Help a fellow out mates. > first year of college > calculus

Deduzco que eres español. En qué uni estudias? Igual esta web te ayuda pero no se si es que estás buscando https://betterexplained.com/cheatsheet/

You literally just write the definitions down and let the autistic connections in your brain do the work.

>>8436992
I'm guessing you're talking about epsilon delta proofs if you're in calc 1, and you don't really need to worry all that much about them, desu.

The material can be presented in a way that goes above your average calc 1 students ability, but all you need to do is memorize the the format. Work on replicating it over and over until you can do it by memory then try to focus on actually understanding it.

Any other proof presented in the book arent necessarily meant for you to understand (and indeed, a lot of the proofs of calc 1 material can't be understood with such a rudimentary knowledge of the subject), they're just showing you a basic idea of why you're doing it that way.

>>8437000
I'm actually Italian, the pura mierda was just thrown out there, I believe everyone can understand it by now.

The link seems interesting, so thanks for that, but it's not exactly related to proofs in the strict sense. I'm looking for something more focused on the actual process of demonstration and how to go about it.

I was lucky I guess. AP geometry teacher assigned a proof pretty much every night.

A proof is just a way of showing how you actually arrive at the anwer for a mathematical operation that you might take for granted.

It's kind of like lawyering. You want to be able to deconstruct the argument being posed by the equation or whatever that you're trying to prove and examine it for veracity.

Just work more of them, and read book examples of them. Really. It's just a skill. Git gud by doing.

If you work through a proof based textbook, you just kind of absorb the proof techniques. You'll see a problem later in the book and just kind of instinctively know "ah yes I know what to do here". It's very autistic, and I don't mean that in a demeaning way.

I'm guessing that there are categories and names for different proving techniques, but I'm not familiar with any of them.

>>8437016
I remember when talking the MIT's ope course the proofs were kind of hard to grasp, specially the geometrical proofs

>>8437015
>I'm guessing you're talking about epsilon delta proofs if you're in calc 1

Don't be too quick to judge. Back in my calc I days we proved elementary theorems like the addition of two even functions yields an even function, prove that a limit is unique, if a function is continuous at a point then the function evaluated at that point exists, etc.

OP, give us an example of a proof you are struggling with? Calculus proofs are usually very intuitive (just see for example how obvious the theorems I listed are) so all you really need to do is to formalize your intuition by quoting definitions and applying previous knowledge.

>>8437028
>>8436992

Meant to also you, OP.

>>8437006
I'm sorry to break it to you but not everyone has those. Wish I did though.

>>8437015
I partly understand what you are saying, but then again sometimes it just doesn't work like that. Let's use an example why don't we. A technique I've seen used rather often is to add and subtract a certain value, and that magically made it all work out. Now that's piss easy to understand when you see it done, but if I had had to do it in the first place I would literally never have thought about that. That's the kind of thing I'm talking about: I need to learn to "see" when some things that are rather basic by themselves can be applied.

I know it's not strictly necessary for me to become a mathematical mastermind while I learn calculus I, but I'm actually doing it more for myself than for the exam. I'd like to feel comfortable around any mathematical problem, provided I know the topic.

>>8436992
I didn't even have math in HS and am doing well with Real Analysis I which is the first time I've encountered proofs.

Kys brainlet.

>>8437031
You're going to need to get autistic in a hurry if you're majoring in a field that requires calc.

>>8437042
Everyone has math in HS you stupid fuck. KYS faggot. You're a meme

>>8436992
>This is the thing. I have never ever done anything even remotely proof-like before

Don't worry, most people have this experience.

>How do I learn to do proofs

You read a book on proofs (http://www.people.vcu.edu/~rhammack/BookOfProof/) then practice. Most early proofs can be solved with just unpacking the definition of what you're starting with and what you're trying to end up with and meeting in the middle. Then you reorder the mess so it flows from beginning to end.

File: 20161025_232608.jpg (590KB, 2048x1152px) Image search: [Google]

590KB, 2048x1152px

>>8437028
Yeah my professor is actually kinda crazy about it. Even though it's a course for an engineering degree (where proofs and rigour generally get less attention, at least where I live) we prove literally every theorem we stumble upon.

And as I said it's not the proofs of theorems that I have problems with, at least in general. I just look at what the professor does and if a similar proof is left as an exercise usually all you need to do is change some symbols. Some exercises though require proofs for more sophisticated things. I'll try to translate a simple one (that I have no idea how to do anyway) from a list we were given yesterday.
"Prove that the sum of the first n cubes is equal to (the sum of the first n numbers) squared".
Hoping this makes sense, anyway assuming I did it correctly basically prove pic related.

>>8437068
You could try proof by induction on that.
It's a useful technique.
Read a book on proofs and logic.

>>8437072
Jesus fucking Christ.
Of course that's induction.
But see what I mean? Now that you told me is bright as the sun, but otherwise it would have taken me ages. Do I just have to sit through all proofs the professor does and absorb his method then?

>>8437079
>Do I just have to sit through all proofs the professor does and absorb his method then?

Not really. You just need to know your toolbox. There are 3 usual methods for proof: Direct, contradiction and induction.

You must first try to prove this directly. Look at the previous theorems for sums you have and see if you can use them to reach your conclusion.

There actually is a way to do this. Odds are you proved that the formula for the sum of n is n(n+1)/2

You probably also proved that the formula for the sum of the n cubed is ((n(n+1))^2)/4

From that you could do some clever rearrangement of the exponents to prove you statement.

But lets assume you do not have these previous theorems, you only have the definition of sum.

Try now by contradiction. Suppose that this is not the case.

Well, here there are infinitely many other possibilities. The sum could be n^2, or 3n or 50 and even though you can prove that all of these cases are wrong, there are infinitely many other cases.

You can't prove infinitely many things m8, so contradiction just can't be it today.

Now by induction.

Do the base case for n=1

Hey, this seems to be getting me somewhere...

and so you keep going.

That is the reasoning you have to go. Try everything and see where and how things click and then follow the logic.

>>8437086
>There actually is a way to do this. Odds are you proved that the formula for the sum of n is n(n+1)/2
>
>You probably also proved that the formula for the sum of the n cubed is ((n(n+1))^2)/4

If you know these two the proof is trivial.

>>8437092
>If you know these two the proof is trivial.

Yeah, but it is a way to prove it directly if you have that previous knowledge.

You don't always have to tackle a theorem by itself and in higher maths this is most of the times itself. You don't prove your statement, you see how your statement relates to simpler statements and these use the truth of the simpler statements to assert the truth of a new, more complex statement.

>>8437096
I'm not OP, but I agree with you, the direct proof is the best methods if you know the sum of the series.

>>8437045
I'm exaggerating, I went the vocational way during HS and there's barely any math. And also since class was full of retards like all vocational courses the teachers also made it even easier so they could pass the exams.

So yeah I had basically no math in Highschool, umad brainlet?

>>8437102
Since my thread is actually turning out pretty well I'd beg you to bring your braggy shitposting somewhere else, thank you.

>>8437086
Thanks a lot for being exhaustive. I'll try to keep those in mind next time.

>>8437106
I'm sorry faggot. Perhaps post your retardation inside Stupid Questions Thread next time instead of polluting this board with more retarded shit.

You won't learn anything from this shitty thread, go grab a textbook you lazy fuck and stop deceiving yourself and procrastinating actual study.

>>8437068
This is really just a coincidence equality. What you should do is find out what ∑n is and then square it and find out what ∑n^3 is and notice that they are equal.

Protip: ∑n^p is a polynomial of degree p+1. Find the coefficients and then prove your result with induction.

>>8437031
You should focus on learning derivatives, infinite limits, basic integrals, and derivative applications rather than proofs that will be covered in another course.

The biggest take away from calc 1 should be a thorough conceptual understanding of the derivative and mastery of algebraic manipulation. You're cheating yourself if you don't achieve this because you're wasting time on proofs and you'll be punished severely in calc 2, 3

>>8437125
You only need to know the sum of the first n to prove the equality by induction.

>>8437138
Thing is, because my degree is in the engineering department they are actually quite unlikely to be covered in other courses. At least, I don't see any in the lists that would make you think that they teach proofs there. So I fear that if I don't understand them know they will be lost forever and I will be forced to learn math mnemonically like any (other) retard. I don't want to be like other retards, I want to be a special retard.

>>8437068
The sum shouldn't be from 0 to infinite. Don't ever do that mistake again

>>8437169
In engineering school, you won't have time for niceities like proofs. Or personal hygiene. Or sleep. Wouldn't worry much about proofs. Unless you're planning on going to grad school, you won't have to do more than a couple handfuls between now and graduation.

>>8437021
>ap geometry

>>8437372
That's bullshit, I'm studying engineering and every important result is proven. Hell, some teachers squeeze in topology, Frechet derivative and other things in the Multivariable calculus course

>>8437430
Yes. Profs write proofs. Engineering students generally aren't asked to because they're too busy doing grunt work. I wrote more proofs in 1 yr of HS geometry than I did in all of undergrad.

>>8437503
But... I want to git gud. Plus yeah I'm planning on going to gradschool, there's not really many jobs you can get with a degree in Engineering Physics only.
> inb4 le eng phys meme ayyyyyy
I know, I know.

>>8437169
>>8437372
I'm in EE and have taken discrete math and complex analysis. I didn't have to, and the other route was only 1 class less, but a lot of students did the same as me.

Discrete math is kind of like an intro to writing proofs. I've heard of it being a freshman class, but at my school its second semester sophomore (generally). Calc 3 is prerequisite.

Complex analysis I took junior year and the prerequisite was discrete (and thus calc 3 as well)

>>8437884
Nobody's stopping you, then. Way to git gud is do moar.

>>8437901
EE and you ddin't have complex analysis (even a baby course) required?

>>8438028
They have a simplified, condensed version of elementary complex analysis baked into the math for scientists and engineers 1&2 class