Examples would be acing Analysis proofs but forgetting how to integrate by parts.
>>8014898
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
>>8014913
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.
>>8014924
only in murica
>>8014924
Why don't you Google it?
>>8014983
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
>>8014946
>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
>>8014898
>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.
>>8015038
is the joke that this means you don't understand it?
is this a meme?
>>8014928
That's still considered a proof.
>>8015045
yes IUTT is a meme lurk more you fucking freshman
>>8014898
I'm getting a PhD in fluid dynamics and had to watch a Khan academy video on vector field curl the other day...
>>8015045
If I bothered reading it, maybe I'd understand it, but I have better things to do.
>>8015064
How did they let you in? How did you get an advisor in fluid dynamics without knowing the basics of fluid dynamics??
>>8015115
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.
>>8014924
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).
>>8015454
>hating on bases horners method
>>8015038
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)
>>8015067
>this is what highschoolers believe
>>8016098
>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".
>>8016281
>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?
>>8014898
>implying I ever learned to integrate by parts
>>8016281
>Couldn't
Couldn't and couldn't be bothered to are two different things
Remembering all the trig identities. I'm terrible with memorization
>>8016468
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.
>>8016479
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.
addition.
Formula for sum of 12+22+...+n2.
>>8014898
> proving continuity using epsilon-delta
>>8016539
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
>>8014898
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
>>8016474
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.
>>8016539
if you let n->infinity, the sum is 0
>>8016543
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.
>>8016545
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.
>>8016742
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.
>>8015468
I'm not hating on it, I just don't get how it's useful other than preference.
>>8016819
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.
>>8016824
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.
>>8016833
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.
>>8016852
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.
>>8014924
Same here and I don't bother trying to. I just do it the ol' fashion way.
>>8014898
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.
>>8016940
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.
>>8014898
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.
>>8014898
I'm a math major.
About to pass a graduate class in Abstract Algebra.
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.
>>8014924
Holy shit. Glad to see I'm not the only one then. Strange.
>>8017038
>>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.
>>8016852
>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.
>>8017052
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.
>>8014898
I can't lie, long polynomial division and completing the square. 2nd year applied math major here.
>>8017134
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.
>>8017159
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.
>>8016175
>this is what sophomores say
>>8014924
because you're a bitch
>>8017163
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.
>>8016728
>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.
>>8016686
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
[math]a^2 = b^2 \iff a = \pm b[/math]
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 [math]\pm[/math] symbol to make sure both roots are accounted for.
Generally
[math](\sqrt{a}=b) \enspace \Rightarrow \enspace (a=b^2)[/math], but
[math](\sqrt{a}=b) \iff (a=b^2 \enspace \land \enspace -\sqrt{a} \neq b)[/math]
and
[math](a^2=b) \enspace \Leftarrow \enspace (a=\sqrt{b})[/math], but
[math](a^2=b) \iff (a=\sqrt{b} \enspace \lor \enspace a = -\sqrt{b})[/math] .
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.
>>8014924
Dude you learn that shit in the 6th Grade.
>>8014898
Had trouble with matrix diagonalization and matrix/row spaces
>>8014898
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.
>>8019250
>ln (0) = 1
>>8019250
>ln (0) = 1
Lel no. [math]ln 0 = -\infty[/math] (but generally undefined).
>e^0 = 1
>ln(1) = 0
Obviously. Anything to the power of [math]0[/math] is [math]1[/math] (except for [math]0[/math], the expression [math]0^0[/math] is indeterminate, as [math]0^x[/math] and [math]x^0[/math] have different limits when [math]x \rightarrow 0[/math]).
Graduated with a pure math degree but still hate really convoluted induction proofs. Usually the ones dealing with factorials and lots of algebra/factoring.
>>8019255
>>8019262
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.
>>8019250
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
>>8019367
Autism
Basic arithmetic desu.
>>8019354
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.
>>8019369
[math]\ln{x} = \log_{e}{x}[/math]
>>8019398
So you assert that non-autistic people don't need to be competent anymore, while a competent person must be autistic?
>>8020102
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.
>>8016728
>Where you find delta1, delta2, delta3...
what do you mean?
>>8014898
For a long time I could only do long division with polynomials; not with simple numerals.
>>8020127
Delta represents difference between terms.
>>8014898
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?
>>8015473
>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
>>8016714
>>8016474
It's 2016. There's no need to memorize trivial shit like that.
>>8016714
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.
>>8021300
Yes, cf the 2008 housing market collapse.
>>8015473
>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.
>>8019369
>integral from 0 to x
from 1 to x. 1/0 is undefined.
>>8021591
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.
>>8021681
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.
>>8021602
so that guy was mistaken about a definition of the natural logarithm.
>>8015143
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.
I really really can't do any proofs that involve congruences, diophantine equations, etc, basically very elementary number theory.
Anyone got any resources to help gain intuition for these, or simply a shitload of resolved problems?
>>8022014
Diophantine equations are hard.
>>8022014
If you torrent "Mathematical Olympiad Resources" there's a few books on diophantine equations.
>>8021447
>hurr durr it's $CURRENT_YEAR, no need for anyone to do any maths anymore because there's programs hurr
>>8019262
Lol no.
[math]\displaystyle \lim_{x\rightarrow 0} ln(x) =-\infty[/math]
You can't just say it's equal, undergrad.
>>8022359
http://mathworld.wolfram.com/AffinelyExtendedRealNumbers.html
>>8022359
You can work on the complex plane and there we have the convention that it equals infinity.
Third year pure maths student. Had to go on mathsisfun .com to learn about even and odd numbers.
>mfw I don't even know what "completing the square" is
I can solve a recurrence using generating functions, though.
>>8022439
also, while I'm in here, how hard is a complete math degree lads? the math classes I've taken in university were hard as fuck for me, but then again I also almost failed algebra I in high school
>>8022448
Not hard as it otherwise will be if you learn basic algebra early on. Some of your higher level math breaks down to being able to do basic algebraic calculation & if you continually can't see how one line proceeds to the next due to the algebraic manipulation you'll have a hard time.
Combinatorics
Never learned it in school and just bullshitted my way around it in discrete mathematics
I have to say that I'm pretty surprised this didn't fuck me over so far and I'm at the end of my masters by now
>>8022329
It's useful to know how to work it by hand if you had to. It's not useful to memorize a bunch of rules.
I'm a math PhD and I literally don't know complex analysis. I BS'd my way through that undergrad class because it was applied bullshit, and have never needed it.
Math major here. Now my weaknesses
> I have to stare like 5 min to commutative diagrams, function compositions, path sums, etc to understand how they work.
> When multiplying cycles, I have to do the multiplication like 5 times to get it right
> I forget continuously classical algebraic algorithms, like Euclid's.
> To do a rotation in R2, I usually switch to C and then switch back. > To do it in R3, first I do it in R2 like above and then I generalize analogously.
There are many more, but it's enough self shaming for today
>>8022359
>Wolfram is an undergrad
If you require the result to be a finite number, then it's undefined, and all you can do is provide the limit as you did. However if you consider >>8022376, then [math]\pm \infty[/math] belongs to the range of the fuction, and you can state such a "value" to be a regular result of the operation.
For calculus, I can't read any notation other than Leibniz.
All you losers getting a science degree good luck getting a job let alone getting laid!
The math stuff you forgot with time is probably stuff which you never fully understood, but rather just memorized at some earlier point in time. Concepts that were understood well tend not to be forgotten easily.
>>8019250
[math]x^1 = x[/math]
[math]x^2 = x \times x[/math]
[math]x^{-2} = \frac{1}{x\times x}[/math]
Using [math]x^2[/math] and [math]x^{-2} [/math]
[math]x^{2}\times x^{-2} = \frac{x\times x}{x\times x}=1[/math]
or
[math]x^{2}\times x^{-2} = x^{2-2} = x^{0}=1[/math]
You must remember that logarithm is the inverse operation of exponential, i.e. [math] log_{10}(100) = 2 [/math] as [math] 10^2 = 100 [/math] and [math] log_{2}(512) = 9 [/math] as [math] 2^9 = 512 [/math]. So then [math]log_x(1) = 0 [/math] as [math] x^0 = 1 [/math].
The shape of logarithmic graph becomes clear if you recall what we did with exponents, i.e. negative exponents gives rise to numbers much smaller than the logarithmic base.
So if we enter a number much smaller than the base into the logarithmic operation we would expect a large negative number; therefore [math] ln(0)[/math] or [math] log_{10}(0)[/math] would tend to [math] -\infty [/math].
>>8015115
Because she knew I wanted to do research - if I want to jerk off about how much simple math I knew I wouldn't have gone to grad school
>>8022864
I'm sure you remember the full details of everything you've ever learned.
>>8022864
Yeah not true. If you graduate and haven't used a certain math proof/technique in x>5 years then it isn't surprising you'll forget about it. I graduated with a pure math degree and don't remember all of trig integration techniques w.o looking them up. The last time I had to use it was years and years and years ago.
>>8022965
Yeah but given some time you could figure them out on your own.
>>8022971
yeah, that's true. I'd have to go back and look at it again and then I'd have it.
>>8014924
Same here.
Senior undergrad and I forgot a lot of stuff, like partial fraction decomposition and series manipulations.
Why do I have the urge to punch the fuck out of the guy in OP's pic?
>>8014898
I have a BS in math, highest honors from a top 15 math and stats school
I am getting a PhD in electrical engineering with a mildly famous person as my adviser
> every encounter with dual spaces and tensors takes hours to sit and think through
> spooked every time matrix algebra, matrix calculus appears
> spooked dealing with function spaces
> spooked when dealing with modes of functional convergence
> spooked when almost sure convergence does not imply Lp convergence
> frequently forget properties of Lp spaces
> frequently forget cauchy-schwarz
> frequently forget differences between hilbert and banach spaces
> unable to remember any important properties and differences between meromorphic and complex analytic functions
> cannot use residue theory
> do not understand green's theorem
> all series and integrals go into wolfram alpha
just shit my life up senpai
everyday i think of dropping out
>>8015064
hahaha this is pretty bad
>>8023685
This shit hurts to read. How the fuck did you ever get a math degree?
>>8023757
Matrix Calculus sounds like a pretty outrageously simple topic but it can get pretty sensitive to details and unclear
> x is an n-vector,
> u:R^n --> R^m
> v:R^n --> R^a
> F:R^a --> R^{m x n}
Now quick, compute the Frechet derivative of:
> det ( u(x)^T F( v(x) )^{-1} x )
with respect to x without looking up the matrix calculus white paper
>>8023685
10/10 would read again.
>>8015067
Try reading the first page. It's dense.
>>8023685
Why would you even need anything more advanced than high school mathematics if you're doing a PhD in electrical engineering?
>>8022917
How do you expect to get any research done if you don't even understand basic calculus?
>>8023860
Ever heard of information theory?
>>8023860
>signal processing (fourier analysis, wavelets)
>information theory
>semiconductors (read: quantum mechanics)
>comms (basically stats)
>control theory
>>8015062
lol people that read buzzfeed know what IUTT is you special snowflake faggot.
combinations and permutations
It's just beyond me
>>8014898
combinatorics. i cant count.
great at analysis/topology/probability though, but cant do combinatorial proofs to save my life
>>8025102
Counting is hard. I'm opposite, better at logic and graph theoretic proof than analysis. Different interest/talents. But I'm closing that gap by studying from baby Rudin.
Completing the fucken square. Have to look that shit up every single time.
Cpsc major here
Call me dumb or whatever but proofs are fucking awful. Math used to be fun problem solving where you arrange pieces of a puzzle to get your answer. Proofs involve endless trial and error. You either just get what you need to do or spend an hour trying to find an unintuitive step you missed. Fuck them
>>8025263
It's okay, most people aren't smart enough for math. The world needs codemonkeys too. :)
>>8025263
luckily for you no one outside of academia gives a shit about mathematical proofs. they just want to see shit works and if you can make shit do other shit that works.
>>8025317
yeah and the code monkeys will make more than us mathematicians and deem as having more valuable skill sets. i went out in the real world as a pure math graduate and honestly, no one gives a shit and it impresses no one.
>>8025173
You're just trying to rewrite an expression as if it were a perfect square, and then adding back in whatever error there is.
>>8016474
> switch to rational trig
> never memorize an identity again
>>8025317
Eh I can do them, its just not particularly fun or interesting
>>8014898
Addition and subtraction of negative numbers
I'm about to graduate an honors math degree and still have little to no idea what sinh/cosh functions are nor their purpose. The only time it came up in complex analysis they defined it and aside from that I've almost never seen it.
Can't do synthetic division either.
>>8026751
explaining what they are is easy; whereas sin/cos map to points on the unit circle, sinh/cosh map to the analogous point on a unit hyperbola (x^2-y^2=1)
I don't know many uses of them other than some integral substitutions though
I never bothered to learn the multiplication tables.
>>8019367
High school-level math shouldn't even be called math.
It's computation.
>>8026751
>I'm about to graduate an honors math degree and still have little to no idea what sinh/cosh functions are nor their purpose
solving integrals or something like that
maybe they just look neat.
>>8026869
So you think that "math" should consist of proof only? How about about PDEs? They are as much "computation" as solving a linear equation is, but certainly are not highschool math.
>>8026809
Are you one of those who look up "3*6" in Google? What do you do if no Google or calculator is available, count on your fingers like a 5 years old?
>>8026894
nah start from the closest pair you know and then reach the desired result by adding.
>>8026756
How about parabolic or elliptic trig functions? Do such things exist, and if not, why not?
>>8026896
>the closest pair you know
Which would be what, if you never bothered to learn these?
>>8026080
So you are a math major who has trouble with "adding and subtracting negative numbers"?
>>8022999
are you kidding me?
>>8026904
the 5 and 10 times table comes to mind easily
>>8026904
I know remember most of it, after 3 years of university math. At school I never bothered.
>>8014898
Whenever I get a receipt, I try to make my tip both ~20% and even off the change. It involves calculating 1-x/100 and I suck ass at it about every third time
>>8021568
Sorry, but what is p test?
>>8028797
see if you can pee straight
>>8027178
Back in my time you wouldn't have passed grade 2 if you failed to prove an adequate knowledge of the multiplication table. Let alone in the 19th century or earlier, in good schools you had to learn the multiplication table to 12, 15, or, in extreme cases even to 25 rather than just 10.
Up to 10 (9 really because x*10 is trivial) is the bare minimum though, because without that you won't be able to do any reasonably quick calculations in your head nor on paper.
>>8026080
I can't do arithmetic so save my life.
Tfw your friends think you're a fucking calculator because you're a math major.
>>8021568
This is why I give my students problems like [math]\sum_{n=1}^\infty \frac{1}{n^{1+\frac{1}{n}}}[/math] on quizzes.
>>8029933
hahaha, nice question man.
Compare the terms to 1/2n is the only way i can see to do it
>>8017038
>Can't remember one of the most important algorithms in all of mathematics
But yeah, I'm going to forget all of Complex when i finish the final next week
>>8028797
https://www.youtube.com/watch?v=gB43EA9659c
The best way to cheese calc II my nigger. Though if the professor is careful you're fucked. It's only really useful in certain situations.
>>8030670
Showing [math] n^{1+\frac{1}{n}} < 2n [/math] for all sufficiently large [math]n[/math] isn't entirely trivial.
Here's another more difficult one that I didn't put on a quiz; decided it was too hard for them.
[math] \sum_{n=2}^\infty \frac{1}{\ln(n)^{\ln(n)}} [/math]
>>8014898
> 3rd highest grade in complex analysis class
> Regularly fuck up matrix multiplication
>>8030709
but for p=-1 you get -1/12
>>8031082
>3rd highest
How does it feel to be a brainlet?
>>8021248
THIS
>>8032080
obviously im able you fucking idiot, i just forget about it all the time
