P R O O F S

I think we can all agree that - at least at shit-tier schools - the focus of teaching mathematics is almost exclusively computational at the early stages.

Myself, having to hold a job on the side... I tend to focus on mastering the computational side ( to get those A's) before worrying about proofs and 'why?'

So Veeky Forums, my question is, how doomed are computationally taught students at upper-division mathematics? Those that have been there, how did you fare? Was your upbringing computational or based in proofs? Any advice?

my school is aware of this and has an "introductory proofs" class to bridge the gap

im sure a lot of other ones also do

get spivak and bang your head on it for a month

>Spivak
>good proof writing
lel no

Anyone who is meant to be successful in mathematics will be capable of teaching themselves.

i have really struggled with whether and how to respond to this. The execution of this message was very nice and respectful, and I genuinely appreciate that. The premise, however, is problematic. Maybe not inherently, but within the context of the sexist society we live in. Men are allowed, and often feel compelled, to think out loud at women, to share unsolicited not necessarily informed thoughts at women. (And usually these men, unlike you, don’t even seem to recognize that their thoughts may not be useful.) Women on the other hand aren’t allowed to be as open. So, if you want to not just be respectful, but actually be anti-oppression, it is better (IMO) not to respond to a woman’s work with the types of thoughts that other men pawn off as insights, if you know what i mean. again, i appreciate your honesty, but i feel obligated to point these things out.

what the fuck are you talking about

10/10 post

i have really struggled with whether and how to respond to this. The execution of this message was very nice and respectful, and I genuinely appreciate that. The premise, however, is problematic. Maybe not inherently, but within the context of the sexist society we live in. Men are allowed, and often feel compelled, to think out loud at women, to share unsolicited not necessarily informed thoughts at women. (And usually these men, unlike you, don’t even seem to recognize that their thoughts may not be useful.) Women on the other hand aren’t allowed to be as open. So, if you want to not just be respectful, but actually be anti-oppression, it is better (IMO) not to respond to a woman’s work with the types of thoughts that other men pawn off as insights, if you know what i mean. again, i appreciate your honesty, but i feel obligated to point these things out.

Not necessary, just pick up Lang's algebra book.

...

You're not necessarily doomed, it's just different. Everyone, even those who only did proofs at university, spent years doing computation first.

Don't focus on memorizing things. In computation courses, you're expected to know techniques for solving specific "cookbook" problems. That's not going to work anymore. Spend all of your effort trying to understand the theory. Don't allow yourself to not understand something, it's easy to get away with this in a computation course, but it won't work in a proof-based course.

You learn the proofs behind grade school algebra in number theory and abstract algebra.
You learn the proofs behind calculus in real analysis.

I have always been terrible at raw computation. I fucked up baby number theory because I just can't compute shit; but proofs and theory are much easier for me.

thats because most useful (in everyday situations, mod mathematicians who do math as a day job) math is computational in nature

>I have always been terrible at raw computation. I fucked up baby number theory because I just can't compute shit; but proofs and theory are much easier for me.
well that either means you're really smart or introductory proofs are really easy

which one is more likely?

>how doomed are computationally taught students at upper-division mathematics?
Completely to be honest, at least if they don't try hard and learn to prove things.

>Was your upbringing computational or based in proofs?
At my university first year mathematics is purely proofs. You have classes in both Linear algebra and calculus.
In calculus we started with set theory and metric spaces, then moved on to the natural numbers, rational, real (by completion of metric spaces) and complex and then convergence. (1.Semester)
Homework sheets consisted usually of 3 Problems about proofs and 1 Problem about calculation (e.g. evaluating a limit. or similar)

All of this was completely new, previously school was purely about computation and learning how to prove things was the central part of the first 2 semesters.

Oh god, it's spreading.

weak pasta

You must be over 18 to post here.
Also, u wont ever be good at proof if you're not at calculation. Anyone pretending the crontrary is straightforwardly lying to you.

buddy I wish I was 18 again.

I'd KILL for that, tbqh.

legt usefull
as for my own experience, i note two important criteria to smoothen the transitions:
1. repetitions of the exercises to the point of tedium
my mind slowly realized the context of when to apply a theory, which is what made it "obvious" when i was in uni. Different ppl need differing levels of repetition over different function families, fields, sets, ets... but bottom line is the proffessor. Personally i feel like a lot of high school hasle in algebra could be cut significantly if the concepts were phrased in a different way, accelerating learning. Remember, kids dont entirely know what they dont understand.
2. Modules & Interfaces- learning the concept in a compsci class, they become so easily generalized and applicable to anything. Soon it's just a question of which layer of abstraction you choose to work with. Choosing the right layer is an art.