vertices are at (-1,0), (1,0) and (0,sqrt(3)).those aren't the vertices of an equilateral triangle
>>16172871You sure
>>16172857green line has length sqrt(3)/7orange line has length 2sqrt(3)/7find the line describing the left side of the triangleparallel line whose distance is sqrt(3)/7point on that line with y=2sqrt(3)/7
>>16160352What if like the white light experiment we are observing reality as a mix and not what it is?
Wildberger is a genius.
>>16173023This is the maths thread. If you want to "observe reality" you can go do it somewhere else.
>>16171714You lose money in the long run. The more tickets you buy the more certain that becomes. Knowing the probability lets you determine what is worth spending your money on.
>>16172830Hope you get well soon, anon
>>16172857-1 + (5/4) / 7 + (3/2) / 72/7 * sqrt(3)tried doing it in my head alone w/o writing anything down
>>16173368I am well. I may seem upset but I'm not. I'm just viscerally aware of the theme of being correct.
>>16173071Lol. Mathematics is an abstract observation of nature.
>>16173806Maths has nothing to do with nature, physics is the study of nature through mathematical methods.
>>16173071That view is retarded and everything wrong with modern maths.
>>16171254ywnbaw mate
How to get into algebraic geometry Which books, resources to studyI know algebra till ring theory, analysis ,topology, complex analysis
>>16174401Haven't studied the subject but heard very very good things about Vakil's "The Rising Sea"
Asking for opinion; any student of algebra knows of the following result:"In a finite ring [math]R[/math] with identity, every element is a unit or a zero divisor"This result is not only well-known, but it is also very easily provable even by undergraduates. So my question is, if I were to use this in an article, do I even need to cite? Is there even a reference to go back to? Like any reader with an algebra background can prove this himself literally within 2 minutes. Is it okay if I just state in the article "the following well-known result....." and just don't bother with any citation?
>>16174401wildberger's rational trigonometry series.
>>16175195Do you use citations when you write 2+2=4?
you ever hear about the graph theorist who liked torturing puppies? he was a real edgelord.
Is there a 2x2 matrix A such that all the following hold:(1) all entries of A are rational(2) neither +1 nor -1 is an eigenvalue of A(3) some positive integer power of A is the identity matrix
>>16176509Sorry that question is dumbI think this one is less obvious though: Is there a 2x2 matrix A such that all the following hold?(1) all entries of A are rational(2) +1 is not an eigenvalue of [math] A^4 [/math](3) some positive integer power of A is the identity matrix
>>16176509>>16176631I mean, are they actually obvious? A 2x2 matrix A that is diagonalizable has a QDQ^T form, so A^n = QD^nQ^T. For 2x2 matrices it's pretty easy to write all the values out, and you see that either the eigenvalues are either +/- each other or it comes out that A is a diagonal matrix, and both don't work for A^n = I unless you got 1 and -1s. This means A would have to be non-diagonalizable. For a 2x2 matrix there's the requirement that (a-d)^2 + 4bc = 0, so you can check that A^2 is also non-diagonalizable, and so on. At no point will you ever hit a diagonal matrix, which the identity matrix, I, is. Maybe something can be said about Jordan–Chevalley decomposition, idk much lin alg.
I like to come up with maths problems by myself and then try to solve them. Here's what I came up with recently.>pick three uniformly random points from a square, connect them with lines to make a triangle>repeat two more times so you have three triangles now inside the square>pick one more random point inside the square>the problem is as follows, what is the probability that the final point lies inside of all of the three triangles simultaneously
>>16176631Consider the companion matrix of [math]\Phi_6(x) = x^2 - x + 1[/math]: [math]\pmatrix{0 & 1 \\ -1 & 1}[/math].This matrix has integer coefficients and has two complex eigenvalues, the two primitive sixth roots of unity.This is the most complex behavior you'll get out of 2x2 matrices, since the largest integer with [math]\phi(n) = 2[/math] is 6.
>>16169562C isn't R^2
>>16176744Lebesgue measure does not use the arithmetic properties of C, so it sees C and R^2 the same.
Why does why does showing [math]b < \frac{n}{n+1}[/math] mean [math]sup \ S = 1[/math] Also any practice questions for finding supremum and infimum using Archimedean property?
>>16176879For every number beta below 1 you show that you can find a bigger element in S. This implies [math]\sup{S} \geq 1[/math].The observation at the start of the solution showed that every element in S is smaller than 1 so [math]\sup{S} \leq 1[/math].Together this implies [math] \sup{S} = 1[/math] since [math] \leq[/math] is a total order.
>>16176888wow makes thanks a lot. Do you recommend any books as such for this? I don't think I would've been able to figure it out on my own to be honest. Syllabus is in picrel
>>16176879God, analysis is gay
Is there a name for the sequences of subsets, i.e. for [math]{\mathbb N}\to{\mathcal P}X[/math]? Possibly ruling out that the values can be empty.Basically nets, but on N.
>>16177235subset sequence
Do you guys think this is a better way of doing 7.8 than the regular way, also how do you think of number
>>16177507The orthodox construction for 7.8
This is elementary number stuff, am I to believe that all these people that do cuckulus here dint even understand the most base number theory
>>16165355>For those of you that do math at a grad level, how do you get over constantly feeling like a retard?You don't. And it never goes away. If you don't feel like that, you're doing something wrong.
/sci/ is ignorant of geometry?
Springer has Greub's Multilinear Algebra on sale for only $17 ATM. Is it worth going through a multilinear algebra book to get a more comprehensive background in tensors or should going through something like Lee's smooth manifolds book be enough?
>>16177838Math?
>>16177685down with Euclid, death to triangles
I'm 24, self studying calculus and interested in going to university for math next year to get a degree for an engineering career but I live in a poor part of a shithole country (South Africa) with only a smartphone and it seems like the syllabus at the five universities I can reach expects desktop computer skills and programming knowledge but doesn't teach them and there aren't any colleges to help.A cheap used windows laptop with okay specifications for running basic matlab, zoom, outlook and antivirus stuff would cost me about 7 months of disposable income (I only have 3 months' worth saved up and can't get a better job or more hours or lower rent+food costs).What can I do to make this problem easier?
>>16178202What does your problem have to do with mathematics?
>>16177885>>16178211you will never be a mod
>>16178202Buy a used old latitude or thinkpad or elitebook. And install mint
>>16177885Yes, I'm not sure if you are aware, but multilinear algebra and smooth manifolds are both topics within mathematics.
>>16178320Your brain is a smooth manifold
>>16171640they don’t anymore, those ones are 41% already. zoomer troons love Rustlang instead
>>16178360Sometimes yeah. I wouldn't be asking for advice from people with more math experience than me if I wasn't a bit smooth brained. If you don't know the answer to the question that's fine, but it's definitely math related.
Euclid mogs cuckulus
>>16178365>>>/g/dpt
>>16177838How come springer sells those books for so cheap? There's some quite popular books listed for 17$, and I doubt that price is generating significant margins for them.
p-adic bros? How do I show that the set {1, 1/2, 1/3, 1/4, ...} is dense in the subset { x in Q_p : |x|_p >= 1}? The book only gives me the hint that the same statement holds for the inverses. But that is trivial and doesn't help me at all.
>>16178445Probably just to move paperbacks they've printed a while ago that haven't sold. Printing paperbacks isn't exactly expensive, and if it's already been sitting on the shelf for a while there's not a ton of opportunity cost for selling it just barely above break even.
>>16178445Maybe that's a softcover book, they are usually cheap
>>16179012It's not expensive to print hardcovers either especially faux sewn hardcover they sell.
>>16179082Well yeah, it's not expensive (hence why you'll see hardcovers for like $30 sometimes) but it's certainly cheaper than the $3-4 the soft covers cost them to print.
finite set theory is beautiful and amazing and incredible and i love it so much and it's just wonderful.
>>16179107I prefer combinatorics
>>16178202I don't live in a poor shit hole country, but in mine universities loan laptops out to poor people for use in university studiesI'd put together a CV of sorts showing what you've been self studying, what you plan to study, basically a document saying im not going to steal this and disappear Enrolling would probably help, if you only have 3 months saved not sure how you plan on funding university but good luckif they dont offer this no ideaIf they require a pc they may have on campus?
>>16178372Archadmides buckbroke Euclid and Cavalieri pointed the line to integral calculusCope and seethe
>>16179085No, I mean they almost cost the same to make.
>>161782021. apply to nsfas nigga, lie if you have to2. every university has a computer lab you can do your work in if you don't have a laptop3. they don't expect you to know shit about programming coming in and you will almost certainly have an introduction to programming course4. you can get a good quality refurbished thinkpad for about 5k
1. algebra or analysis?2. d4 or e4?
>>161795161. I'm an algebra pilled analysis maxxer2. f4
>>16179197finite set theory is part of combinatorics so it's okay
so much disinformation peddled in mathematics teaching. like the "proof" that the square root of 2 is irrational. All it does is prove that it isn't a rational number. it doesn't define irrational numbers, it doesn't prove that the square root of two is a number, and it doesn't prove that it's an irrational number. At the heart of this is just relegation of the meaning of number to meta-mathematics, where it's dealt with extremely unseriously, using terms which aren't so precisely defined.
>>16179532>f4Retard
>>16179956>All it does is prove that it isn't a rational number.which is what it claims to prove.
The very thing it was required to show
>>16180010Ha! It's supposed to look retarded. This adds to the humiliation of the defeated opponent.
>>16179532>not f3If you play any opening other than 1. f3 2. Kf2 I spit upon you
>>161799561: no rational number is the square root of two2: there is a non-negative square root for every non-negative real (closure of sqrt)2: is trivial and left to the reader.
>>16171714>1 ticket>1000 tickets >0.000000001% >0.000000002%Midwit that can't even conjecture statistics on a hypothetical. Astounding. Assuming they were randomized and unique, the odds would be 1000x better which would absolutely make a difference and you would see it repeated over so many trials.
My understanding of math is that of an 8th grade. That's no joke. I completely dismissed maths when I was in high school and then went to the humanities. I started a Master's in NLP though and I'd like to get back to math and have some understanding of it, particularly for research papers.Any ideas of where to start? I'm comfortable with programming by the way (Python, R, TypeScript) so I thought that perhaps learning some things with programming could be fun (with numpy for instance?) but I don't really know how to achieve that and if there are any resources online for tards like me (didn't find any). Otherwise if you have textbook recommendations I'd appreciate it.
>>16180533AOPS Prealgebra.
>>16177838>>16178445Print-on-demand garbage. Get an old library copy from abebooks if you have to. Have some taste. Or even better, use your library. And actually do problems. Stop becoming a book collector, and actually do math.
>>16180570Well actually Springer publishes the best or edge of the science books
>>16180570I don't think so? The last thing I got from Springer that was on sale was GTM 264 and my copy of came with a piece of paper showing a print date about a year before I ordered it. I'm sure a lot of their stuff is print to order, but my guess is that some of the sales are for things that were printed for some bulk order that didn't go through or something or "regular stock" that didn't sell quickly or something.
How do I pirate math books? In the past I used to google book title + pdf and often find it, but google search has become unusableIm interested in the workbooks of Chris McMullen
>>16180533so just get a high school maths book and go through it again? There are tons of free resources online also
Maths illustration I created by myself
>>16180936That's a neat illustration and really intuitively demonstrates what's happening with that geometric series. Good work!
>>16180603>>16180616Retards like you is the reason why publishers got away with their awful print quality.
>>16181099Springer has great print quality.
>>16181171Well when you read kindergarten books many things look like poor quality ;d
>>16180936I was way too distracted by the cool picture to realize that the only mathematical statement shown here is 2^2 = 4.
>Gauss grew to dominate his children and eventually had conflicts with his sons, because he did not want any of them to enter mathematics or science for "fear of lowering the family name", as he believed none of them would surpass his own achievements.Based af
>>16181270>BASED AF
>>16181307For the gen alphas like you: Gauss had the skibidi rizz.
>>16181099Where does my post say anything about print quality? I know a lot of Springer stuff is print to order, I'm just saying the book I got on sale recently wasn't.
>>16181270based. when Gauss was a kid, JS Bach’s kids and grandkids already busy fucking up the Bach family name. I wouldn’t want my retard mongrel Hapa kids associated with my legacy either
>>16181171Used to, old Springer prints are beautiful. What you get from them nowadays are shoddy print-on-demands.
>>16181270HAHAHAHA omfg, such an asshole thing but you see his point a little. Like if MJ or Lebron forbade his kids from playing
I'm reading Knuth's Concrete Mathematics, and there is something very basic I cannot understand. How does I get to the U_n = 2^n solution which I should get withou being a genius as he states? Lmao. I'm actually retarded, my badFor context, this is a proof by induction from the Hanoi tower recurrence.
>>16181852[math]U_n[/math] is just [math]U_{n-1}[/math] times 2.Since [math]U_0[/math] is [math]1 = 2^0[/math], [math]U_1[/math] will be [math]2 = 2^1[/math], [math]U_2[/math] will be [math]4 = 2^2[/math], [math]U_3[/math] will be [math]8 = 2^3[/math]...the pattern sticks out pretty quickly, and since you're just doubling each time there's not much room for it to throw a curveball at you like a lot of the "obvious" patterns (i.e. traps) will
>>16181864Thanks! That helped. One thing that I think is hard on studying math is that I have to rely a lot on baby steps. So I had to rewrite what you said in a way I couls understand. This gets better with practice, r-right...?
>>16181873forgot to sned my train of thought
>>16181874>>16181873i can't read your handwriting but reading math does get easier with practice because you notice patterns and so most of what you read will be 'standard' and something you have already worked with before.
