

Ask HN: Where did you top out in math classes? - andrewparker

Pretty much everyone (except perhaps tenured professors of mathematics) hits that point in their math training when they realize "I'm just not smart enough to get this."  What point in your math career did you hit a brick wall?
======
g00dn3ss
Recent evidence tends to indicate that 'not smart enough' is probably a myth.
Almost everything can be attributed to exposure and effort at some point
rather than some innate smartness.

A lot of advanced math takes some serious concentration to understand. For
some non-practical aspects, I found that I lacked the motivation rather than
ability to understand it . One particular class where I seemed to hit my
tolerance was a theoretical linear algebra class. I could understand the
practical applications of most of the topics but some of the theory seemed
just out of reach. The book was extremely dry and I think the professor may
have been taking lessons from Ben Stein.

Give me a private tutor, a theoretical linear algebra for dummies book, and a
pending disaster for which this is the solution, and I bet the outcome would
be a little different.

~~~
doubleplus
Would you happen to have any links or book references to this "recent
evidence"? While most of success comes from effort and discipline, I've always
been under the impression that only the naturally gifted (who also have
discipline and drive) can/have achieve/achieved certain things. The dwarf down
the street from me will never be a professional football player, and someone
with a 100 IQ will never be an astronaut. I've always felt the you-can-always-
achieve-whatever-you-want-no-matter-what-if-you-want-it-bad-enough approach to
be more than a little cliched and misguided. If recent scientific evidence has
disproved this stance of mine, I'm open to changing it.

~~~
elai
To be honest, I believe that all intelligence comes from innate motivations
and practice. You suddenly become 10x more "intelligent" when you actually
give a shit or get some innate joy or obsession relieved when you do it. If
that is something that is constant within you, you become more and more
practiced and a virtuious cycle results. Nothing is too hard to explain, it's
just mathematicians are really horrible at communicating.

~~~
byrneseyeview
For whom, though? Brains are complicated, but if yours is severely damaged
(through a stroke or head injury) motivation is not necessarily going to fix
that. And as far as I know, there aren't any permanent ways to raise IQ. Some
environmental factors lead to higher childhood IQ, but these vanish by
adulthood. And there are tricks people can use to bump up their scores on IQ
tests, but I haven't seen a situation in which practicing for test A raises
your score, years later, on test B. This stuff is just more static than that.

The danger with what you're saying now is that someone with an IQ of 90 --
someone who could be a fine contributor to society in lots of practical,
necessary fields that don't require lots of abstract thinking -- could be
inspired to throw away lots of time and risk lots of frustration trying to be
a mathematician. We should deal with the fact that wasting education on
someone who can't use it is as much a tragedy as failing to educate someone
who can use it. By pretending that 'smart' just means 'trying hard', you're
doing more harm than good.

~~~
DaniFong
The problem may be that our predictors are terrible. There are a lot of Nobel
prize winners who later discover their 'dismal' performance on IQ tests. I
know grad students at Princeton who've confided sub-100 IQ scores, bad SAT's,
horrible performance on one math test or another -- it's like this big,
shameful secret for otherwise brilliant people.

Everyone carries around the absurd burdens of judgments and measurements, but
they don't always mean what people think they mean.

~~~
byrneseyeview
Are there any other quantifiable variables with such high predictive power?
I'd be really interested if there were some other test that could better
estimate the odds that someone would get a degree, earn lots of money, stay
out of jail, vote often, delay having kids, etc.

It would be interesting to know more details, which I'm sure you can't divulge
without violating someone's privacy. But it would be neat to find out if those
people had other skills that correlate strongly with IQ, like the various
digit-memorization/recitation tests, or reaction time. Were these people
autistic? Were they taking a test in a language they didn't know too well?

~~~
DaniFong
They weren't autistic, and there didn't seem to be any strange behaviors
socially, and they were quite inquisitive and swift on the uptake.

I once heard IQ defined as "ability to navigate bureaucracy, getting the
answers others think correct in a manner testwriters imagined, and color in
the lines" (paraphrased). This may have something to do with the phenomenon
here.

The odds that someone would 'get a degree, earn lots of money, stay out of
jail, vote often, delay having kids, etc.' seem to have more to do with
successfully conforming to certain values of society's upper-middle class.

I think I'm capable of inventive thought, but I don't particularly want to get
another degree, or earn much money, or delay having kids, or vote often, and
the sort of things that one has to do to stay out of jail, are, honestly,
quite often absurd, and I often rail against them.

And if you start to observe, closely, just how these things are tested, you'll
start to get the impression that maybe bright people will find their ways
through the cracks more than anticipated. There's an enormous weight given to
quick answers -- time directly influences scoring. Linear answers are
expected, and alternative interpretations are docked. There's often
insufficient information in the questions, or it's based on a model of the
world that's wrong. Domain knowledge like mathematics or vocabulary is brought
into it. Analogies are made to hone in on _one_ relationship from the many
that could exist. Scorers of essays give insufficent weight to substance and
too much to form -- despite their lipservice, they are indeed swayed by big
words.

Even tests like GRE physics are bad. They claim to be testing rapid physical
intuition, but in practice what divides good from poor scores is prior
experience with 100 simple systems and the ability to get the factors of 2 and
pi right with three minutes per question.

~~~
byrneseyeview
I think your quote comes from Cosma Shalizi. Thomas Sowell addressed that
complaint years before by noting that most of the countries where you find
that modern complexity are pretty nice places to live, whereas other places
are hellholes. The correlation between IQ and income holds true for places
outside of the US, too, so one might be tempted to think that a bureaucratic,
find-objective-answers, fill-out-these-forms-in-triplicate society is better
than most of the brutal alternatives.

"...seem to have more to do with successfully conforming to certain values of
society's upper-middle class. I don't particularly want to get another degree,
or earn much money, or delay having kids, or vote often, and the sort of
things that one has to do to stay out of jail, are, honestly, quite often
absurd, and I often rail against them."

My point is that, all else being equal, you _could_ get a great job if you
chose to, and that if you do illegal things, you apparently do them in such a
way that you won't get caught. IQ seems to correlate with the ability to delay
gratification, which itself seems to be a better predictor of success than IQ
(sadly, it hasn't been tested in a rigorous, long-term way -- so it can't
match the hundred or so years worth of data people have compiled on IQs).

One of the reasons that these tests emphasize time is that 'quickness' is a
component of IQ. Francis Galton, the first guy to really study the subject,
liked to think of things in that way -- and given that physical reaction time
correlates so well with IQ, he had a point.

I agree that the essay part of standardized tests is messed up. Lots of the
recent changes to tests seem to arise from political correctness. Test-makers
found out that you can't design a test that has predictive value without
getting politically incorrect results, like lots of men on the extremes, or
lots of high-IQ Jews and Asians and low-IQ Mexicans and blacks. So they
periodically adjust the scoring mechanism or the test to get bell curves
closer to the same median and standard deviation (more focus on the median
than the SD, since most of the people who complain about such things don't
know what 'standard deviation' means). So keep that in mind when complaining
about the essay, or the rebalanced scores, or the analogies (which were
dropped from the SAT -- analogies happen to be more IQ-weighted than other
categories of questions).

~~~
DaniFong
For the most part, life in latin america seems a lot happier than in more
bureaucratically encumbered states. So I don't really buy that argument.

My main point is that truly excellent thought doesn't depend on the same
skills that would allow scoring highly in an IQ test. In many cases such
skills would inhibit it. In an IQ test it helps to rapidly adapt to the
assumed constraints of the problem and come quickly to the closest, most
linear answer. If you have a mind compelled to bring questions back to
reality, to challenge assumptions or think of things from many different
angles, you'll do, on the whole, more poorly than if you had not. But these
behaviors are sometimes precisely what you'd want!

~~~
byrneseyeview
_For the most part, life in latin america seems a lot happier than in more
bureaucratically encumbered states. So I don't really buy that argument._

The millions of immigrants from there to here don't seem to buy your argument.
Which Latin American countries do you mean?

"... truly excellent thought doesn't depend on the same skills that would
allow scoring highly in an IQ test."

I happen to agree with you! One thing that's bugged me for years is that you
can't design a test that distinguishes, in advance, between cleverness and
original stupidity. So that means that whole lot of time-consuming activities
can only be measured after the fact if at all. The difference in our views, I
think, is that I would argue that IQ tests measure the kind of raw data-
processing skills that are useful in any situation (the military tests people
heavily, and for all tasks they've found that IQ correlates positively with
results -- I think for some technician jobs, it explains about 60% of the
variance in individual performance). There just aren't any studies I know of
showing that people with low scores on IQ tests go on to succeed in any
measurable way. It would be convenient, to say the least, if you argued that
the success-deficit among low IQ people is more than compensated for by a
success-surplus that happens to be impossible to measure. So I'd like to know
if you can find some way to quantify your argument. It would change my
thinking on a lot of subjects if I found that doing poorly on an IQ test
predicted doing well at some other task.

~~~
DaniFong
In happiness surveys, Latin America does pretty well -- I think as a region it
comes out on top.

This is contentious, but for most of the immigrants, they didn't move because
the culture was more enjoyable here. Most of the Latin American immigrants had
ther livelihood strip from them in two stages: one, from general
industrialization pressures that have affected practically every country,
forcing specialization into cash crops to compete, two, increasing competition
from the USA and other countries, coupled with crop failures endemic to semi-
arid areas.

The few areas in which modestly educated Latin Americans could reliably
compete were in _illegal_ cash crops (for which they had less competition in
the USA), which continues to cause economic distruption and criminal activity,
and manual labor. Those forced into either business might have better chances
in the USA, but on the whole they're happy countries. When you're there, you
can feel it.

As for success and low IQs, if I recall correctly, someone got the bright idea
of testing Caltech professors while Feynman was there -- this may have been
prompted after he won the nobel prize, and found out his score from highschool
was 125. When they tested the professors, the scores were surprisingly low. I
forget who it was, but someone got to make a big deal of his 105 score, since
it was three points higher than Feynman's.

My point is that these measures can be stunningly irrelevant, and, if so,
while they might have some utility for, say, selecting an undergraduate class,
they are often best ignored by an _individual_ when it comes time to decide
what one is capable of.

------
rtf
I don't know, how about every subject?

Multiplication. Long division. Algebra. Geometry. Trig. Calc.

I was never very motivated to study math. The problem was, my older brother
was very into it(and now is a math grad student, ever-so-slowly getting his
thesis together). This set a model that I could not hope to emulate, but it
only meant my mom pushed me more, talked to the school to get me into the
advanced/accelerated classes I didn't really want to take. She probably would
have done some of that without my brother around, but not as much.

This led me down the "please the parents" line of study, which naturally meant
some surreptitious, embarrassed attempts at cheating. This only made me feel
worse, of course.

In college I started into computer science, thinking that I at least liked the
programming. But integral calc sunk me for good, and in a particularly bad
quarter that was my low point, I tried taking linear algebra as well as a
repeat of calculus, thinking that perhaps the extra pressure would do
something good.

Of course not. I dropped linear algebra and failed calc again. After that, I
decided to declare in economics, restarted calculus with the "ez-for-econ-
majors" series and sailed through those courses with a solid B average. I
struggled through, but passed on the first try, the two intermediate econ
courses which started introducing serious mathematical modelling. The
remainder of the major was electives, and not difficult ones.

I never knew, until after that whole period of my life was over with, exactly
what was holding me back. Now I'm pretty sure that it's about motivation and
dedication. My brother is fairly normal but can get interested enough in math
problems to sacrifice his well-being. The genius researchers of the field
sacrifice well-being regularly, without really knowing it, and are typically
slightly unhinged socially.

As for myself, I tend to run away from a challenging math problem. So, even if
I'm forced to tackle it, it will probably take me 10 times as long to solve as
it would my brother(not even factoring in his years of experience now). Once I
overcome those hurdles particular to a new category of problem I am fine, but
I have to take considerable effort to do so.

Summing that difference up over a long-term period like that of a college
course, the best students can zoom far ahead because of this motivation
factor, even if they aren't necessarily the _smartest_. Indeed, many math
students reach the upper-division levels on memorization alone and get stuck
from there, as proofs take on more and more importance. That's a major failing
of current math education in the United States - overdependence on rote
techniques. (The former Soviet educational system, OTOH, had probably some of
the strongest math education, and much of it has been translated to English -
pick up a book from that period and you will probably see a small and dense
text that introduces high-level concepts in great, if unforgiving, detail.
Very different from the thick drill+practice textbooks I'm used to.)

My conclusion: many academic fields can accommodate a half-hearted practice.
Math is not one of them. And our society doesn't respect that difference,
shoving it under the rug as "I'm just not good at math."

~~~
plinkplonk
"The former Soviet educational system, OTOH, had probably some of the
strongest math education, and much of it has been translated to English - pick
up a book from that period and you will probably see a small and dense text
that introduces high-level concepts in great, if unforgiving, detail. Very
different from the thick drill+practice textbooks I'm used to."

Could you provide a url for some of these? Should I look up any specific
publishers? Thanks in advance!

~~~
gunderson
I second that.

This is one of the best ones:

[http://books.google.com/books?id=ikMAzFXpFOsC&printsec=f...](http://books.google.com/books?id=ikMAzFXpFOsC&printsec=frontcover)

btw if anyone wants to do a collaborative chapter by chapter self-study, just
send me a private message. I have had it on my shelf for a while but haven't
taken the time to do a few pages a day as intended.

------
DaniFong
I'm not sure I ever had that reaction. I explored a few topics in different
lectures in grad school which were pretty obtuse: ergodic theory, for example.
I didn't get it, but I assumed it was because the topic wasn't suited to
lectures, and after learning of the basic direction they were headed in and
setting out myself, I found I could get pretty far.

I've seen others give up on some topic rather than the method they used to try
to understand it. It's the equivalent of someone saying "I can't get math"
because they're spending all of their time remembering formulae, or someone
saying "I'm no good at programming" while spending their time reciting bubble
sort line by line in preparation for the exam. Giving up on higher mathematics
is like that. Almost always, there's some path to real understanding -- you
just have to find it.

------
geebee
In retrospect, I topped out in my upper division coursework for the math
major. I still got B's and even some A's in those courses (Real Analysis,
Abstract Algebra), but I was reduced to studying solution sets rather than
mastering the material creatively. This was when I got more interested in
applications (optimization, scientific programming, etc).

I figured I'd pick a grad program in Industrial Engineering so that I could
get away from math and more into applications. Unfortunately, I picked
Berkeley. A graduate intro to optimization was pretty much a series of proofs
about convex sets. Same deal for stochastic processes (it might be different
with different professors, though). BTW, this isn't meant as a knock on
Berkeley - this theory focus is a big part of why it's such a powerhouse
program. But it probably wasn't the right choice for me. I've heard Stanford
is more flexible (I've also heard the grass is greener, so who really knows).

At this point, I topped out in grades as well as understanding, because I
didn't have the motivation to continue. I tanked, and squeaked by with a MS. I
actually missed problems that I would have gotten right as an undergraduate. I
was thinking "I've had enough of proofs, I just don't want to do this
anymore."

In a way, I got a lot out of the experience. My interest in academics waned,
and I pretty much just started hacking with like-minded students. In other
words, I finally, belatedly arrived at the process of becoming self-educated,
which is really the only kind that sticks, right?

------
nostrademons
Long division. 1st grade.

I never really topped out, because I always figure that when I don't
understand something, I'm not smart enough to get it _yet_ , but that doesn't
mean I'll never get it.

This pattern started, as I said, in 1st grade with long division. My dad had
been trying to teach me math early, and I whizzed through addition,
subtraction, and multiplication, but I just couldn't understand long division.
My mom (who always took a dim view of acceleration) said "Just let him learn
it in school with the other kids." So that's what we did, and when 3rd grade
rolled around and we did long division in class, I got it right away.

I did similar things with algebra (dad first tried to teach me it in 2nd
grade, didn't get it then, but I started rederiving it on my own in 6th grade
and my teachers figured it was time to get me an algebra textbook) and
logarithms (which I first tried in 8th grade, but didn't understand for 4 full
years...that was my block through all of high school).

As for how far my formal mathematical training has gone - I aced up through
vector calculus in college, and also took discrete math late in college and
aced it. Also took Functions of a Complex Variable and Mathematical Logic, but
got lost around halfway through each of them. Passed, but not really competent
in them.

~~~
eru
Most of us have forgotten how to do long division on paper - I guess. It is
quite a nice exercised (if a bit geekish) to rediscover it on your own.

------
mnemonicsloth
With one notable exception, math seems very easy to me. I open the book, write
down verbatim anything labeled _Definition_ , _Theorem_ , or _Lemma_ , and
trace through anything labeled _Proof_. There's nothing particularly hard
about it -- you just have to make sure you actually _do_ every step listed
inside your head.

It is a little slower than reading for pleasure, but with practice, I'd say
only by about half.

I think the primary reason I do well, though, is that I take adderall for
ADHD. Stimulants make it trivially easy to maintain the necessary level of
focus, but whenever I forget to take them before a lecture or study session,
I'm gnashing my teeth and tearing my hair out by the end.

~~~
jfarmer
As with most subjects there are levels of understanding.

One level is the ability to understand what other people are saying or doing.
Another is the ability to do it yourself.

Once you get to higher level classes, at least where I went to school, the
reading is relatively light but the work is relatively hard.

I don't think most people had trouble understanding the proofs -- they had
trouble applying the lessons in a novel way to exercises and problems they'd
never seen before.

------
tjr
I went to Cornell College, which schedules classes on a "block plan", one
class at a time for a month each. My first semester, I took four consecutive
courses in calculus. By the fourth one, I was extremely burned out on math and
barely squeaked by.

I ended up taking a couple more math classes before graduating (discrete math
and linear algebra), have continued to study math on my own, and have recently
been contemplating a master's degree in math, just because I want to learn
more.

All of that is to say, I'm not sure that the math brick wall is constant, but
perhaps sometimes you need to take a break to allow your mind to digest what
you've learned so far.

------
ctkrohn
When taking 2nd level honors linear algebra, we were given a takehome exam. I
spent ~40 hrs on it and got just under the median grade. I was able to pull
out a decent grade in that class, and I graduated with a degree in math, but
now I know I'm not smart enough to hack it as a professor.

Not that I'd want to, anyway. Math is a great subject, but it's not what I'd
want to do with my life.

------
cperciva
Algebraic number theory, when I was a graduate student in Oxford.

Well, sort of -- by that point I was pretty firmly on the CS side of the
fence, and was just sitting in on the number theory classes out of interest. I
probably could have grokked class field theory and L-functions if I had taken
the time, but I was busy and it wasn't my research area...

------
epi0Bauqu
Didn't. Just lost interest.

~~~
mattmaroon
Same. Realized I wasn't going to go through life as either a mathematician or
a physicist, so didn't pursue beyond Calc 2.

------
ekzept
there's learning on an academic track timeframe, and there's learning. there
are lots of courses i took which i did not do well gradewise, but i learned a
lot, enough to go back and re-learn the material at my own pace and better.

ultimately, all learning is self-taught.

------
strlen
My undergraduate degree is in Computer Science, which at the time I attended
the university was (if one was doing their degree in the College of Arts and
Sciences vs. School of Engineering) in the math department. In the end I ended
up going further than I would have naturally (just by the nature of department
requirements).

First response to this question would be "what kind of math"? In terms of
continuous math, I've topped out at Differential Equations (much like any
other CS Major). In terms of discrete mathematics I topped out at abstract
algebra (the first class that made me sigh with relief upon seeing actual
numbers) and combinatorics. I felt that I could certainly go on further in the
discrete field (I particularly regret not taking number theory - other than
what I've learned in cryptography courses - and graph theory).

I could have received a Math major, but that would have required taking the
analysis series (real and complex), which I felt would go beyond my level of
abilities (particularly since I was aiming for an early graduation and wanted
to take as much of classes that I felt would interest me more).

------
jimbokun
I was required to take two semesters of Statistics as an undergrad. I didn't
think it was especially difficult, but I didn't see applications for the
things I was interested in (mainly Computational Linguistics at the time).

A few years later, pretty much all Computation Linguistics/Natural Language
Processing research revolved around Machine Learning approaches, which is
largely Probability and Statistics applied in various ways. I really kicked
myself for not taking Statistics more seriously at the time, and not learning
more.

I was away from this field for about a decade, but have been working with
researchers in this field again in my current job and have been taking classes
to catch up. In addition to Probability and Statistics, I've been learning
Linear Algebra as fast as I can and want to take a course on Optimization.

So, I suppose the moral of the story is: you never know when that particular
branch of Mathematics that doesn't seem at all relevant to you might suddenly
turn out to be very relevant.

------
jfarmer
I have yet to find it, but Algebraic Topology took me a long, long time to
get.

~~~
mnemonicsloth
My first thought on reading this was "dude, you stole my answer."

After thinking about it for a while, though, I think General Topology is
worse. I still don't get it. Or, what's worse, maybe I do get it, and just
don't care enough about the subject to register that fact.

~~~
davo11
I got it I think and still open up the books every now and then, but it was
about topology and model theory that I started to question its applicability.
I remember asking my lecturer this (I could have phrased it a little better in
hindsight, I sort of burst out during a lecture 'whats the point of this' The
lecturer got a little upset :-)).

Transfinite numbers are always my favorite example of something way out there,
different sorts of infinities and which infinity is bigger than the other, the
models are beautiful, but I couldn't spend my life arguing about them. I think
for most people maths starts losing its relevance a lot earlier, it justs
takes some longer to admit it, because it's prettiness is so seductive :-).

------
rms
Calculus III... I think I could have got it, but it's tough material and I had
a terrible professor, so I didn't really learn any Calculus III. I passed and
did much better in my final math course, a one semester differential
equations/linear algebra hybrid course.

~~~
rms
Also, my first semester I took one class of "Honors" calculus which was a
proof based differential+integral Calc course. I dropped that really fast in
favor of Calc II. So I also hit a wall at proof based calculus. Most of the
people who actually took the class didn't get it either and resorted to
memorizing all the proofs needed to derive calculus.

------
vegai
I never bothered to invest much to the math classes. The benefit didn't seem
so large.

Of course, now I see how completely stupid that line of thought is. The time I
saved by not attending classes or demonstrations was indeed not well spent.

------
a-priori
My most advanced math course is currently Calculus II (integral calculus and
so on). However, I don't believe it's my "wall", and I'm planning on taking
courses on differential equations and linear algebra whenever I have some
time.

------
rw
Set theory & mathematical logic.

Learning math is all about spending time with the material. I find that upper-
level math is easier than lower-level topics. Less grunt work, more pondering.

~~~
mnemonicsloth
Foundations proofs are _the worst_. I can still remember proving something
like "For every left-paren, there is a matching right-paren." Ugh.

------
thorax
I don't know if I topped-out, but I did lose interest. Calc III felt hard with
not very much useful information (my comp sci advisers basically gave me grief
for taking it). Linear Algebra sparked my interest again, but only because it
started out wicked hard and then (just like with Calc years before), it just
"clicked" and suddenly it was a lot easier/interesting. I didn't pursue
further because after I graduated I preferred diving into new compsci (and
engineering) concepts rather than focusing in math areas.

------
voidfiles
Last class I attempted was trig, and failed completly. I enjoy math, but have
given up untill after I finish collage.

------
edw519
I'm still asymptotically approaching the "top out limit point".

------
nothingHappens
I very nearly hit that point taking Differential Equations my last semester,
but thanks to persistence and a very helpful prof, I got over it. Not sure
where I'd have ended up if I kept going, but I've always regretted not taking
more abstract/"modern" algebra

------
Tichy
Seems to me all or most human understanding of maths is poor. Most things,
even if we can prove them, we can not really understand them.

I wonder if there is a different way to understand maths out there.

~~~
nazgulnarsil
you're probably a victim of rote learning math classes. learning math for real
(getting it) is not a linear process. lots of aha moments where lots of
concepts fall into place suddenly and then you move on to more advanced
things.

that said, I would consider everything below calculus to be merely clever ways
of tallying stones. algebra can be tricky at times (abstract algebra sucks)
but it is really not that interesting in of itself (yes you can solve a lot of
practical problems with it but the questions aren't generally interesting, so
the answers aren't that interesting). you do need to have it down pat in order
to "get" calculus however. And if you "get" at least the basic concept of
calculus down a lot of things fall in to place.

OTOH I could be totally biased and/or wrong, but I personally didn't really
see how math could describe complex systems in a way that let me _get_ those
complex systems until calc. Some really mind blowing aha moments.

~~~
Tichy
I did understand a lot of maths, I just mean that I think the way we do maths
often is not really understanding. If we have proved something with a hundred
step proof, I might be able to verify every single step of the proof and
conclude that it is correct. But we might not really have a feel for why it is
correct. Can't really think of a good example right now :-/ I mean usually we
jump through quite a few hoops to prove something - maybe there are other ways
of looking at it that would make more sense.

One example might be the autistic people who just know if a number is prime or
not. Not sure if they are really doing anything special, or just calculating
really fast, though.

~~~
eru
If you search long enough you usually hit upon a prove that does looks more
like a really explanation than like pulling a rabbit out of a hat.

------
cousin_it
Got my masters in math, then kinda lost interest, but I'm pretty sure that
everything is understandable with a little effort. When I get genuinely
interested, no effort is required at all.

------
jamiequint
Vector Calc, because I stopped caring. Somehow Diff. Eq. held my interest but
vector didn't. Calculating the area of partial 3D oval objects for the sake of
doing it was painful.

~~~
eru
Diff. Eq.: Difference Equation or Differential Equation?

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eru
Perhaps differential equations for me. But that's more a question of
motivation. I like optimization more and look forwand to having more lectures.

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streblo
Multivariable Calc and Linear Algebra kicked my ass. I didn't really do much
beyond that.

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maxklein
Math is pointless if you are not planning to apply it at some point in your
later career. Learning algebraic topology when you are studying digital
circuits is like learning literary analysis - it may make you feel smart, but
it's a damn waste of time.

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akd
My first math class at MIT. :-\

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loowee
Geometry, Logic, Trigonometry

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LPTS
For me the brick wall was social, not related to the math, and I hit it in
geometry class in 10th grade. Our teacher was an idiot, and had trouble
solving the more difficult proofs at the end of the homework. Day after day I
would go up to the board and write down the solution to the problem he
couldn't solve. Then, I would get an F for not turning in my homework, which I
rightly considered to be a waste of my time, and the people who copied down my
answers would get an A's. That was when I decided I had enough formal
mathematical education. I taught myself the math to do AP chemistry in high
school and tested out of pre calculus in 2000 in college. I am currently
teaching myself calculus from Michael Spivak's Calculus. You couldn't get me
back in a math class, but I love learning math.

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pageman
did he mean "tap out"? as in UFC "tap out"?

can't get enough of Math (although I barely passed Linear Algebra and
Numerical Analysis). Maybe it's the challenge. I shall try more of it when I
take up a Masters in CS. :P

