# Math majors: What is the most basic math you have trouble with?

Examples would be acing Analysis proofs but forgetting how to integrate by parts.

d[fg]/dx = df/dx g + f dg/dx
∫d[fg]/dx dx = ∫df/dx g dx + ∫f dg/dx dx
fg = ∫df/dx g dx + ∫f dg/dx dx
∫df/dx g dx = fg - ∫f dg/dx dx

QED

Integration by parts was a godsend, as 10 minutes on substitution on the last day of calc 1 was not sufficient in teaching it

I've graduated with a BS in math, I tutor calculus, I'm in a PhD program for computational chemistry, but I don't know how to do polynomial division (synthetic division).

Oh well.

HS

only in murica

I've taught it to myself, but I never need to use it in my tutoring and end up forgetting. I see somebody here asking about it once in a while, which is why I even remebered to comment about it in this thread

>haha look at that idiot playing with his topoi
>i bet he doesn't even know enough FORTRAN to program a model of molecular bonds

for real though, mathematics is super huge, and people working in one field might know nothing about another field
a good real life example of this is how our lord and savior Terry Tao actually asks questions about math on math stackexchange
i can't imagine you need to do any sort of mathematical heavy lifting with polynomials in computational chemistry, especially any sort of manual work

>What is the most basic math you have trouble with?

not a math major, but I'm struggling a bit on inter-universal teichmuller theory. I mean it makes sense in my head, but it's hard explaining it to others.

is the joke that this means you don't understand it?

is this a meme?

That's still considered a proof.

yes IUTT is a meme lurk more you fucking freshman

I'm getting a PhD in fluid dynamics and had to watch a Khan academy video on vector field curl the other day...

If I bothered reading it, maybe I'd understand it, but I have better things to do.

How did they let you in? How did you get an advisor in fluid dynamics without knowing the basics of fluid dynamics??

There are some specific shit everyone forget. I mean, I remember PhDs forgetting how to compute some basic integrals. What you must prove is that you have the tools to learn shit on your own.

Synthetic division is useless, though.

I've timed myself (granted, it wasn't rigorous), and I only take slightly less time when doing it instead of the normal division, and mostly because it avoids writing a lot of x's.

Normal division is easier to understand, and if I'm pressing for time I just use a calculator or computer. There's no space for synthetic division to be useful unless I'm missing something huge (which I know I might, as I'm an engineer major, not a math major).

>hating on bases horners method

You can only truly grasp it if you have the mind of the samurai.

fucking convergence/divergence tests. Who the fuck has time to remember that shit I haven't taken Calc 2 in years and I don't think there's any physical application for them so I never have any practice (physics major here)

>this is what highschoolers believe

>this is what freshmen look like

Had a professor with a PhD from an Ivy that couldn't and wouldn't do algebra/arithmetic whenever a math computation was reduced to it. They'd say "And whatever that comes out to equal to is the answer".

>couldn't
I promise you he could, but is it really doing anyone any good to watch him do simple shit you've both done thousands of times?

>implying I ever learned to integrate by parts

>Couldn't
Couldn't and couldn't be bothered to are two different things

Remembering all the trig identities. I'm terrible with memorization

Still it's a bit weird and possibly sad to think that there are maths professors out there who would get terrible scores on Putnam exams.

even more embarrassing when you think that a lot of physics and engineering lecturers would actually do better than a lot of say algebra lecturers.

For some limits, I'm dependent on L'hospital's rule because I forgot how to conjugate fractions and all the little algebra tricks.

Why would that be sad? That's like saying it's sad that there are architects out there who can't swing a hammer very well. Who gives a shit, tedious calculation is not his job and it's not what the class is about.

Formula for sum of 12+22+...+n2.

> proving continuity using epsilon-delta

i meant 1^2+2^2+...+n^2

Base change matrices. It's dumb but I always have to think hard of which base I should express in terms of which in order to do what I want

god damn I hate motherfucking taking the squares of shit I don't know why but that fucking shit will never be easy for me to do in my head and I don't fucking know why FUCK

Dude, nobody remembers all the trig identities after trig/calc I/II. I had a class my final year in college where you'd periodically get something like integral(1/(1+x^2)dx) and nobody would remember that it's just arctan(x). The professor (who I'm sure also couldn't be assed to remember them) never took off on a test if you forgot them.

if you let n->infinity, the sum is 0

I hated this with a passion. I finally figured out basically what it meant and never took any 4000 level analysis/topology classes so it wasn't too bad. Of course, the 3000 level topology/real analysis class I needed it for straight up sucked.

Once I learned how it was derived it made sense. Where you find delta1, delta2, delta3... and that determines the degree of the polynomial that expresses the sum then you use linear algebra to figure out the constants.

Not a math major, but I´m taking ordinary differential equations and I forget to complete the square.... yeah

Taking ODE right now. My professor lectures himself and my book is shit, so I'm having a little bit of trouble because I haven't taken linear algebra yet. I'm very much pulling through though. Just a little more work.

I didn't see completing the square in any class after algebra II and before number theory (including ODEs and PDEs). The only reason it came up was solving polynomials in mod n.

I'm not hating on it, I just don't get how it's useful other than preference.

You taken any upper level linear algebra? Bases are really important, and it's pretty important to understand what a basis is, and how there are many many different bases that are just as valid.

I have a problem with the names here, given that I didn't study this stuff in English.

Is linear algebra the same as "vectorial" algebra? If so, then yes, but I don't know what exactly you mean by bases.

Never heard of vectorial algebra. We have vector algebra, but that's usually pretty elementary (algebraic operations with vectors), so that's probably not what you mean. What did you study in vectorial algebra? I've taken three linear algebra classes: one freshman year that was super super elementary (solving basic linear systems, row reduction, and the very basics in eigenvalues/eigenvectors), one junior year call linear algebra I which was more proof based (introduction to vector spaces/subspaces and linear transformations, rank-nullity theorem, onto/1-to-1/well defined in terms of linear transformations, introduction to bases/change of basis, matrix exponentials (only a little bit, this is mostly focused on in a class called non-linear diff eq), and markov chains), then finally an upper level class called linear algebra II which was much more theoretical (more in depth study of eigenvalues/eigenvectors, direct sums, invariance, inner product spaces, Gram-Schmidt process, orthogonality, and the Jordan Decomposition theorem). Does vectorial algebra sound like any of these? I'm referring to what I've called "linear algebra II", having a really good foundation on bases was crucial to the first 1/3 of this class.

From the looks of it, my curriculum mostly sprinted through your first two classes in a single class and that was it.

No wonder I have a pretty shallow understanding of the topic, and couldn't even recognize it in English.

Same here and I don't bother trying to. I just do it the ol' fashion way.

Combinatorics. Also graph theory, which is somewhat closely related.

Bothers me a bit because graph theory is pretty cool but I suck donkey balls at doing it compared to other topics in math.

I see what you're saying. I struggled hard with linear algebra II because it's hard as shit (professor graded really hard and had a thick accent). Then again, I placed out of the first one (I was in a special program that taught a lot of the same material as the first class does) and did alright in the second one (never went to class). The last one was optional, I could take any combination of math electives, but I wanted to avoid real/complex analysis classes and topology so I took linear algebra II as the lesser evil.

the MOST basic math I have trouble with is arithmetic. I can't multiply by 7 in my head to save my life unless it's with a multiple of 5.

I'm a math major.

Still can't do long division with polynomials. For whatever reason, I can never seem to remember the algorithm.

Also anything complex analysis I have absolutely no recollection of despite doing well when I took that class.

Holy shit. Glad to see I'm not the only one then. Strange.

>>Still can't do long division with polynomials. For whatever reason, I can never seem to remember the algorithm.
It's the exact same thing as integer long division.

>solving basic linear systems, row reduction, and the very basics in eigenvalues/eigenvectors
I'm surprised that was enough material for a full-length class. That's like 3-4 weeks in a normal linear algebra class.

Yeah, well my school does it usually the first semester (plus it has tons of non-Stem majors who need math credits). Also, it's like a 2 credit class instead of 3 like a normal class. It's extremely elementary, I placed out of it and went straight to multivar and diff eq (even though I had already self-studied those in high school).

>tfw I took the "honors" track, meaning I was basically expected to know everything before it was taught to me
Fuck my school. I took real analysis, topology, and abstract algebra without ever having learned what linear algebra was about or how partial derivatives work because I was expected to know these things without ever having taken classes in them.

And I was always stunned at how my classmates knew this shit better than me, starting giving up feeling like I'd never understand any math again, until I finally took a slightly easier class and realized all these people are idiots compared to the classes I was in before.

My answer is line integrals OP. I passed Complex Analysis and then had to look up what they are online one day because nobody in graduate analysis was willing to explain it to me OP.

I can't lie, long polynomial division and completing the square. 2nd year applied math major here.

I did similar. I took a bunch of "honor" courses where everyone already knew the material to some degree and it was "advance" in the sense they didn't cover the basics. I managed to get by in all those courses without fully understanding everything and having gapping holes in my knowledge. I ended up going back and studying those subjects again (on my own) starting from the basics and re-learn it. Should have stuck with the basic courses and learned the material the right way the first time. But least I'm catching on fairly quickly through my self studies.

Exactly.
Well in my case I want to graduate and then go back and study it on my own, now that I at least have a framework and understand enough math I could probably teach myself like you ara.
Good on you for doing that though.

>this is what sophomores say

because you're a bitch

Thanks man. The internet is a great resource. I've been watching various lecture videos, reading textbooks online and doing endless amounts of problems until I master the concepts. I let it truly internalize and then move onto the next topic. I feel like I'm actually learning a lot more math this way than anything I learned in my undergrad program.

>Once I learned how it was derived it made sense.
It's an early problem in spivak. supposed to figure it out using just the 12 given axioms and induction. I don't even... maybe I should switch majors. I don't have to be the best I just wanna be really confident with math.

If you square (or generally raise to an even power) both sides of the equation, you may end up with an equation which is implied by the original one, but not equivalent to it. As such, the new equation can have more solutions than the original one. This is because

$a^2 = b^2 \iff a = \pm b$

The opposite is true when taking square (or generally even) roots of both sides of the equation - then you receive an equation which implies what you are taking the root of, but itself can have less solutions (because the radical symbol always denotes only the principal root. That's why e.g. the quadratic formula has the $\pm$ symbol to make sure both roots are accounted for.

Generally

$(\sqrt{a}=b) \enspace \Rightarrow \enspace (a=b^2)$, but
$(\sqrt{a}=b) \iff (a=b^2 \enspace \land \enspace -\sqrt{a} \neq b)$

and

$(a^2=b) \enspace \Leftarrow \enspace (a=\sqrt{b})$, but
$(a^2=b) \iff (a=\sqrt{b} \enspace \lor \enspace a = -\sqrt{b})$ .

Fucking salt water mixture problems in Diffy Q my first year. I am a senior math major and been a tutor for the class for a while so I can do them now, but I hate them with a passion.

Dude you learn that shit in the 6th Grade.

Had trouble with matrix diagonalization and matrix/row spaces

I majored in biological mathematics

I could never fucking remember ln(1) = 0 and ln (0) = 1 and that e^0 = 1.

Every time I had an exam I would start by writing that down.

However I had no problem biological models or anything like that.

>ln (0) = 1

>ln (0) = 1
Lel no. $ln 0 = -\infty$ (but generally undefined).

>e^0 = 1
>ln(1) = 0

Obviously. Anything to the power of $0$ is $1$ (except for $0$, the expression $0^0$ is indeterminate, as $0^x$ and $x^0$ have different limits when $x \rightarrow 0$).

Graduated with a pure math degree but still hate really convoluted induction proofs. Usually the ones dealing with factorials and lots of algebra/factoring.

Kill me I still don't know it

You all sound like fucking idiots.
> Billy! OMG! You got a math degree?
> Yep! I got a B.S. at a shitty Uni so I'm a mathematician now!

Can't do high school level math.. rot in hell, faggots.

Did math but never learned what ln(x) actually is..
an integral from 0 to x of (1/t).. oh.. what's that? ln(1) = 0

I don't remember the trig identities, I probably would be bad at computing integrals.

Adding 3 digit numbers mentally in less than 2 seconds

Autism

Basic arithmetic desu.

Then you don't really understand neither logarithms, nor exponentiation. Trying to learn math by memorizing things is the worst possible strategy, no wonder you keep being confused if you (apparently) never tried to understand this.

$\ln{x} = \log_{e}{x}$

So you assert that non-autistic people don't need to be competent anymore, while a competent person must be autistic?

The point of the thread is to point out trivial math people forgot. For you to point out the fact the math is trivial is pure autism as that is the point of the entire thread.

>Where you find delta1, delta2, delta3...
what do you mean?

For a long time I could only do long division with polynomials; not with simple numerals.

Delta represents difference between terms.

completing the square

Finding the set of points of 2pi/3. I blank out and it takes me a while to remember that shit

Is it really bad to apply a method or concept to solve some problem, without understanding how the method itself exactly works and how it was derived?

>tfw I have a test on that tomorrow
I seriously fuck this stupid stuff up every time unless it's like a harmonic or a p-series what the fuck man

It's 2016. There's no need to memorize trivial shit like that.

You literally just draw a triangle.
My calc teacher in high school made us do it for every integral like that. Draw a triangle and it all becomes intuitive.

Yes, cf the 2008 housing market collapse.

>not just using the p test every single time
>not just using the integral test if that doesn't give you an answer

I cheesed the shit out of calc 2. I remember my professor wrote some question which was supposed to be extremely difficult but he forgot you could use the p test. I was the only one who did it too. I remember I had to explain to him why it worked and then he spent like 45 minutes working it out and concluded the P test did in fact work.

>integral from 0 to x
from 1 to x. 1/0 is undefined.

so?

Usually random trig integrals or whatever. The intuition for how to solve an integral or differential equation pretty much disappears if I haven't had to do one in like, a month or so.

I can absolutely never ever remember the quadratic formula. I always derive it manually when I need it.

Really? The quadratic formula has been burned into my brain since about 2nd grade. If there's one thing I'll never forget it's that.

so that guy was mistaken about a definition of the natural logarithm.

This, a lot of basic degrees are less about proving that you know something and more about proving that you can quickly learn and master the concept.

When you spend so much time sweeping through advanced concepts it's inevitable that you're going to forget some of it. At that point you're just expected to learn it again.