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Recently I've become fascinated with tessellation and spent the past couple of weeks collecting pictures of mosaics from around the world. Eventually just looking at them was not enough and I want to go deeper, understand the geometric shapes and its secrets better. Not even sure why but periodic tiling feels like a brain massage to me, like I'm about to fall out of bottom of how I usually perceive the world around me. So I picked up the book Geometry by Cambridge University Press. Feel free to give a hollow laugh: I honestly thought I could just skip the math part of geometry (yes I'm an idiot) and appreciate its resulting surfaces. While you can do that, if you want to appretiate geometry even at a surface level, you need to know the bare minimum of maths. The book suggested a good grasp on the basics of linear algebra and algebraic structure. I thought 'OK, I'll read the wiki entries as a lazy primer' and quickly realized I forgot even the basics of mathematical symbols. I guess it's true after all, if you don't use it you lose it.

Long story short, I'm currently going through Pure Mathematics for Beginners. The good part of being dumb is when you learn a single thing it feels like a whole new world just opened up and it feels really good.

So yeah, maths thread.
Previous one; >>30554


I suggest you read Grünbaumand Shephard's Tilings and Patterns, ir you really want into the math of it.
I don't understand all that shit about geometry without math, geometry *is* math. If you just want to use the pure, synthetic geometry, you can, you don't really have to learn linear algebra or analysis or modern algebra. Pick up Ogilvy's Excursions in geometry, or Coxeter's Geometry Revisited, and do read Euclid.


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Thanks, I didn't know about those, that's really helpful and thanks for responding.
>I don't understand all that shit about geometry without math
Well wiz, I don't think there's anything to understand really. Geometry is very pleasing to the eyes even if you have no idea what the hell is going on. It has an aesthetic value. I love geometric patterns and I have no knowledge of maths but I'll work hard to change that.
>do read Euclid
Yes, it's pathetic I'm over 30 and have no grasp of plane geometry. But I'll be changing that in the upcoming months.


I'm just really fascinated by probability especially when it is counterintuitive and against common sense.

I don't agree with Stephen Pinker on a lot of things, but when he said that probability should be the type of math most emphasized in education to influence a rational worldview. I do agree with that.


I just don't get what do you mean by geometry without math. It's a contradiction in terms.


I think libartsys can appreciate math topics such as geometry in a conceptual and aesthetic sense, without really knowing the numbers behind it. That is how I'm with Bayesianism


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…I think maybe what OP wants is picrel.


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I mean I thought I would be able pick up a geometry book and enjoy it without knowing anything about the math behind it. This is possible but not that satisfactory. I can have fun with the visual representations of conic shapes in a geometry book without knowing anything about their equation forms. For example, a person can appreciate tapestry with patterns that uses only shapes derived from a conic section without knowing what a conic section is.
Yes, that's what I meant.
That looks interesting.


Fair enough. My point is that you might not want to stack up on abstract math just to get started with geometry.


A video on the quasiperiodicity of the Penrose tiling.


Is there any wiz out there studying math for school or hobby? If so, what are you studying?


I've been reading a lot of popsci books on Bayes and its biased towards Bayes of course. But it makes it sound like only an idiot could believe in the frequentist approach. Even though some of the smartest minds in history did. Well the smartest minds believed a lot of things that are outdated. But this is still an active debate to this day. And yet I never get to hear what the frequentist approach side is.

Well objectivity is important. And when the layperson thinks of an objective statistic, they are more likely to think of it in the frequentist approach. Updating probability just from the subjectivity of the standpoint, sounds like the opposite of science.



If you're wondering how to get into math from the beginning, take a look at this video.


Studying math made me realize something interesting about my brain. I was just solving some basic trigonometry problems and this straightforward calculation came up 31²+23²-2·31·23·cos(95°). I know all the basic operations involved and how to proceed here and still got it wrong. Twice. I have very short, almost imperceptible attention lapses that really shows up when I'm working on mathematical problems, even simple ones. My focus drifts away to some other thought while working on a problem and when my focus returns I realize I made some ridiculous mistake, not because I didn't know what to do but because my hand kept moving while I was not paying attention to what I was doing. I'm having flashbacks from my school days when I would look at a test, realize I knew the procedures to solve the problems and thinking I did very well and getting a bellow average grade. I bet that is what was going on even back then. Those lapses are not something I notice regularly but when doing something that requires full attention and a step-by-step procedure it shows up in all sorts of stupid blunders.

Anyway I'm OP and I'm almost done with basic algebra and trigonometry so I can finally jump into some calculus soon.


I have no degree, is it too late to go back to school at 22 for math?


It's never too late to study what you enjoy. As long as you have the resources and time to do it, I don't see why age should have any relevance at all in your decision.



I laughed at this. 22 is still ridiculously young. I got my Bachelor's at 30.

I understand that one cannot truly understand this until you get older. It is hard when you perceive that everyone is doing better than you. Don't worry about that, the only person you should compare yourself to is your past self.


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I'm studying Linear Algebra, and it's pretty fun. I'm mainly interested in maths so I can understand special relativity, and perhaps have a shallow understanding of general relativity. Pic rel is Mind and Nature by the famous mathematician Herman Weyl, he writes a lot about the philosophy of mathematics, and explains more complex topics very well


That's pretty cool wiz. What material are you using for your studies?


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An Illustrated Guide to Relativity by Tatsu Takeuchi
Eigenchris's video course on Relativity,
Fundementals of Physics Halliday and Resnick 10th edition


right now I'm studying discrete mathematics to get better understanding for game programming and CS


It's a pretty good thing to have a goal to push with your math learning. I'm currently trying to get some mathematical maturity before I jump into calculus and then hopefully topology. But I don't have a particular goal in mind and sometimes I get that 'why even bother' feeling. I just keep going because math truly is beautiful. I envy mathematically inclined minds.


I want to brush up my calculus so I can properly study several topics in physics, mainly classical mechanics, astrophysics, and celestial mechanics. I'ma bit of a brainlet so for me it's slower to read a page full of mathematics, but it's generally doable, with plenty of water and breaks.
Besides the physics, I would also like to take that geometric knowledge and use it to make computer graphics, probably with WebGL.
My main problem (besides low IQ) is my (undiagnosed) adhd, though maybe the latter is just the former in disguise.
Based. I just downloaded it. I'll give it a read.


The Math Sorcerer's yt channel has become nothing but clickbait garbage for the past several months. I just unsubscribed.


Today marks one month since I began studying mathematics. I had to relearn pretty much everything, starting with fraction sums. Since I have nothing else to do I was able to put 6h+ everyday into it. The way I do it is basically I pick a book and read from begining to end, doing all the exercises. I don't know why so many books refuse to give the solutions btw, it's really annoying. How the hell are you going to check your work? I began with Ace Geometry highschool geometry book which goes from explaining what a line is to calculating volume and surface area of spheres. It took me about 3 weeks to go throught it all. It's not that hard when that's the only thing you have in your life. Lots of focus. Going through the basics of geometry gave me just enough mathematical maturity to start with algebra. I'm using Beginning & Intermediate Algebra by Lial, Hornsby and McGinnis. Yesterday I finished the chapters on linear equations and just started on rational expressions. It's interesting. Math is so different from the stuff I've spent my time with before, there's a silent elegance to it (silence as in the focus is not melodrama and emotions, like in works of fiction for example). It has a unique type of beauty to it. Too bad I didn't notice this years ago. I'm trying to make up for lost time.


Well done wiz. How old are you and why did you decide to return to mathematics?


I'm in my 30s. I'm not sure of the reason. I never cared for mathematics, my academic background is in philosophy and my thesis was on Thomas of Erfurt. My inclination was always towards history, language and grammar ever since I was a kid. After leaving school I never again put my brain to any use and for a decade did nothing but consume entertainment, from studying Renaissance paintings to watching some anime. Then one day I had this strong feeling I had "finished" entertainment and everything else I cared about in the past. There's nothing else for me to harvest from the arts, history or philosophy. And that's when I picked up geometry. Again, I'm not sure what caused this shift. Maybe it was always inside somewhere. Most of my family is involved with numbers to some degree. My father is a chemical engineer, my aunt is a chemistry professor and my uncles are civil engineers, so who knows. I finished Beginning & Intermediate Algebra btw, did over 90% of all exercises in there, filled 3 notebooks with it. It was fun. I'm now going through a book called Calculus A Complete Course by Robert Adams and Dr. Christopher Essex and it's not as interesting as algebra imo. My plan was to continue studying more advanced algebra but after doing some research online, I was convinced calculus is a very important step towards mathematical maturity so I'm biting the bullet and will go through at least this one book before returning to algebra.


>is it too late to go back to school at 22 for math?
I got into uni at 28(have not finished it yet) for an EE degree. You should never use your age as an excuse to learn something.


>be math sorcerer
>decides to make a video about book X
>opens book
>"Man I love the smell of math books, they smell so mathy"
>"This book is about X, it talks about X and I guess people that wants to learn X will read it"
>"The table of contents is on things about X"
>reads the first few lines of the first chapter
>"That is it guys, can't wait to see what book I'll show next"


I know youre just starting on your maths journey, but do you plan to look at the more pure side of things?

If so, it is mandatory to get a good grap of basic set theory as it is the language of pure maths. A book i can absolutely recommend for starting with abstract algebra is "Abstract Algebra" by Dummit which is very accesible (if you can read set theory).


Yes, in fact it sounds like a very fascinating part of mathematics. I have to tread carefully though, it's very easy for me to veer off into "tourism mode" and end up just perusing a great quantity of topics without ever actually learning anything, so I have to keep a very strict focus.
What about you anon? Did you went to school, it's a hobby, or both?


Dummit and Foote is a great book, and it's quite accessible, too. That said, it's big, and that can turn out to be intimidating for somebody approaching the subject for the first time, or who wants to get a more succint introduction. It's a book that'll take you several months to get through.
As a shorter alternative, I suggest Van der Waerden.


I am still going to school, finishing my bachelors in maths next year. Math has always been a hobby of mine and im very happy someone like you, who didnt really appreciate it at first, got into it.

To me solving problems and understanding the beauty of concepts gives me an insane dophamine rush and i hope it is the same for you.

Youre kind of right about tourism mode, but you shouldnt hesitate to stop somewhere with a certain subject. Maths is big really big and at a certain depth in a topic the return rate for other subjects becomes lower and lower. So you should also not just keep going or always doing everything in a book (at the start this is ofcourse less applicable).

Good luck on journey, i hope it'll be a fun one.

Yeah youre kind of right, since im not a self studier i didnt really see the pitfalls since everything is guided for you. So you should probably follow this anon's advice.


Halp I want to study math but I always get stuck doing the exercises. I just gst mentally blocked and grow impatient because usually it's 25+ exercises and I just want to get on with the book.
Any advice is appreciated.


Skip them and do them later? If you're stuck on a problem, leave it and try it with a fresh perspective. Doing exercises will help you get an intuition but you don't have to do every single one. You can even just find other, easier exercises online and work your way up to the harder stuff. It's not a race or competition, just enjoy the math and follow where your curiosity leads you.



Usually, most of the questions aren't 'unique'; if there are 40 questions, most of them are just differently stated versions of the same question.

If you believe you understand the subject matter but still struggle with exercises, try looking up the answer to one of the questions you are having trouble with and attempt to solve similar questions on your own.


dont do them then, or just do a few.
Modern mathematics education is a disgrace because nobody wants to learn with dozens of tedious exercises. I hope you actually have good learning material


doing the problems is how you develop maths intuition tho?


I'm the person who started this thread. Since someone bumped it I might as well say I kept going until reaching differential calculus. I filled about 2 notebooks with exercises. After that, about a month ago, I stopped with math focused books and picked up a textbook on electronics. It's amazing how much math helps in understanding things like magnetic fields and just electricity in general. I could even predict some of the behaviors on the theoretical part of the text. I really feel I'm making good progress, can't wait until I reach the meat of the thing and start reading schematics and study electronic components.


Anyone got/read/knows Linear Algebra book from Peter D. Lax?


is anyone archived old math threads?


I started self-studying math 3 years ago, have read many books already, started with basic pre-calculus stuff and now Im reading my 2nd book on differential geometry. I've found it made me sharper and helped revert actual cognitive deterioration.
How is the study going for you wizs? Have you found any benefits besides enjoyment?
Don't be shy to look at solution online, then write them down (important) while making sure you understand each step, at the start you will do it for most excercises and you will slowly develop technique.

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