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How do I learn math as fast as possible?

Anonymous Sat 13 Jun 17:18:01 2020 No.11793993 View Reply Original Report

Quoted By: >>11794015 >>11794564 >>11794890 >>11798350

I know:
•Differential Calculus (and I understand what integral calculus/the fundamental theorems are)
•Basic Linear Algebra
•Basic Abstract Algebra (mainly group theory)
•A vague idea of what real and complex analysis are
•Everything they taught in high school

I want to learn more but I don't know exactly what to focus on first and cégep (Québec college) is way too slow. Should I use mainly books or the internet? And does anyone have any specific recommendations of fields to study, books to read, or youtube series to watch?

Anonymous

Anonymous Sat 13 Jun 2020 17:21:35 No.11794015 Report

Quoted By: >>11794185

>>11793993
Can you solve basic pdes?

Anonymous

Anonymous Sat 13 Jun 2020 18:13:54 No.11794185 Report

Quoted By: >>11794253 >>11794585

>>11794015
No, so would that be the next logical step? Should I get ahead in calculus before moving to analysis?

Anonymous

Anonymous Sat 13 Jun 2020 18:32:26 No.11794253 Report

Quoted By:

>>11794185
You can do them in either order, but make sure you have the basics understood to the point of intuition before touching topology or algebraic geometry.

Anonymous

Anonymous Sat 13 Jun 2020 19:48:22 No.11794564 Report

Quoted By:

>>11793993
https://4chan-science.fandom.com/wiki/Mathematics

Anonymous

Anonymous Sat 13 Jun 2020 19:55:32 No.11794585 Report

Quoted By: >>11794806

>>11794185
No you fucking retard that isn’t the next step.

Anonymous

Anonymous Sat 13 Jun 2020 21:22:32 No.11794806 Report

Quoted By: >>11794914

>>11794585
I can't quite tell cause I have Asperger's syndrome but I think you're being sarcastic.

Anonymous

Anonymous Sat 13 Jun 2020 21:49:23 No.11794886 Report

Quoted By: >>11794988

It doesn’t really matter what you do next as long as you find it interesting.

What subject did you most enjoy?

Anonymous

Anonymous Sat 13 Jun 2020 21:50:37 No.11794890 Report

Quoted By: >>11794988

>>11793993
bro bro bro,
go to ontario, do 1 more year of high school, then you can come back to quebectabarnak and go to an university

FUCK YOU JANNY

FUCK YOU JANNY Sat 13 Jun 2020 22:00:15 No.11794914 Report

Quoted By: >>11795020

>>11794806
The next step is to learn multivariable calculus and introductory real analysis. An excellent place to start with both would be the second volume of Apostol's Calculus or the Hubbard and Hubbard Vector Calc text, and for Analysis either Principles of Mathematical Analysis by Rudin or Tao's Intro to Analysis Vol I. You cannot and should not jump into diff eq if you don't know linear algebra or multivariable calculus especially not PDE's.

Anonymous

Anonymous Sat 13 Jun 2020 22:28:30 No.11794988 Report

Quoted By: >>11796905

>>11794886
I find abstract algebra and related fields very fun to learn about because it really feels like I'm discovering something new and not just the same old stuff that gets reiterated with incremental advancements in high school. My issue is that wikipedia has its limits as an educational resource. I also want to make sure that I cover all the bases for a career in math or involving math.

>>11794890
Too late, already done my first year of cégep, no point. Hopefully next year goes as well or better and I can get into Waterloo or McGill. Sucks that the Euclid contest was cancelled but I did all the others in high school and came 1st in the school in grade 10 and 11 and I think I'll be able to do the Euclid next year.

Anonymous

Anonymous Sat 13 Jun 2020 22:38:39 No.11795020 Report

Quoted By: >>11795039

>>11794914
Thank you for the explanation! I would've assumed that I could go straight into learning differential equations after calculus. I was going through the beginning of a book about it during my time at the library before the lockdown (I stupidly never took it out) and I kind of understood the beginning but looking back I was missing a lot of prerequisites and I didn't know why it seemed like such a jump. Do you think that this textbook [https://open.umn.edu/opentextbooks/textbooks/multivariable-calculus] would be adequate for multivariable (also including vector) calculus, or is there some reason to buy the non-free stuff? Sadly my school's library's math books are mostly very, very basic calculus, and then random stuff like Bessel functions with no in between. (That one was even more challenging to digest than the diff eq one and I only got through a few pages before getting to the point where I just didn't even understand what was being said.)

Anonymous

Anonymous Sat 13 Jun 2020 22:44:43 No.11795039 Report

Quoted By: >>11795115

>>11795020
That textbook looks fine, its a little light on the kind of rigor you might be hoping for, I didn't see really any proofs in the exercises but you wouldn't be missing out on any of the essential computational aspects. If you did not know already you can use libgen.is to acquire pretty much any modern math or science textbook. You really want to have a solid background in lin alg before you jump into diff eq, but wouldn't necessarily need multi. If you do want more formalized content to work with I would highly recommend looking into something like Shifrin's Multivariable Mathematics or Apostol/Courant's books on multi (especially if you are already familiar with abstract algebra, which I presume implies you are comfortable with proofs).

Anonymous

Anonymous Sat 13 Jun 2020 23:12:15 No.11795115 Report

Quoted By: >>11798366

>>11795039
I'm very comfortable with proofs and want stuff as formalized as possible. Is it safe to use libgen though? I'm aware that the website breaks the law, but I mean, am I likely to get viruses? I presume that a PDF file wouldn't contain a virus but I'm just trying to be safe.

Anonymous

Anonymous Sun 14 Jun 2020 12:13:31 No.11796905 Report

Quoted By: >>11797612

>>11794988

Well, if you want something completely new you might like to try some topology.

Some people may say that you need to have some real analysis under your belt first but I don’t think it is necessary to do things in that order (a large part of real analysis is understanding the topology of the reals anyway, and it can be nice to ‘build up to it’ from point set topology rather than ‘down onto it’ from the function based perspective of real analysis textbooks).

I would highly recommend Munkres textbook, simply called ‘Topology’. It has essentially no prerequisites, starting from logic and sets and from there into topologies, continuity, compactness, and all the weird and wonderful spaces in the topological zoo (long line! Hawaiian earring! etc., etc.)

Anonymous

Anonymous Sun 14 Jun 2020 16:40:45 No.11797612 Report

Quoted By: >>11797986 >>11798006

>>11796905
I've looked into topology, that's another field that I find has the same appeal as abstract algebra but forgot to mention cause I haven't really learnt in depth at all about it yet. (Don't worry, I don't mean I'm just one of those doughnut-coffeecup people who thinks they know what topology is cause they saw one example of a homeomorphism.)

Also don't lie groups sort of connect manifolds and group theory if I understood what they are correctly? That's a part of math that I find very interesting, like the stuff where you see space/geometry arise out of a bunch of abstractions. My understanding of math kind of reached a milestone when I saw how space could be conceptualized in a way that made no reference to the universe.

Anonymous

Anonymous Sun 14 Jun 2020 18:22:43 No.11797986 Report

Quoted By: >>11798233

>>11797612

>(Don't worry, I don't mean I'm just one of those doughnut-coffeecup people who thinks they know what topology is cause they saw one example of a homeomorphism.)

I would caution against this style of thought: not a single person has been born into this world knowing the definition of a homeomorphism. There is no shame is not knowing something! Motivation has to come from somewhere, and the coffee cup-doughnut is certainly provocative: it asks, without distance, without shape, what can be said about space and geometry?

Related to the above...

> the stuff where you see space/geometry arise out of a bunch of abstractions.

I would argue this is backwards: it is not space and geometry which arose from the abstractions, but the it was the abstractions that arose from the space and geometry! The questions of topology, the sense of the subject, came many years before the definition of a topological space. Likewise with groups: it is only after experimenting with different concepts that one sees, ah, this one captures the essence. I can this no better than Arnold:

"What is a group? Algebraists teach that this is supposedly a set with two operations that satisfy a load of easily-forgettable axioms. This definition provokes a natural protest: why would any sensible person need such pairs of operations?

We get a totally different situation if we start off not with the group but with the concept of a transformation (a one-to-one mapping of a set onto itself) as it was historically. A collection of transformations of a set is called a group if along with any two transformations it contains the result of their consecutive application and an inverse transformation along with every transformation.

This is all the definition there is. The so-called "axioms" are in fact just (obvious) properties of groups of transformations. What axiomatisators call "abstract groups" are just groups of transformations of various sets considered up to isomorphism"

Anonymous

Anonymous Sun 14 Jun 2020 18:28:23 No.11798006 Report

Quoted By:

>>11797612

To answer your question: yes, Lie groups are objects which are simultaneously manifolds and groups; they are used to describe continuous symmetries of spaces.

Anonymous

Anonymous Sun 14 Jun 2020 19:28:40 No.11798233 Report

Quoted By:

>>11797986
The doughnut-coffeecup remark was actually kind of repressed feelings of inadequacy on my part, I'm so inundated with pop-math on the internet that sometimes I feel like I have only superficial knowledge and so felt the need to reaffirm (for my own psychological well-being) that I have made efforts to go beyond that. You make entirely valid points.

Anonymous

Anonymous Sun 14 Jun 2020 20:00:54 No.11798350 Report

Quoted By:

>>11793993
read a book on an airplane

Anonymous

Anonymous Sun 14 Jun 2020 20:06:14 No.11798366 Report

Quoted By: >>11798448

>>11795115
>PDF file wouldn't contain a virus
https://en.wikipedia.org/wiki/PDF#Viruses_and_exploits

Anonymous

Anonymous Sun 14 Jun 2020 20:31:14 No.11798448 Report

Quoted By:

>>11798366
Thank you, I wouldn't've guessed that was at all possible.

Anonymous

Anonymous Sun 14 Jun 2020 21:54:12 No.11798718 Report

Quoted By:

>all of these HORRIBLE answers
Download ACT practice apps. Do them. You'll quickly see where your holes are. I retook the ACT at 25/26 years old and was scoring 25/26 on the test as well. I *casually* studied for 3 or 4 months and took the official ACT at a local high school and got 31.

Anonymous

Anonymous Mon 15 Jun 2020 12:32:13 No.11800818 Report

Quoted By: >>11801156

Not OP

I want to teach myself calculus, The books I'm eyeing are "A First Course in Calculus" by Serge Lang and "Calculus" by Michael Spivak.

By the looks of it, this is going to be time consuming either way.. the Lang book looks much easier.. I haven't done math since high school and am in my mid 20s.

So should I read Lang first and then Spivak or is this a massive waste of time? Spivak's focus on proving everything puts me off, I'm not sure I'm up to it.

Any other suggestions for books would be appreciated.

Anonymous

Anonymous Mon 15 Jun 2020 15:26:23 No.11801156 Report

Quoted By:

>>11800818
You'll regret it later if you don't learn a certain level of formality. Calculus formality may be unintuitive, but it relates to other fields of math that actually underpin calculus.

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