/sci/ - Science & Math

>>11718940
step 1 don't ask for advice.
step 2 solve any type of problem on your own.
step 3 profit?

>>11718961
the books i'm reading right now have like 15 exercises per chapter, that's too little for my taste, i remember when i was studying math in college they gave us a shitton of exercises every week for all courses.
i can get the books from libgen, i can get the lectures from the MIT page, but where do i look for more exercises/problems/tests ?

>>11718940
>i

>>11720763
not sure if obvious, but I'm not a native english speaker.
Im not even sure whether you guys capitalize the first letter on a sentence
also >thread

>>11719073
Shuams...

>>11718940
>best strategy to become a homemade mathematician
You can't become a homemade mathematician. You can become learned as a self studying student in math, but being a mathematician is an activity that requires actual communication and acceptance from the community. That's associated with higher education and publishing with a center or university backing you on good faith.
Anyway, the picture you posted is bad. You do calculation problems first to gain some intuition about the structure's 'casual behavior' and then formalize with rigor afterward. This is why almost everyone does calculus before introducing proofs. The books in the study guide you posted are neat, and some of them good, but presented in this manner they are wildly disorganized, repeat a lot of the same information, and underprepare you if they're supposed to be some "primer of undergrad math."

>>11718940
>>11723900
Augmenting to this, I'll give my own list in sequential order. Everything I list within a subcategory can be studied concurrently or relatively quick succession. I assume you know middle school algebra and some basic trig.
Introductory exercises, use khan academy and MIT OCW
>Calc 1-2, vector calculus from your favorite intro calc book. Rogawski's early transcendentals is standard and pretty good.
>Basic matrix arithmetic.
>ODE's and PDE"s.
Transitioning into proof mathematics. MIT OCW and webpages are your best friend
>Book of proof
>How to solve it
>as much Concrete Mathematics by Knuth you can do. His explanation of techniques is really nice.
>proof based linear algebra text
Core
>Abbott's Understanding Analysis up to differentiation theory. Then switch to baby Rudin, do up to integration theory.
>Algebra by Artin or Dummit+Foote, do group theory, symmetry and isometry, group actoins, and linear representation
>Topology either by Munkres or Willard, do at least up to metrization.
>Lovasz, combinatorics
Core pt. 2
>Folland or papa Rudin for measure theory, integration theory, exact forms, etc
>Artin and D+F again for ring theory, number fields, field theory, and galois theory

I've left out topics like logic, graph theory, number theory, etc., which are also great, but you can get into them after or during the core, which will give you enough maturity and experience to go through anything else in the canon.

>>11723900
>You do calculation problems first to gain some intuition about the structure's 'casual behavior' and then formalize with rigor afterward.
How horrifying. I find the exact opposite approach works.

>>11723974
Imagine using TWO books for proofs.

NGMI.

>>11723988
French math is a mental illness.

>>11723995
>Imagine using TWO books for proofs.
???
Book of proof is a primer to proofwriting.
How to solve it is an informal text about how to start tackling problems and general approaches as a novice.
Concrete mathematics is a repository of really good problems (especially in its analysis chapters) that are connected by ways to intuit form.
Linear algebra is linear algebra.

Exactly what two books are 'for proofs?' Furthermore, why take issue with these two when the list OP posted has 2 core intro to proofs books before and AFTER basic analysis, as well as 2 supplemental books?

>>11723988
What's funny is that the process of going from intuition -> rigor is the natural progression of creating new mathematics. People use rigor to help check their intuition - mathematics is not the rigor itself.

>>11723974
not OP, but thanks for the suggestion on Rogawskis early transcendentals, looks like a good book :)

>>11718940
>analysis before basic mathematic

Holy fuck I can't handle the autism

>>11724252
yes almost every picture list of books to read on this site is bad. The CS lists are similarly bad.

>>11718940
I'm a brainlet but no lol, it's bad
Analysis before Basic
Analysis before Calc even (while the books suggested will construct the reals as well anyway)
Just take any precalc, Spivak and a Linear Algebra book

>>11718940
>i don't want to be a brainlet anymore, what is the best strategy to become a homemade mathematician?

>>11724060
>>11723988
I doubt that. Having some intuition is just so useful, and it's just how people learn in general.

I don't know though. My first approach to Linear Algebra, for example, was pretty much axiomatic, starting with vector spaces, and it was ok. But I think there's something to fucking around with arrows on r2/r3 and transformations on those spaces

>>11724732
it's possible with a semester of linear since the objects are well behaved to follow nothing but rigor. A lot of what you see in, say, analysis, will be intuition followed by "how do I translate my hunches into actual solutions to problems?"

>>11719073
exercises are only good if you know the practice is actually helping u

theres no point in repeating the same exercise over and over you arent trying to win a maths competition

bumpa

By reading math books you're robbing yourself of the joy of discovering it on your own :)

>>11727486
The answer is already here >>11723974
>>11727591
reinventing the wheel isn't productive, interesting, or intelligent use of someone's time. You might you're clever for half-assedly reproving a lemma or two here, but you're really not lmao

>>11727602
>reinventing the wheel isn't productive
wrong
>interesting
it is
>intelligent use of someone's time
it is.
You know not that of which you talk about.

>>11727615
>You know not that of which you talk about.
This is ironic, coming from someone advocating to reproduce centuries of work to get anywhere. It also ignores that most of the time, you can figure out the basic and intermediate results for yourself by doing close reading instead of sitting in a vacuum and "rediscovering mathematics bro."
>wrong
it legitimately isn't. Also, rebasing the foundations isn't the same as reinventing the wheel, so no you don't get any points for your esoteric foundation of mathematics using a new structure BasedAndRedpilledSets.

>>11727627
You are at best a third rate mathematician. Your opinion is irrelevant.

>>11718940

>>11727627
you must have a lot of time to devote to solving big boy problems since you're not wasting many years relearning centuries worth of foundations and building blocks. what are you working on?

>>11728172
>what are you working on?
Open problems in analysis, given it's my research area :)

>>11718940
bump