How do I teach myself mathematics?

Euclid's Elements is still an excellent way to learn geometry, a truly beautiful form of mathematics, and also relatively intuitive. It's also a bonafide work of Ancient Greek literature. Have fun!

>Euclid's Elements has been referred to as the most successful[5][6] and influential[7] textbook ever written.
en.wikipedia.org/wiki/Euclid's_Elements

Here's the full text, along with interactive figures:
aleph0.clarku.edu/~djoyce/java/elements/toc.html

I wasn't very good at math in high school but have learnt to love it. I want to major in it but I'd like to go through all the material of a mathematics undergrad before pursuing it. Which textbooks and resources should I use in order to build a bachelors level of mathematics understanding.

Based Euclid!

Math student here, user.
Khan Academy is pretty nice for starters, you can pick up where you left off at school, all the way up to calculus,differential equations and such.
Another very good website, as you progress, is Paul's Online Math Notes, as it provides good explanations and examples.
As for books, well I think Veeky Forums has a good FAQ which can help with that.
Mathematics is a beautiful study and it's really worth studying, so I hope you enjoy it. Good luck user.
Also

I meant beautiful subject*

brainlets should kts not shitpost

I am definitely interested in this historical approach. Are there any other works that "hold up"?
Would "Basic Mathematics" by Serge Lang be a good start?

This thread is shocking. I always thought the majority of /lit would hate math like all my English and Literature profs/teachers

>I am definitely interested in this historical approach. Are there any other works that "hold up"?

Newton's Principia Mathematica, although that is a fuck-load more advanced. Don't start there.

True philosophers see the value in all intellectual pursuits. Just because some of us might have stranger language skills doesn't mean we aren't interested in math or science.

Pay no attention to generic textbook recommendations (whatever bullshit you'll find on Veeky Forums). Most expositions are shit. Total garbage, worthless.

This is a pedagogically optimal reading list:

Lang, Basic Mathematics
Spivak, Calculus
Spivak, Calculus on Manifolds
Kuga, Galois' Dream: Group Theory and Differential Equations
Halmos, Finite Dimensional Vector Spaces
Abbott, Understanding Analysis
Rudin, Principles of Mathematical Analayis (as supplement to Abbott only)
Remmert, Theory of Complex Functions
Jacobson, Basic Algebra I
Milnor, Topology from the Differentiable Viewpoint
Morita, Geometry of Differential Forms
Kato, Number Theory 1:Fermat's Dream
Knuth, Concrete Mathematics

More advanced (pick and choose):
Jacobson, Basic Algebra II
Edwards, Galois Theory
Remmert, Classical Topics in Complex Function Theory
Silverman, Rational Points on Elliptic Curves
Cox, Primes of the Form x^2 + ny^2
Hatcher, Algebraic Topology
Kato, Number Theory 2: Intro. to Class Field Theory
Wilf, generatingfunctionology
Bondy, Graph Theory

It's hilarious watching people on lit approach maths in the same way they approach literature. Wanking over the famous figures and history of maths rather than learn how to actually do it.

The lit approach will definitely lead to more pseudo Intellectual cred

I am asking here specifically because I would like the more "aesthetic" approach to mathematics rather than the brute engineers approach.
Noted. What about things like Abel, Gauss etc.?

The closest thing I have read to a math textbook is "Formalized Music" by Iannis Xenakis, and it contains several references to Gauss and uses Gaussian techniques. Getting through this book was pretty hard and I don't know how much of it I've actually retained, but it at least made me interested.

You could read Disquisitiones Arithmeticae, but you might appreciate it more with a modern approach to number theory first. Abel, I don't know, probably not good for introduction.

Fuck off, retard, what do you fucking know? Are you a practicing mathematician, brainlet?

mathoverflow.net/questions/28268/do-you-read-the-masters

>Gauss' Disquisitiones proves quadratic reciprocity by induction on primes. So it is possible to prove theorems about primes by induction, which seems very counterintuitive at first. Such an inductive technique was recently used to great effect in the Khare-Wintenberger proof of Serre's conjecture on the modularity of 2-dimensional mod pp Galois representations.

>I agree 100% with Igor and Andrew L., on the benefit of reading the creator's version of the same thing available from later expositors. I have gained mathematical insights from reading Euclid, Archimedes, Riemann, Gauss, Hurwitz, Wirtinger, as well as moderns like Zariski.... on topics I already thought I understood.

>Once as grad student in Auslander's algebraic geometry class, I vowed to try out Abel's advice and read the master Zariski's paper on the concept of a simple point. I was very discouraged when several hours passed and I had managed only a few pages. Upon returning to class, Auslander began to pepper us with questions about regular local rings. I found out how much I had learned when I answered them all easily until he literally told me to be quiet, since I obviously knew the subject cold. (To be honest, I did not know the very next question he posed, but I was off the hook.)

I heard it is, yes.

You should obviously supplement reading classics with solving exercises. Nothing would work without the latter.

You could say the same thing about Philosophy. I find the history of a field to be very ellucidating for understanding the concepts that have been accepted today.

Buy whatever books match your understanding. Be it HS, college or Uni level. Do them.

How is that hard

>It's hilarious watching people on lit approach maths in the same way they approach literature
I've never seen this happen. Most of the advice in this thread isn't like this at all.

I bet you could fit your brain in your pocket.

? What the fuck is wrong with that guide.

Are you gonna read "History of Maths" in Wikipedia and learn it that way? The fuck.

I'm in the same case, OP, except I have no time to read anything. I started spending a lot of time on www euclidea.xyz , I wouldn't say it teaches maths, but it's absolutely great, at least to develop some taste for it.

real nigga

you're fucking retarded

youre so retarded just go to uni

yeah because mathematics is an absolutely discipline with no flaws and absolutely not affected by history

>Fuck off, retard, what do you fucking know? Are you a practicing mathematician, brainlet?
ur a virgin lel

I'll probably just fail every class because my groundwork is terrible. I've never had a good math teacher either, and especially not in uni.
Don't shit on people trying themselves.

Why?

you're a dumbass neet virgin

Through reason
Also be a genius

is me. I think the remedial courses are the best way to go, unless you're willing to put in at least a few hours in a week independently. My undergrad course has 12-17 hours of lectures a week, and students are recommended to work anything from 35 hours a week plus (people tend to do far more).

The issue you will find is that unlike literature there is a huge amount of foundational stuff you must do before you can understand anything advanced at all. The higher thought stuff you're talking about I would imagine he means for research mathematics, which you will never attain unless you do a maths PhD.

That said, it's very much a worthwhile thing to do, and extremely rewarding if you are genuinely into it, but beware of trying to fulfil some kind of glamorous ideal - it's not what maths is about.

If you're interested in abstract stuff try reading up on group theory, graph theory, number theory maybe. It should be relatively straightforward to understand the basics, requires few prerequisites, and it builds up in very interesting ways.

I seriously wouldn't recommend reading historical stuff in order to learn things for the first time. Modern mathematics is very different to when Principia was written. By all means read old stuff out of interest, or to supplement your main studies, but to use 400 year old textbooks as your main source for learning maths does not seem like the best way, to me.

How could I forget - I strongly recommend you get hold of The Princeton Companion to Mathematics. Edited by Gowers with articles from the world's leading mathematicians, the entire first section was specifically written for people with only school and some elementary university maths to understand. It has historical essays and entries on the most cutting edge stuff out there. Seems perfect for you. It's quite expensive but you might find a copy in your library - if you do I recommend just reading through the first few hundred pages of that. Good luck!

I can't do basic common core 9th grade geometry, and I have a deeply ego-damaging emotional response every time I attempt to teach myself even the basics.

I read literature, philosophy, and history in my spare time. Am I emotionally stunted because of my troubles with mathematics during my youth or am I just retarded?

depends

what are your standardized examination scores?

I reccomend

Start with the Neanderthals.

>I am definitely interested in this historical approach. Are there any other works that "hold up"?
On Conoids and Spheroids by Archimedes
On the Measurement of a Circle by Archimedes for the derivation of Pi
On the equilibrium of planes, the quadrature of the parabola and on floating bodies by Archimedes for the foundation of physics and hydrodynamics
The Sand Reckoner by Archimedes for the foundations of Astronomy

I am currently reading On Conics by Apollonius, very rewarding.

And by the way, if you read Euclid's Elements rewarding, you'll enjoy these but all of Archimedes works are a definitive step up from Euclid and reading On Conics is like sticking your head in a blender sometimes. Holy fuck is it intense. Ancient geometry/arithmetic is intense and rewarding.

Nigga doesn't know about my Mesopotamian square.

If you've spent a long time away from mathematics, go to Khan Academy. I am not joking. Start with their basic algebra course and keep advancing. It will help you remember much of the basic mathematics that you've forgotten and give you exercises so you can practice. But since mathematics isn't just number crunching, you could start studying set theory on the side and reading some philosophy of mathematics.

Enderton's book on Set Theory is quite traditional if it's the first time you're tackling the subject. Hrbacek and Jech's 'Introduction to set theory' is also a good introductory test, but when they're proving some stuff they do some jumps that a beginner wouldn't be able to follow, but it is a good text and it covers not only the very basics, but the basics of advanced topics (Large Cardinals, Filters & Ultrafilters, Combinatorial Set Theory etc). In the philosophy of mathematics, I'd strongly recommend reading Imre Lakatos' doctoral thesis called 'Proofs and Refutations'. It is superbly written as a dialogue and it is a very interesting read even if you don't know much about mathematics. I don't think this book is still widely discussed in Academia, but it is a great read nonetheless and it will make you think about the nature of mathematical truth, proof and objects.

Good luck.

Another thing: if you grasp basic set theory (and I don't mean naive set theory) you can venture forth into the realm of discrete mathematics. Graph theory, Combinatorics, Logic and Theoretical Computer Science (Michael Sipser's introduction is a great place to start) are very approachable and known for their recreational effects.

The reading will have to wait for a year, or a half, if you have the touch. First, you need to build the foundation just from definitions, so acquaint yourself with basic stuff like what a set is, operations on them, what is a function, what is a field, and build rational numbers and real numbers - stuff like that. Find a person who will check your proofs. Poke around in different areas that require almost no prior knowledge; right now, try to answer those questions, for example -
1. There are two players and three piles of rocks between them. In one move, a player can take any number of rocks, but only from one pile. The player who takes the last stone from the table wins, players go in order. Whcih configurations of piles lead to which player winning? Develop the winning strategies.
2. You have a looped string with N beads on it. There are three colors at your disposal. How many different strings can you get?

Don't waste your time and energy reading these works if you're interested in mathematics. Do mathematics instead.

>implying those aren't rigorous mathematical proofs

Brainlet detected.

are all of you hobby mathematicians or professional mathematicians?

go to a community college, apply for financial aid for $1 classes, learn as much as you can handle and fully utilize tutors that they have there. Note that this method is exponentially more difficult than self teaching because unlike self teaching you are expected to output particular results.

Physics. What better expression of mathematics than the empirical world?

Learn algebra, and then pick up 'Calculus' by Spivak. He has another book called calculus on manifolds, avoid that. Just get 'Calculus.' It's going to be difficult, but it's very well written and the exercises are a blast. It works it's way up from simple axioms of algebra, which is why a familiarity with algebra is required.

This is not a regular calculus textbook. It's geared towards mathematics, and showing the mathematical beauty underlying calculus. You set out to prove every theorem, and derive it all from the ground up. He really gets into the nuts and bolts of it, it's a beautiful book.

If this is too hard for you. Do Euclid first. That'll get you used to proofs, and get you ready to tackle this book again.

From there you'll know enough math to be able to find good books for whatever else you're interested. I recommend Rubin's analysis, or calculus on manifolds by Spivak. Linear Algebra Done Right is pretty good. Mathematical Tools for physics is a free online book if you want a lot of applied math in an intuitive form.

Each book should take you a good while to get through. Months at first. Don't expect it to be easy. Do all the exercises or you're wasting time.

If you're interested in Math applied to philosophy (this is Veeky Forums, so I suppose that's the case) read More Precisely: The Math you need to do philosophy. Shame It doesn't have exercises, but it's a good introduction.

The Princeton Companion to Mathematics is in Libgen.

Depends what aspect of mathematics you want to learn, and what you even want to do with the information.

Want to grasp the concepts and apply them? Buy textbooks.

Want to truly understand mathematics for yourself and its conception? Read any history and philosophy of mathematics, from the Sumerian system to modern mathematics.

Start with intro logic textbook for math majors.

OP here, thanks for all the tips lads

Will start with "Basic Mathematics", then look into the Spivak book(s).

Also found Princeton Companion to Mathematics on libgen, but I also see that my university has it, so I might borrow it from there instead. Will hold off on historical texts for now, but I will definitely look into it later as I kind of want to understand mathematics as a discipline, not just the nuts and bolts (at least to the extent that is possible).
I will see what my workload is like next semester and if I have the time. I'm doing medicine so my workload is already quite large (and features quite a bit of moving for practical work)

Kahn academy

I thought Basic Mathematics is very good

I'm surprised how little this thread has mentioned proofs. An appreciation of higher level mathematics depends on your ability to understand and develop proofs, and every math student I've met spends at least a semester learning proper proof writing and propositional logic. Studying advanced math is superficial at best if you don't have a good grasp on proofs.

You basically have to resort to textbooks to learn proof-writing (or take a course) unlike the snobby pure math books that people are namedropping here for other "advanced" topics. Here's a link to a relevant thread that might put you in the right direction.

mathoverflow.net/questions/62629/textbook-recommendations-for-undergraduate-proof-writing-class

The fact that there is a proof-writing class makes me sad... That we have managed to dissociate so much proofs from learning calculus and algebra that a separate course is needed is quite a feat in absurdity!

Only buy textbooks from springer

>!

Geometry --> linear algebra --> topology

I understand where that guy's comment is coming from, but I think there's a lot of misunderstanding floating around that leads to some erroneous conclusions.

For one, I don't know of any courses that ONLY focus on proof-writing, there's usually an umbrella intro course that covers a wide range of fundamental topics that focuses on the student creating proofs.

I told some user that I really wanted to learn proofs but was really shit at math and wanted to know where to start. He just said I was a retarded faggot.

"Shit at math" is pretty meaningless because its such a wide field and it's unlikely you're bad across the board.

Also, don't expect to be good or to "get" a lot of this stuff immediately. Struggle is a constant partner and anyone else who says otherwise is full of shit. Math, more than anything else I've studied, has required hours of extra work, reading and playing with concepts. If you're expecting a book or lecturer to give you everything, you're fucked.