Why is linear algebra so fucked? I set the curve in calc 2. I

>>8317101
>american """education"""

>I set the curve in calc 2. I thought I was smart.
>calc 2
>smart
>i

oh I'm laughing

I found calc 2 hard
see:
http://www.rug.nl/ocasys/frw/vak/show?code=WPMA13001
and im not american

>>8317113
a lot of people on here say calc 2 is hard??? so i thought at least I could pass linear

>>8317101
>What does inductive reasoning mean???
What the fuck is wrong with your math education if you haven't learned that yet?

Inductive reasoning works like this:
>have a claim that is somehow related to natural numbers
>show it is true for some natural number
>show that if it is true for some n, then it is true for n+1, when n is atleast the number it was already shown to be true for

I'll give you an example. The sum of n first positive integers is n(n+1)/2.

>the base step
If n=1, then n(n+1)/2=1*2/2=1, just as the "sum" should be.

>the inductive step
Suppose the sum of n first positive integers is n(n+1)/2. Then the sum of n+1 first is n(n+1)/2 +n+1=(n^2+n)/2 +(2n+2)/2=(n^2 +3n +2)/2=(n+1)(n+2)/2=k(k+1)/2 with k=n+1, like we wanted it to be.

Since we have one example of the claim to be true (n = 1), and we know that it being true for some n atleast 1 implies it being true for n+1, we can then conclude it is true for every n atleast 1.

That's inductive reasoning.

>>8317101
>How can I get good at proofs?

By doing them. Doesn't your major have a freshman course that quickly teaches set theory, number theory, algebra (abstract), logic and proofs so that everyone can handle the courses of actual math?

>What does inductive reasoning mean???

It is called pretending that you know more than you know because you know just enough to pretend like you know more.

In many systems induction is an axiom and given that linear algebra stands on top of set theory, arithmethic and algebra I would say that if you look deep enough you will find that axiom but it doesn't really matter, induction is supposed to apparent.

Suppose you have a list L of n objects, which means you have at least an object number 1 and an object number n, but you also have everything in between. Also, in this set you have a relation called the sucessor function that maps an element of L to another element of L that is supposedly the one next to it.

Now imagine you have a property, lets call it P(x)

Now imagine you have another set S so that every element of S is an element of L that has the property P(x)

When doing induction you first want to prove that S is nonempty so in your example the author proves that S contains at least the case for n=1

Now if you can prove that for every element of S, its sucessor is also in S then that is enough to know that every element of L is in S.

You just do lots of proofs until you get good at them. They all come down to connecting intuition with rigorous logic, and that's something you can train.

>>8317101
Welcome to math, son.

>>8317118
>a lot of people on here say calc 2 is hard
A bunch of fucking biologists maybe. That or some high schoolers. Calculus is all about bashing your head against practice problems. Just repeat the same strategies on the test and, congratulations, you got an A.

In later courses, where the petty computations are really only there to waste time or are completely nonexistent, you actually have to think about how you'll approach the problem.

>>8317101
>not just proving this as a special case of the structure theorem for finitely generated modules over a principal ideal domain

do you even math?

>>8317101
algebra is easier than you think. In most cases you just try to see reasons where there aren't any. In algebra you state simple rule which are absolute and based on them you make other predictions. Most common question is: "why we introduce some rules". Answer is simple enough - we observe some behavior from MORE complicated objects than simple numbers (like matrices) and we want to find patterns in their behavior. Why? Because it speeds up calculations. It's like looking from a higher point of view at fighting armies rather than analyzing every single soldier.

>>8318373
This is the typical myopic mathematician view of calculus 2. There are a lot of interesting and translatable strategies in problem solving that you could have acquired in cal 2, but instead you were just a typical algorithm memorizing monkey just like those 'fucking biologists' you hate.