Throw in vector analysis and complex analysis, right around the time you study differential equations.
You should also probably get probability theory.
Spoiler
Get it? Probably get probability theory? GET IT?
And idk about your case, but I thought Fourier series was already included in the first DE class you can take. Laplace and Fourier transforms come a bit later, but sometimes it gets squeezed into that first class.
Proof is indeed important for higher math.
And also, I think for most pure math degrees, they get into a couple of classes on number theory. It’s a wholly different topic from the usual string of 2-3 yrs calculus, there are almost no pre-reqs so you can take it whenever.
I feel comfortable with trig, and algebra. I’m definitely going to have to look into this geometry thing, all I remember from that course is stuff like distance formula, Pythagorean Theorem, basic formulas for shapes, and section of a shapes, which I’m comfortable with (at least that’s my impression), but there may be something else…
One thing I’m completely not comfortable with, and I know it’s essential for things like integral ( e^(x) / x ) dx is math that uses n and ! symbols, and I never really had a class that dealt with that or took the time, and turning polynomials, sequences, or functions from one form to the next is foreign to me.
Especially since it’s important for thing like power series, convergence and divergence (things I have to look over for sure)
Nor have I ever taken a probability/statistic course neither. So I’ll look into that.
So it’s Logic, Geometry, and Statistics…Gonna go to the book store and see if I can find some good bargain paper back books.
By “!”, I’m guessing you’re talking about factorials, right? Unless you’re fucking with combinatorics or number theory, you don’t really used factorials for anything. As far as what you’re saying, it sounds like you’re weak in Calculus 2 since that’s where most of that stuff is covered (eg power series, summations, products, etc…).
This conversation made me go back and look at my college transcript…fucking hell, dude. Any reasonable person upon looking at it would wonder why I ever decided to major in math in the first place since I apparently sucked at it lol (2.9 major GPA).
I looked over that stuff over the weekend. Got a little more comfortable, but I felt that was what I was weakest at, in calc 2. Especially since its important for certain non elementary functions.
I looked over a base geometry book, but I don’t think that a the one I should be looking at…
As far as I can tell high level geometry is a pretty isolated branch of math. Not really sure why you’re bothering it with it since you seem to be on some sort of engineering track.
Sigh, cryptography kicking my ass this semester. So many algorithms to memorize… Bombed first exam, not looking forward to the second or the final
Probability theory has been rather easy so far. Very little to memorize and most of it is rather easy to derive. I’m also taking statistics this semester, so there’s been a ton of overlap in the material; especially material for the first exams.
Very little proofing required in either class which is awesome. Hopefully the rest of my 400s will be light on proofs. I’m still sick of them from Advanced Calc
Yo man, the set containing exactly just the number 1 is also a subset of the set of all real numbers. It shouldn’t follow that the subset is infinitely large, which is clear in this case, where the subset has just one element.
Just prove that by contradiction. Assume there is a finite amount of primes Pi. Let P = 1+P1P2P3*…*Pn. P isn’t divisible by any number on the list, but all numbers are divisible by at least one prime. Therefore, there are primes that aren’t on the list: a contradiction to the assumption that there are a finite amount of primes.
I had no idea (or forgot) what Vieta swapping was, so I pretty much wanted to cry after trying a few of the first problems.
I’m trying to brush up on my number theory since it was probably my favorite class in college, but I think I started a little too high with he IMO questions lol
A merchant has an old-fashioned balance scale (google it if you have to). He knows that one arm is longer than the other though. Trying to be fair, he weighs half his customers’ orders on one arm and half on the other (edit: poor wording. He weighs half of each order on one arm and half on the other). Does this even out in the end, or does he benefit or lose as a result?
Assume he only sells one item (say, flour) and that somehow he can actually divide the order in two with his broken scale.
