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 No.338[Last 50 Posts]

All good communists study math.

What are you studying right now? What is your favorite field of mathematics and why?

Personally, I really like the book "Linear Algebra Done Right" by Sheldon Axler. It is on Libgen if you are interested and I attached a pdf.


What maths do you think are must-learns in your opinion?


First order logic is really the most important, and euclidean geometry is also essential. Those are the only two I would say are truly must-learns, but linear algebra is ludicrously useful so there is nor reason not to study that as well. If you want to understand contemporary classical economics then you should learn dynamical systems as well, but the whole algebra-calculus track is a prerequisite for that so the barrier for entry is a bit higher.


I know this is probably babby-level for most people who would visit this thread but I'm taking Discrete Math this summer. Any tips on how to study it or what the most difficult concept in the course is?


Yeah I could say a lot about that. Discrete or Intro to Proofs is where math starts to get serious at the undergraduate level, you could say the same about analysis, but the techniques used in analysis are what you learn in discreet. What's really cool about that class is that it opens up all sorts of areas of mathematics to you, where as before discrete the track is pretty linear: pre-algebra, then algebra, then pre-calculus, then calculus and so on. That track continues through Vector Calculus, Ordinary Differential Equations, Nonlinear Dynamical Systems, Partial Differential Equations and so on, but there are a ton of other really interesting classes that tend to only have Discrete as a prerequisite (Linear Algebra, Abstract Algebra, Higher Geometry and so on). If you know some basic calculus, discrete also equips you with everything you really need to start digging into analysis, which is where math really gets interesting imo.

It will probably be pretty different from math classes you've taken in the past, and you may find it particularly challenging even if you are generally good at math. The inverse may be true as well though, I know students who had a really hard time in math generally and then began to excel once they got to proofs. I can't say if this will be the case for your class, but in the experience the workload tends to be quite a bit lighter in terms of homework, the tests don't have so many problems on them, and there isn't nearly as much computation involved as in something like calculus or algebra.

Unless you had a really good geometry teacher or have a background in computer science or philosophy it is likely that some of the ideas presented in the class will be pretty novel to you. In earlier math classes there are shortcuts to doing well in the class if you don't understand the content: memorizing formula, grinding problems etc. There is no way to fake proofs. My first advice is to have a system for taking good notes. If you have a hard time taking notes, look into finding a way to record lectures or get notes provided. Look over the notes regularly, use a highlighter to mark certain definitions that come up regularly, and rewrite new notes as you go that takes the most important concepts from your previous notes.

Next is to read the textbook, and utilize office hours if they are available. Between the book and your professor, all the answers to questions you might have are yours for the taking. This really goes for all math class at the college level, and is something I wish I had taken to heart when I was in school.

Third is to write things out in plain English rather than only in mathematical notation! People don't tend to think in mathematical notation, so it's hard to understand the math you are doing if that's all you're writing down. This also goes for math in general, but people tend to look at me funny when I recommend this for classes before discrete or proofs.

In terms of preparation the best thing you can do is to start reading the book ahead of time. The hardest concept is going to be different for different people, but when I took the class I remember a lot of people struggling with proof by contradiction, so you might want to look into that ahead of time. I've attached a textbook (second attatchment) which is actually a book on analysis, but it also contains an introduction to proofs which is the part of the class I am familiar with (I think discrete also includes some other content but I could be wrong about that).

Good luck and if you run into challenges feel free to post questions in this thread and I'll do my best to help you out.

(The first attachment is a book on real analysis, just for anyone interested)


Wait nvm looks like only the second attachment came through which is the one you want anyways.


Aww, thank you very much for your helpful and thorough response! I appreciate it a lot. I'll take a look at proof by contradiction. I have looked at the textbook we're using (125967651X) and it really does look quite interesting to me even though I'm a person who usually struggles with math. (My biggest problem is just remembering all the little rules and gotchyas about computation, which as you said, I can usually get better at by just grinding problems)

But I'm somewhat excited to start this class because it looks very different than Calculus and I am already familiar with a lot of the logic operations/concepts at the start of the book. And as you said, it's a prereq to Linear Algebra which I very much want to learn for my programming endeavors. It's just a bummer I have to take this class online cause of the virus… I learn much better in person.

>Third is to write things out in plain English rather than only in mathematical notation!

That's a really good tip that I hadn't thought of doing. Thank you again for your help anon, I'll ask you if I run into any troubles with the course.


Discrete math is completely different from "math" that's taught in grade school, aka continuous math. It's not particularly difficult, it's just not taught as much as it should be. It's thought of as challenging mostly because we're taught to think about math according to continuous math and we don't get the fundamentals of discrete math the same way (lots of practice at a young age). There's a number of reasons the discrete side of math isn't taught to kids, and they have more to do with the system education exists within than the nature of the math itself. It's harder for a teacher to grade proofs, for one. There's less investment into understanding how to effectively teach the content for another. And then of course discrete math is actually much more broadly applicable than (continuous) math and (bourgeois) primary education is kind of designed to make you hate learning and think it's useless to your life…

Some of the fields of discrete math are in use by everyone constantly, without realizing it (or realizing that the formal math could be very helpful), such as:
&ltSet Theory (Venn diagrams etc)
&ltGame Theory (strategy)
&ltGraph Theory (series of two-way relationships)

Good luck. Hopefully you have a good teacher. That can make a huge difference with this material.


File: 1608527963268.pdf ( 28.7 KB , mathbook.pdf )

If you have a hard time remembering gotchas then I think you might find discrete to be a relief! There is hardly any of that, there's just a lot of principles and definitions you have to understand. The rest of this post is kind of theoretical. I had hoped this thread would get into some of the questions >>352 brought up, but don't feel like you have to know all the stuff I'm about to launch into to do well in or understand discrete, and also keep in mind I might be wrong about some of it.

I want to add something to what you pointed and my wording might sound like I'm contradicting you but I don't think that anything you said is wrong.

The math that you learn as a little kid is discrete math, and this is by necessity. Integers is the obvious example, when you learn to count "1, 2, 3… " you are learning a discrete system of numbers. When you learn basic operations as a kid you don't learn them over the real numbers, but rather the integers. Once you get to division though you are usually introduced to fractions which is really where everything goes awry in terms of there being any sense to contemporary western math pedagogy. I always suspected there was something very spooky about them as a kid and there absolutely is. Fractions are great, don't get me wrong, but they are introduced WAYYYYY before the student has the context to understand what the hell their teacher is on about. You need to know how operators can be defined and how they work in the abstract before it makes any sense to use them to construct a new number system. By new number system I don't mean fractions, I mean the real numbers. And by that I don't mean that Pythagoras was actually right about irrational numbers, but rather that we teach fractions AS THOUGH Pythagoras was spot on all along.

We introduce integers, then operations, then once we get to division we introduce fractions, and then we say "oh so here's another way to write fractions: decimals! and btw all these new numbers in between the integers are real numbers" When really they are not equivalent. To show how they aren't equivalent though you need square roots which aren't usually introduced until later.

All this is to say that fractions should really be introduced alongside square roots. My bias is towards a geometric explanation for both of them, partially because it is visually elegant and intuitive, but also because this way the actual weight of what is being taught would be made apparent. This would be a radical shift though since it would mean delaying teaching fractions quite significantly which would create all sorts of problems if it wasn't adopted universally. I'm not sure if we can even make the changes to the way math is taught that we need to under capitalism because of how important it is to capital that new workers know a very specific set of operations. Anyway, I'm off on a tangent which I guess is fine. I attached a pdf that I think is the vague beginnings of a book I want to write on the topic of math pedagogy. Let me know what you thing if you're interested.

We tend to equate logic and proofs with discrete math because at the college level they are introduced around the same time, but they aren't really the same thing (even though the actual classes are pretty much the same). Proofs are important to continuous math as well and if you study analysis you'll see what I mean. It's just that for some reason we delay proofs until grade what, 14? They really ought to be being taught to elementary schoolers.

Man I'm tired. I dunno if this post is even going to make sense when I read it tomorrow but I hope someone gets something out of it.


>programming endeavors
Cool! I am really bad at programming. I've tried to read the SICP but I always get stuck on like the third chapter or something.

What kind of stuff do you want to make computers do?


File: 1608527963896.png ( 49.27 KB , 240x240 , 0044c79bfd3e897511c4c817f0….png )

My favorite feild of mathematics is probably a toss up between topology and calculus.

Topology because it is the study of what is logically impossible but objectively rational and calculus because predicting the future is neat. I'm lay, I have not yet even started college, but, I think I about summed it up correctly.


File: 1608527964787.gif ( 742.32 KB , 500x281 , 51939-a-certain-scientific….gif )

My experience is the complete opposite. In "practical" classes you just have to master the application of a handful of methods and you are good to go. It's easy, just do tons of practice exercises, it's honest work. Meanwhile, for proof heavy classes ever other solution has a "notice that…" part with some twist that no mortal could think up in the heat of an exam. I could barely pass these classes.


My favourite field would be combinatorics. I know it might not be considered to be an actual math discipline but I always preferred to study actual techniques and gotchas instead of abstract theories or proofs.

got unemployed recently so I finally have enough time to go back to solving exercises in concrete math and attempt to solve some project euclid's obscure problems. sind halp I'm depressed and enlightened at the same time


File: 1608527965698.jpg ( 19.58 KB , 474x402 , sponoza.jpg )

Yeah people tend to have an easier time with one or the other. I think part of it has to do with different types of intelligence: verbal reasoning vs processing speed and working memory. I think there's ways to improve in either area though.

I am sorta skeptical of psychometrics but I think it's more relevant for mathematical ability than for a lot of other fields. I have slow processing speed and poor working memory to the point that it constitutes a learning disability. I grew up in a very working class intellectual type household (no TV but lots of books) and I've read every day for most of my life. I always thought I wanted to be a journalist so math was the last thing I was expecting to major in.

When I got to proofs I had a much easier time. Discrete was an easy A, Linear Algebra was hard but I seemed to get it more quickly than most. Vector calculus was brutal for me though and I do envy people with strong computation skills. I think both are necessary in advanced math, so if you only have one you gotta try to develop the other, or find someone you can work closely with who's has the inverse strengths and weaknesses. That's sorta what I did. My best friend when I was in college was a math physics double major. He is wicked smart and can do computations way faster than I can, he struggled a bit with proofs though which I thought where a breeze. The times that I was doing really well in school was when we took the same classes together and would do all the homework together.

I'm glad that there are some people in this this thread with both areas of strength. With our powers combined we shall crush the enemy!


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Tell me something about combinatorics! I don't know very much about it, although one of the professors I worked closely with had done her PhD in that field I think.

Tell me something about Topology! I was really excited about taking that class but I dropped out before I got to it. I know that there's some trippy stuff related to set theory that you learn in topology, clopen sets and so on.


I am only semi-familiar with it myself. I do know that topology is considered extremely difficult and requires a highly advanced understanding of mathematics.


File: 1608527966344.jpg ( 222.28 KB , 1280x720 , cirno-math.jpg )

How do I teach myself mathematics? Suppose I "buy" myself a textbook and start reading it and doing the exercise, how do I know if I actually understood something, how can I make sure if I didn't make mistakes? How can I ensure that I don't just forget all of it the next day?


File: 1608527967377.png ( 4 KB , 233x236 , pythag.png )

Libgen is your friend when it comes to "buying" yourself a textbook hehe. I would say that you understand a theorem when you can both apply and prove it.

So take the Pythagorean theorem for example. Being able to apply it means that you can find the length of the hypotenuse of any right triangle given the lengths of the legs. It also means that you can find the lengths of one of the legs given the length of the leg and the hypotenuse.

If you can do those things you are half way to understanding it. The other half is being able to show that the theorem is true for ALL right triangles. There are dozens of proofs of this theorem but my favorite goes like this:

With any right triangle you can take 4 copies and arrange them into a square like in pic related.

There are two ways to find the total area of the construction. So for any right triangle the following equation will hold true…

>(a+b)(a+b) = 1/2(4ab) + c^2

The left side is the obvious way to find the total area, and the right side you get by using the formula for the area of a triangle, and then adding the yellow part in the middle (c)^2

I'll leave the rest of the proof to you, but it's pretty simple from here. Just simplify the equation and you'll derive the Pythagorean theorem.

I think intro topology is a 300 level class at most schools so about as advanced as NODEs or Higher Geometry or maybe Abstract Algebra, but less advanced then analysis which is what you usually have to take to finish and undergraduate degree in math.

I don't think there's any reason you couldn't start learning topology once you know discrete / proofs, which really isn't all that much content. I didn't take it but I had friends that did and it sounded challenging. Lots of set theory involved.


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Thoughts on common core?


Absolutely disgusting
Kill it with fire


File: 1608527969113.jpg ( 25.38 KB , 576x432 , remove.jpg )

I mean, math pedagogy has been fucked since the burning of the library of Alexandria, but the common core is particularly trash.



What's wrong with it? I am not a burger so I only saw the outrage memes and there the problem always was that the meme-maker was too much of a dumbass to read the exercise's text.


A lot of people have been sleeping on z-lib, it's what I use for a lot of my books, though they can usually also be found on libgen.

>Euclidean geometry
please no

Personally I like combinatorics and I've been trying to learn topology and group theory, which are pretty cool. Can anyone explain what the fuck category theory is? I can't seem to get a grasp on it.


>category theory
Nope! I would like to though. Post a related pdf and I can take a shot at it. I know group theory but not topology or combinatorics.


Common core actually help me graduate highschool. I would have been fucked with out it. I don't see why people rag on common core. Not everyone is the same.


>Not everyone is the same.
Exactly anon. That is why we hate common core.


I've been trying to get through this pdf but it just feel really dense to me.

Oh, really? Then it's better than the impression I had of the American school system. It seemed like unless you were rich or talented they wouldn't even make the slightest effort to help you catch up. Depends on the school and teachers as well of course. Aggressive standardization however isn't good for learning.


File: 1608527977506.pdf ( 1.26 MB , 1612.09375.pdf )

whoops forgot .pdf after internet crapped up.


Recently finished my undergrad dissertation and feels good, my focus is in physical model and numerical analysis at the moment.

I have many books downloaded and made a bunch of learning resources myself so let me know if any one is interested in anything.


To add, have any of you guys got any tips on burnout? I have like no motivation to get my less-loved courses done


Thank you anon! I will check that out.

Nice! I dropped out before taking analysis or starting my thesis. I did get to do a teeny bit of original research which was fun. It was in geometry but such a undeveloped area of geometry that I can't really say more without doxing myself.

Please share pdfs, the more the better! An annotated index would be cool too, but if you just want to do a dump I can try to index them.

I'm not a good person to ask about that really, I tend to get overzealous, go all in, get burnt out quickly, take time to lick my wounds, and then jump back in. This pattern doesn't get you very far in academic settings which is why I dropped out. I am interested in research mathematics rather than something more lucrative like actuarial science so it didn't seem like there was much point staying in school and racking up debt. I would rather just work on my research independently so I have complete autonomy.


>category theory
it's the cool kid of mathematics that arose from the study of algebraic topology and geometry, which supplants the notion of sets with objects called "categories" containing _collections_ of objects (without set structure, so no russel's paradox etc.) and morphisms (basically arrows between objects). the morphisms represent different things based on what the category is, but as an example: the category *Set* of sets has all sets a objects, and functions as morphisms. This generalizes set theoretic mathematics in a trivial way, but also exposes more structure when we think about set-theoretic properties instead as being relations on the morphisms and stuff like that.

This was a loose summary, but I strongly recommend checking out one of the many books available on the subject at an introductory level (you should probably have abstract algebra to understand examples, depending on the book choice). I learned from Mac Lane, but it leans heavily on mathematical maturity. I've heard good things about awodey at an introductory level, especially if you are interested in learning about category theory's deep relations to type theory.


I don't understand how that is different from group theory.


what do you mean? nothing necessarily has the structure of a group (existence of a unit, inverses, a product with associativity) - so it's not group theory.


Gotcha, so is group theory a subset of category theory then?


This conversation is a little over my head, but if you're patient I think I can wrap my head around it. I learned about groups in the context of geometry, specifically in defining "geometries". I haven't studied groups much in the abstract.

Is a group a type of category?


…or are they different because groups are defined in terms of sets and categories aren't?


it would be more accurate to say that group theory can be phrased in terms of category theory and subsequently generalized. For example, the isomorphism theorems are an immediate consequence of the "canonical decomposition" - a property in the category of groups (and a lot of others) that morphisms can be written as the composition of a surjection, an isomorphism, and an injection.


a group is both a type of category and the object of another. We may talk about *Grp*, the category of groups as objects and homomorphisms as morphisms. But a group can also be described as a category with a single object and morphisms corresponding to group automorphisms.

In the category *Grp*, the objects are groups and defined on sets. But one can take the properties expressed in this category and _categorify_ them to talk about more abstract objects. Ultimately, however, a thing with all the properties of a group is a group.


That makes a lot more sense, thank you anon!

I thought I knew what morphisms are but I'm realizing I kinda don't… book suggestion?


You're probably confusing morphisms with group homomorphisms. In *Grp*, the morphisms are group homomorphisms.

> book suggestion

I mentioned Awodey earlier, but another good one is Fong & Spivak's "Seven Sketches in Compositionality", for which Baez has produced an online course with accompanying videos https://www.azimuthproject.org/azimuth/show/Applied+Category+Theory+Course


>You're probably confusing morphisms with group homomorphisms
Yes you are correct. Thanks for the reading recommendation!


I am a highschool dropout who don't know shit about math but wanna learn. What you recommend first?


File: 1608527982249.pdf ( 4.68 MB , Elements.pdf )

From my biased perspective as a geometer and classicist I'd say the best place to start is pdf related.

Another place you could start is by reading Godel, Escher, Bach: an Eternal Golden Braid by Douglas R Hofstadter. It's not exactly a math book, but it takes you on a sort of idiosyncratic tour of some questions in math, logic, computer science and art. It may give you an idea of what exactly you are interested in.

There's some math related YouTube channels that are pretty fun too. My favorites are Vihart and 3Blue1Brown. There's also Numberphile which is kinda hit or miss imo.




A Brief History of Time by Stephen Hawking might be another good place if you're at all interested in cosmology. Reading that was definitely one of the things that motivated me to get into math.


Thanks for the recommendation, I'll try to check it out. Can you explain how its structure differs from sets to avoid Russel's paradox?

If you want an intro to some undergrad topics I can recommend
It requires some mathematical maturity and understanding of proof-based mathematics, but it motivates its stuff a lot better than most DTP textbooks. It also doesn't require too much highschool knowledge afaik, I haven't read all of it. I'm afraid I don't know any good highschool level materials to recommend.

Is Elements good? I feel like classical geometry isn't the greatest intro to math, because it's so narrow, but then again I'm biased against classical geometry.

Piggybacking on the 3B1B recommendation I can recommend mathologer.
They don't have as much highschool stuff as 3B1B, but it's pretty interesting.


>Is Elements good?
It's great in terms of demonstrating what can be accomplished with logic. It's also good in the sense that you don't need any outside knowledge to understand it, although some parts can be challenging. It's important to note that you need to be highly motivated to get through it because there is zero motivation provided by the text.

What do you find narrow about classical geometry?


>What do you find narrow about classical geometry?
I was unclear, I meant that only focusing on classical geometry is pretty narrow, as with any subject. Though I am biased because I never really liked classical geometry. Maybe I just never saw the good parts, but proving that certain things hold for arbitrary configurations doesn't feel like a natural or motivated result.


File: 1608527983000.pdf ( 94.59 KB , Analysis.pdf )

Here have an analysis book and a cheat sheet I made. Don't enjoy it that much but one of my best courses grade-wise.

In my mind you would have to stay in school to get qualifications to then become a researcher, are you doing it in your free time or do you make any money off it?


Oh I can't do multiple files it seems, here's the textbook


Third time's the charm


Gotcha. I guess I kinda like that it is arbitrary, it feels pure in a way.

Thanks for the pdf! Analysis is pretty cool I would have liked to take that class. I posted the elementary analysis book that I use here >>347 but I should really get around to studying real (which is what that textbook looks like at first glance)

I don't know how one would make money off of research unless you mean like a stipend from an institution. To me research just means making novel discoveries in the field. Anything you could submit to a journal is research in my eyes.


Well freelance work in the mathematical fields, modelling would probably be your biggest friend there, but would need some commercial application. e.g. musicians could pay for models of musical instruments to see what they'd sound like.


Gotcha. I currently work as a math tutor, mostly for college students but some high school / middle school students as well. Picking up some other kinds of freelance work would be cool though.

What modelling strategies / books / software do you recommend? I did a bit of modeling in school. Took part in the COMAP MCM which was fun, although the problem my team ended up doing kinda sucked. We where given a spreadsheet with several million data points so we spent most of the time just trying to get MATlab to parse it correctly.


Nice, I don't think I'll ever get my eyes back to their pre-hundreds-of-hours-starting-at-MATLAB's-retina-burning-design state.

I'd recommend learning all you can about numerical ODEs and PDEs. MATLAB is quite useful useful I won't lie, although if you do anything big you'd probably want to learn C/C++. This book is amazingly comprehensive in its field of finite difference schemes in a musical context, a masterpiece. You could also look at finite element models too.

Whoops file too large, here you go
the format sucks but couldn't find it quickly


I took ODEs in school as well as a class on Nonlinear Dynamical Systems and Chaos. We used mathematica rather than MATlab in that class.

Nowadays I use GNUoctave for everything. I think I should probably learn R as well though.

Thanks for the link, I will check that out :D


Ah and yeah C++ was my first programming language. Learned it when I was 13. I haven't used it in a while but I still have a compiler and a pretty good reference book on it (C++ Primer Plus)

Why do you recommend C++ for math modeling?


>Nice, I don't think I'll ever get my eyes back to their pre-hundreds-of-hours-starting-at-MATLAB's-retina-burning-design state.
Lmao sorry to throw shade but that is sorta what you get for using the graphical environment instead of running it in a terminal emulator…


> Matlab in terminal
say sike right now…

oh god why did no one tell me???


just type matlab -nodesktop in terminal lol


You can also call call MATlab scripts as functions in BASH if you get your configs set up properly which is very convenient. Idk if function is really the right word there but whatever.


GNU Octave is more or less a MATlab clone and it runs in the terminal by default. It is a lot easier to do >>535 sort of thing with which is why it's the main Mathematical Programming Language I use.

Out of curiosity, what operating system do you use? This might be a little off topic but it would be cool to hear a few perspectives on how people configure their workspaces for mathematical modeling.


I have no idea why would anyone recommend C++ to anyone but professional programmers… it is so easy to make some silly mistake and completely destroy performance. You have to constantly keep in mind a thousand little idiosyncratic rules, it is better suited for the lawyer than the scientist.


This is life changing, thanks a lot. Mathematicians aren't usually very tech savvy so I guess this never came up with my colleagues.

I currently use macOS for a few reasons. There's no reason to use any software for modelling in particular. The most important stuff is done on paper.

My workspace configuration though is minimal with a tiling wm (yabai), usually need a vim w/latex up, a pdf of something I'm looking at, probably a web browser too and another desktop with code running. So clean and organised is a necessity for me (also because autism).

I recommend it simply because when you get to a certain level on complexity you need the fastest thing you can get. If you are a hobbyist then C/C++ is the only way you're going to get this kind of speed (I've heard of some models taking days on super-computing university grade machines) especially within musical applications, you want to get as close to real time as possible. There are easier ways to convert from MATLAB to C if I remember correctly though.


Thoughts on Wade's vs. Tao's analysis books? I'm trying to pick one to self-study with.

>Out of curiosity, what operating system do you use?
Archtard here. Might switch to gentoo later.

>Mathematicians aren't usually very tech savvy
It could just be a demographics thing, but most of the people I know who are going into pure math are good at programming. Though of course, they aren't mathematicians yet.

Out of curiosity, what reasons do you have for using macOs? I don't want to come off as elitist or anything, but the best one I can think of is ease of use.


I also use Arch. Never tried Gentoo, but I'm considering trying either that or LFS.

>It could just be a demographics thing, but most of the people I know who are going into pure math are good at programming.

Interesting. Could be that I went to a liberal arts school but not many of the other students in my department where into computers. I think I met like a total of 2 other math majors who knew their way around a terminal, but it's possible people where hiding their power levels idk…

I'm not very good at programming, and I think of that as being a different skill from being "tech savvy"


I used Wade's, so I can recommend that. The cheat sheet I posted >>498 is based off Wade.

Students around me either were pure math, and that's where their interests lie solely, or were very applied and did a lot of programming. Of course pure mathematicians would be naturally better at programming than say, a painting student, but I haven't encountered many that actively enjoyed it. If they did they wouldn't usually be 'into' technology, so would be like 'what is this hackerman terminal shit', similar to what >>549 said.

Regarding MacOS, I got the laptop before I was really into free/open source software, which is unfortunate, the reason I don't change is because currently I have a good workflow and while still in the academic year would be dangerous to swap. Also I make music, the propitiatory software for it is just so much better. When summer comes I think I'll make a partition and have a music-boot, would help with focus as well.


What about Fortran? As far as I know, it is still the most suitable for scientific computing. In fact it seems to dominate HPC.


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Did you write that pdf anon? It looks like a work in progress


Yes! Barely started it.


Yeah I've met some people that liked it but no one in my field of interest. I have no intention to ever learn it however


I don't either.

I know: BASH, C++, Python, Lisp, Mathematica, and MATlab/Octave

I want to learn: R and that's really the only one

Is there anything I am missing?


I don't really see why you'd need more than that for mathematical related things alone. Why learn R? Does python/MATLAB not give you everything you need? I did do some R but it just seemed like a waste of time


Maybe it does. I don't really know stats and I have a really hard time staying interested in it whenever I do study it… My reason for learning R is more that it would be a way to stay motivated studying stats lol


File: 1608528012202.png ( 65 KB , 310x350 , ProofGeneral-splash.png )

What do my anons think about proof assistants and interactive theorem provers? Like Coq, Agda, HOL, etc.? Is there any value in this level of formalization of proofs?


Looks interesting! I have never used one but perhaps I will try one out. I have always just written proofs by hand but just reading about them online they look like they could be useful as software.

In terms of the question "is there any value in this level of formalization of proofs" I think the answer is yes. Formalization, while sometimes annoying, generally helps eliminate ambiguity. I don't want to establish conventions about how proofs need to be expressed, because that would be limiting, but specificity in logic and notation is always good.

Have you used this software before?


I did play around with Coq, although I was more interested in proving the correctness of algorithms than with mathematics. But at that time it turned out that I was too un/edu/cated to understand what was going on. I want to give it another go.


What's the implementation language? I have really enjoyed my time with both Lisp and Haskell.


Coq is written in OCaml, but ACL2 is in Common Lips and Agda is in Haskell. They all implement their own language that you need to write your theorems and proofs in.


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Based and Zerzan-pilled


Fuck you
I hate maths. It made me gay and I can't stop sucking dick.


I don't see how that's a bad thing.



I've always been more of an Arts guy, but I recall only one instance in my life where I enjoyed maths.

Once was in high school where one of our substitutes figured out I like medieval stuff.
And so, in his infinite patience, he design a few lessons just for me around building a trebuchet.
It was awesome and so quickly I began to "get" it.
Alas, less than two weeks later our normal maths teacher came back.
As he barked at us to open our books, I asked if I could continue with the previous teacher's work as I was nearly done. He then said "Why? What are you? Too stupid?" then chuckled.
It was at that point that I fully disengaged from maths. So much so that I was put in to the "Special" maths class, but since we had to take roll-call in our normal class there was extra shame at being the "most autistic in the normal class".
But regardless, I did enjoy playing with blocks and doing maths a different way. It was just a shame it was branded as the "retarded" maths group because I learned a lot from our teacher. She was a bit alternative, but she truly saw the beauty of numbers in everything because she said she could "see" them in different colours. I'm not sure if that's true however or just what she told us.

Don't know why I felt compelled to tell you this, perhaps because I'd like to try to learn maths again. Alas, I don't know where to start since I stopped learning in grade eight :\


>I want to write on the topic of math pedagogy.
As I teacher, though not maths as mentioned before, I'm going to read this. Looks interesting.


Thanks! Like I said it is very rough and not even a fully formed idea. I wrote it in one sitting a couple months ago and haven't gone back to it. I might start working on it again since I am hitting a wall with my current project (critique of cockshott) and I try to rotate between works to stay interested.

Let me know what you think!


>I've always been more of an Arts guy, but I recall only one instance in my life where I enjoyed maths.
In school we are encouraged to categorize ourselves this way. I am an arts guy. I am a math guy. I am a stem guy. It is easy to see why this is encouraged. It serves the interests of capital, by categorizing students by aptitude, and shoehorning them down tracks where they will end up with specialized educations that allow them to form a particular skill set that will allow them to perform a particular function in the capitalist sphere of production. The renaissance man or woman is of little use to capital, and they may even constitute a threat to the status quo because they are more likely to grasp the totality of our situation.

>And so, in his infinite patience, he design a few lessons just for me around building a trebuchet.

>It was awesome and so quickly I began to "get" it.
Sounds like a good teacher. For me the "getting it" moment came in college when I took proofs. I had already chosen math as a major, but I chose it in particular because it was the class I had always struggled the most in, and I had this bizarre idea that this meant I should pursue it. I've always been motivated by challenge and turned off when things come easily, which is kind of a double edged sword because it makes it hard to stick with things once they start to click. As soon as I had contributed to a novel discovery I dropped out. I don't think the paper was ever published. There where financial reasons to, and I was getting more involved in organizing, but that was definitly part of it. I realized that I could be a research mathematician if I wanted (which up until that point had been my goal) and I realized that is not what I wanted to do. I needed to work on a less achievable goal like ending capitalism. This might sound defeatist, and it absolutely is, but it's how I operate.

>As he barked at us to open our books, I asked if I could continue with the previous teacher's work as I was nearly done. He then said "Why? What are you? Too stupid?" then chuckled.

So many math teachers come across as straight up sadists. I didn't find this to be the case in college, but I hated most of my math teachers through grade school. My high school geometry teacher was really cool though.

>So much so that I was put in to the "Special" maths class, but since we had to take roll-call in our normal class there was extra shame at being the "most autistic in the normal class".

I also can't stand the way that students are encouraged to think that getting it = being smart = having value. It's not just schools that do this, parents who want their kids to get good grades all the time carry just as much culpability.

>She was a bit alternative, but she truly saw the beauty of numbers in everything because she said she could "see" them in different colours. I'm not sure if that's true however or just what she told us.

Synesthesia? It's a real thing and it can have some really interesting implications for mathematical ability. I knew a woman with synesthesia who could recite digits of pi for like half an hour straight. Not slowly either. I don't know exactly what colors had to do with it, but she said it was everything.


I'll just semi hijack this thread…

Is there anyone here who would like to add me on discord and do math with me? (Don't worry if you "suck" at math too, you can't possibly be worse off than me in this haha)
I working my way out of being math anxious af and barely know what 2+2 is, and I feel like it would be pretty cool to have based Comrade to teach me more.

We could do an exchange teaching wise: For example I could:
Teach you economic history, political theory, anglosaxan ethics, sociology,
or summarize literature with critical comments on e.g.

Parts of Capital and side literature to Capital.
The dialectic of enlightenment, hegemony and "socialist" strategy, classical sociological theory, a contribution to the critique of political economy, texts by Lenin, Trotsky, Marx.

I could teach you how to (hate to use the term) "network" or, if you don't want to use that pesky term, act like a fucking sociopath in line with capital-logic.

And yeah also, EU time zone is prolly a good thing 4 ya if u don't wake up super early and are free in the mornings in burgerland or south america.

If you read this and find it interesting just reply here. I'll be checking this post again tomorrow around the same time, so be online then and then I'll send a privnote with my username :)


Sure anon. I normally do that for work anyway but it's kinda dried up since we entered this recession and all. I've actually got a discord server that I set up as a sort of curated library of math related content, but I never got around to finishing it and I've barely given anyone the invite link.

[email protected](dot)ch


… it would also be chull to take on a pro-bono client since I normally do in person sessions and haven't yet gotten the chance to test out my whole screenshare, wacom tablet setup on my machine running windows (which is the one I use discord one, no way I'm putting that spyware on my main computer lol)


Sounds comfy


hello comrades, what's 3+2?


Try this:

>sudo apt-get install octave

>3 + 2


if your distro doesn't come with bc by default then that's a little odd, but the nice thing about bc is that you can just do
>bc 3+2


>bc 3+2
&ltFile 3+2 is unavailable
I'm on arch.


i'm studying the finite element method


I'm more of a finite difference man, have you ever studied that?


I personally find math incredibly boring, don’t care for it.


Linear Algebra


Everybody now some good books on that go rigorously through the math of a planned economy?, (aside from the soviet ones).


Do any of you guys have an interest in a thread where we go through sections of a textbook on linear algebra together and return to the thread at least once a week to discuss what we learned. I don't think this would necessary for me to learn the material, and I intend to learn it anyway, but I do think learning would be more fun this way.




I would lurk and help people out, especially if it's linear algebra!


Alright I'll post a thread this sunday using the syllabus from MITs open course


Is there any material for people who never took calculus in highschool? Mine's was shitty. Any online courses or books?




Thanks, man.


I'm in my final year of math now (Europe), can't fucking wait to finish this shit, math is a fucking tragedy.
I'll probably do a masters in numerical analysis or just go berserk and do topology and geometry.


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this is now an applied math thread.

abstractists gtfo

Post ODEs/PDEs


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many many courses on youtube.

if you want something more structured and gamified start with KhanAcademy.org

The calculus playlist is great.



for you

-→ >>3074


I’m taking differential equations and my textbook is useless as fuck. is there an accessible alternative that has more example problems?


Do you happen to know any good courses online or whatever on discrete math? I found it pretty interesting but my professor was NOT GOOD at explaining the material and since COVID happened we kind of rushed through the class so I left feeling like I didn't entirely understand all of it


Can any mathsanon explain to me how to actually understand math? Because I just don't seem to master the tasks, that require you to truly understand the Essence of Maths. The only way I solve those Tasks, is when I look at the Solutions and this can't be the Point though, am I right?.

t.Fag who studies Chemical Engineering


You do it every day and at some unknown point it just becomes an extension of your mind. The essence can only come from solving problems, usually with other people to get different perspectives, and creating a set of skills which you can call upon to solve problems.

I remember in middle school trying to desperately remember which axis is the x and the y, and how linear equations work. However these attempts are actually counterproductive IMO. At a certain points of maths you let go of trying to 'get' it, and just move on, then after solving future problems it may come to you.


You just do it. You want to develop a certain set of skills which are useful in the sense that, when solving problems you always ask yourself
– why am I doing this?
– what happens without this assumption?
– what happens with this assumption?
– why does method work for a finite case but an infinite?
– where have I seen similar structures as this?
and so on. It's a skill really, took me 3 years to get somewhat good at it.


Why is math "essential" to learn? Can I get on by with my bachelor's in Aerospace Engineering? I'm not a mathematician by any means, but I don't see what other math I can learn that can really pragmatically benefit me.


Maths include statistics and understanding of statistics is very useful to avoid falling for propaganda.


I’m not a mathematical type, I like things involving theory, writing, critical thinking, etc.


Do any one of you have experience in "competitive" mathematics? Olympiads, putnams, etc? Or are most of you just Marxists who like mathematics?


It worries how different countries teach maths and how different their methods are

IN my country we had BODMAS but apparently everybody else learn PEDMAS


Why is the Fourier-series such a powerfull tool in applied mathematics, engineering, physics etc.?


Can I apply this thinking to other sciences like physics too?


Anyone still here?


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What the best way to learn math when you suck at it ?


Mix it with programming IMO. Learn Mathematica or something while learning math. Mathematica actually comes bundled with tutorials that basically teach you a lot of typical math to show how to use the language. But I think it kind of gives you tools to start playing around with math for projects you might have, so the practical applications give you problems to solve that help internalize what you’re learning.


If there exist such magical pedagogical solution, you would have heard of it by now. The only way is plowing through. Read and write along the solution manual if you must. You can't learn anything abstract this way but familiarizing differential calculus is just a matter of grit


Tons of practice. There's no way around it.


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What are the material implications of quantum computers on Gödel's Incompleteness theorum?


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pink = all - 4 green = red + blue

The rocket pigs version: https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/

>differs from sets to avoid Russel's paradox?
The standard solution is based on von Neumann's work and predates category theory. Cantor's naive sets are renamed to classes. Classes are partitioned into sets and proper classes. Sets are those classes that can be built up using ZFC, which removes unrestricted comprehensions. You can no longer take "all X [with P]", you have to take "all X from S [with P]" where S is already a set. The question becomes whether the class of all sets is a set. The resolution to Russell's paradox is to provide the negative answer by becoming the proof that the class of all sets is a proper class rather than a set.


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Just saying, Bordiga was an engineer. Makes sense, he was autistically literal and uncompromising like a STEMy vs the artsy-fartsy Gramsci who spawned generations of culturally obsessed navel-gazing "Marxists" with his post-hoc "theories" justifying his failed politics.

This is why I love Bordiga, he does math so I don't have to.


I think everyone who is interested in math should study linear algebra algebraically so that they can know duality (by studying dual space), Erlangen program and the foundation of non-Euclidean geometry (by studying bilinear forms), Lie groups (by studying classical groups), representation theory (by noting that S_n is isomorphic to the group of permutation matrices so that every finite group is isomorphic to a matrix group.), etc. Of course it could be challenging but it would give them more mathematical maturity than randomly studying tons of other fields.


I would just use Rudin's PMA but if I have to choose one of them, I would choose Tao. It reminds me Spivak's calculus.


>Is Elements good?
It is really good for your free time. For a degree, it is useless.
Some parts of Elements are really mind blowing. For example, he understands number theory by geometry. For him, the number '1' is the same as a segment of which the length is 1, "a divides b" means one can measure a segment 'b' by a segment 'a' so that the greatest common divisor means the greatest common measure by which one can measure both 'a' and 'b', etc.


Category theory is a must if you are into some fields like algebraic geometry, number theory, topology, etc. In those fields, people use it more than set theory.
The power of category theory comes from its relativism, generality, intertwining many fields into one. Unlike set theory, you can map topological spaces to groups, their homeomorphisms to homomorphisms in category theory. Of course you can do like that with any other mathematical objects. And you can build a category theory without objects (in fact, the identity morphisms are sufficient to replace all the objects) so you can get all the property of objects not from the objects themselves but only from their relations. Thus you can get result by only drawing some diagrams. This is called "Abstract nonsense" (https://en.wikipedia.org/wiki/Abstract_nonsense).


I want to learn why, when logical paradoxes exist, we can be certain proven facts are true and not logical paradoxes. I have An Introduction To Formal Logic (attached) and A Modern Formal Logic Primer (https://tellerprimer.ucdavis.edu/); will these help me? If not, what can help me?


Anyone still here?


yup still here


Anybody still here? >>7018 is still waiting for an answer so if anybody can answer, please do.


>Anybody still here?

>is still waiting for an answer so if anybody can answer, please do.

You want an explanation why paradoxes exist ?
That's a really big ask.

Maybe there's a philosophical error in symbolic languages.


No, I want an explanation of why we can use logic to determine what is true and what is not given that paradoxes exist. Logically there shouldn't be paradoxes and everything should either be true, false or meaningless but this isn't the case (Liar's paradox for example, http://tdx37ew3oke5rxn3yi5r5665ka7ozvehnd4xmnjxxdvqorias2nyl4qd.onion/wiki/List_of_paradoxes?lang=en#Logic for more) so how and why can we use logic to prove things when it clearly fails at some points? I also asked if the books I have will help me answer these questions. I asked nothing about why paradoxes exist but asked about their implications on the validity of logical deductions and if the books I have will help me answer this question or give me some required knowledge before it can be and if these books do neither then I asked for some books that will.


>Liar's paradox

<This statement is false

is self referencing, if you feed it into a logic interpreter it will cause an infinite statement expansion, and the interpreter will never actually get to the point where it can perform any logic operations.

If you want to know about this, read about Godel's incompleteness theorem or in computer science the halting problem.


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Because everything we know revolves around a series of assumptions apriori: Things like laws of physics, fields, assumptions about foundational asthmatic. There are things that are true simple because they appear to be the most reasonable explanations for what we observe. Even though our methods do not appear to be perfect they have repeatedly delivered the most reasonable and logical explanations for our observations for centuries and thus demand the benefit of the doubt in the continued use.
The only way this could be challenged is if there was a system of logic superior to the one we currently have today, which, is completely possible, so, if you have a methodology of logic greater than what we currently have, or, a scientific methodology better than the methodology we currently have then explain it….

It's kind of like democracy: It isn't perfect but it's the best we have.


that's a ridiculous amount of the best girls on the m²


>Logically there shouldn't be paradoxes
Formal logic is a human invention that approximates something in the real world. It's not ideal. That this instrument can lead to paradoxes only tells you that this tool is flawed and you should be careful with your recursions.

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