Alright fags, I'm learning math on my own -- for fun. I'm

Let me explain better. If you were designing a bachelors to grad level program of pure math from the ground up, which classes would you require and in what order?

just watch anime instead
math is useless

Let me ask you this: What comes after 1?

>>7960082
Basically how it's done, fag. Just follow MIT OCW or something.

Combinatorial problem and exercise by lovazs.
There is nothing more important than learning how to solve problems in math

Go through calc 1 and calc 2 for a safe ground. With multivariable calc many people take linear algebra and vector geometry along side it. After calc 2 really you can jump into real analysis or diffeq with whatever time you have. Obviously things like upper level diffeq or real analysis, or vector calculus should be taken later. That should be a few years of studying there probably if you really want a full understanding of each course.

>>7960085
1.01

>>7960079
Linear Algebra using a book like Strang. I'm assuming by calc 1 you mean all of single variable calculus. You could also go on to multivariable after single variable.

>>7960091
Thank you

>>7960097
fuck you

>>7960094
That's correct. Thanks.

>>7960098
That escalated quickly. Worth it tho for the few anons who do post solid answers.

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>lectures feel too slow paced for me
>not in a I'm smart sense, but in a I can read faster than listen to some guy talk sense and it's faster to look at already done diagrams and professional examples
>tfw

Anyone else know this feel? I hate going to lectures.

>>7960092
1.0...1

>>7960292
>1 comes after 1

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>>7960124

>mfw my uni records my lectures and posts the vids on the internet
>mfw download them and play them at 1.25x speed, pausing to take notes whenever I want

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>>7960378
>mfw taking mechanical engineering online
>mfw I get to do this with all of my classes

>>7960385
which online college?

>>7960385
University of North Dakota has an online engineering program. You have to go there for 2 weeks in the summers for the labs, though.

>>7960428
was meant to reply to >>7960424

Study a shitload of algebra, first some group theory, then ring theory/commutative algebra. Alternatively algebra and topology, and then algebraic topology and homological algebra. And, naturally, watch animu

bump

try and teach yourself the math that high school teaches in the same order, then look for a course outline of a bachelors in math and copy that

>>7960079
go for linear algebra and calculus 2. maybe some computer aided problemsolving?

>>7960079
NUMERICAL METHODS

>>7960292
That's not even a proper number you fucking mong.

>>7960083
>math is useless^(-1)
fixed

>>7961673
Then how about 1 + dx ?

>>7960079
here are topics I would teach for an undergrad curriculum in order:

calculus and real numbers - why completeness is key property, convergence and limits, continuity, riemann integral, differentiation, fundamental theorem of calculus, approximation of continuous functions by polynomials

algebra - intro to groups focusing on examples (finite groups, linear operators), first isomorphism theorem

linear algebra - finite dimensional vector spaces, linear operators as matrices, intro to spectra (eigenvalues)

topology - definitions and examples of topologies, continuity, compactness and quotient spaces, Urysohn's lemma

functional analysis - convergence and completeness in function spaces, Lebesgue integrable function as Cauchy sequence of Riemann integrable functions, linear operators on function spaces, compact operators, intro to spectra

algebra - intro to group representations and characters

algebra - rings. ideals, and factorization, basic number theory, exact sequences and commutative diagrams

babby differential geometry - multivariable calculus, differential forms, stoke's theorem

algebraic topology - fundamental group and covering spaces

babby homo algebra - definitions and examples of functors

algebraic topology - simplicial and singular homology

babby commutative algebra and geometry - basis theorem, nullstellensatz, ideal-variety correspondence

complex analysis - holomorphic functions

algebra - fields, galois theory

optional topics:
differential equations, basic logic (propositional and predicate calculus, completeness / incompleteness), set theory

---------

This is probably enough math to get you into grad school if you're good at it.

>find a bachelor that would interest you
>look up the plan/syllabus on a university
>download/buy books and self-study
>look up problem sets and exams in said university
wow that was hard

my path:
>Calculus
>differential equations
>numerical methods
>multivariable calculus
>linear algebra

>>7961780
Rigorous calculus is for faggots, It was never rigorous until fairly recently (150 years ago) despite being over 300 years old. It doesn't need to be introduced rigorously, it's a method, not a foundation of mathematics.

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>>7961800
Well, enjoy manipulating symbols and crunching numbers without understanding, which is pretty much all the calculus they teach you in high school is. What's the point of memorizing all those integrals and integration techniques when wolfram alpha can do it for you these days.

If it's utility you're after, numerical methods is way more useful than "non-rigorous" calculus. But OP asked for how to go about learning pure math.

>>7960079
Discrete Math (inductions proofs, combinatorics, graphs, modular arithmetic)

Linear Algebra and Probability would be good too. You need to know single and double integration for probability.

>>7961716
I can't remember the name, but there is a theorem that states that between every two real a, b such that a < b there is a rational c that satisfies a < c < b. It can be proved pretty easily once you prove that the floor function is defined for all real numbers.

So you can see it just matters on your definition of "1.00...1". If you define it as a number that is infinitely close to 1 but still not equal to it, you can just set a = 1, b = 1.00...01 and find a new c to suit your definition. It can't therefore be constant and it follows that 1.00..001 is not a real number.

It's mostly just semantics, really.

>>7961673
>the reals are the only number system imaginable

>>7961812
>numerical methods is way more useful than "non-rigorous" calculus.
Mediocre bait

Hey /sci/, please give your advice regarding my shitty /lit/ thread and call me a dilettante retard:
>>>/lit/7858537

Posting ITT to avoid shitposting a new thread here. I want my self-education to have rigour and not just "math is like, the language of reality, man" shit, like I'm already beeing accused of in the thread.

>>7961782
Aware of this technique obviously but that's implying universities have it right. I wanted the opinions of other senpais, hence my thread.

>>7960378
That's awesome

>>7960082
This information is already readily available. Just look at the pure maths program of any decent university.