
Formerly good at math, but I've lost my skills. Any advice to grow them back? - gulbrandr
http://math.stackexchange.com/q/23566
======
wheels
I'd felt exactly the same a couple years back, but the root cause was rather
amusing. When I started working on stuff for Directed Edge I dove into a lot
of academic research. I found myself struggling with a lot of it. I really
believed that my math abilities had slipped significantly since my glory days
and continued with this perception for several months...

...until I picked up some stuff that I'd thought was hard in college. I was
dumbfounded at how easy it was. What had changed was not my math abilities,
but my perception of what constituted _hard math_.

~~~
nostrademons
I've noticed the same thing. I'll routinely struggle to understand an academic
paper with a notation-heavy theoretical bent, but when I found I had to dig
out high school math for a couple 2D-graphics problems recently, it all came
back easily.

When you're in high school, you don't realize how much of a gulf there is
between Ph.D/MS-level (or even professional-level) math and what you learn in
school. The public school system teaches you the barest foundations; there's a
gigantic world out there beyond it.

------
cletus
I have a similar problem actually.

In high school and even the first year of university I was pretty much a
natural at math. I'd been doing algebra and trigonometry since I was 10,
calculus since I was 13 and started on differential equations at 15.

Not that this made me any kind of child prodigy mind you but it was a fairly
isolating experience because my first 18 years took places in isolated towns
with <15,000 people so I just didn't come across other people like me or with
similar interests. But I digress...

The second year of university maths bored me senseless and it sucked all the
fun out of maths for me. Three hour proofs, numerical methods (in particular)
and so on. So I stopped doing it and just did CS instead (originally I'd been
intending some kind of double major equivalent).

Having not used calculus (for example) for years I can still remember how to
derive/integrate, etc. So I retain a decent part of what I knew (or so it
seems). But the one area I suffer in, largely because I never got that far, is
in deciphering academic papers. This applies to CS too, which is where it's a
pain.

I like dealing with actual code rather than abstract ideas put in text (and
the vaguest of algorithms that you can't just take an implement, or at least I
can't).

So my situation isn't identical to yours but I really would like to know how I
could improve my maths and CS in this area.

~~~
tel
There's an incredibly common roadblock in math education when you make the
jump from mechanical maths to creative maths. On one side, math makes sense as
a set of powerful rules which help to guide you to understand and analyze the
world. On the other side, math is more like a penpal friend while you're
living in a foreign country. It offers advice, but largely you're on your own
in a confusing land.

Academic papers are written from the far side of that roadblock. They're often
best considered anecdotal pointers to how to survive abroad rather than
comprehensive guides like textbooks (or review papers) offer. Reading them is
thus both an exercise in deciphering something distant from your comfort zone
and learning to apply its vague knowledge to your own situation.

In order to understand academic papers then, you've kind of got to become a
traveler yourself. At that point you appreciate the vague note passing because
even though it's difficult, there's a real opportunity there to see something
few ever have before.

\---

So practically, academic papers are never easy to decipher unless you're
basically part of the same communities as the authors (or they are really
dedicated and skillful communicators who have an uncommonly deep understanding
of the topics they're writing about). If you're doing work that cannot be
solved by what exists and is common knowledge today, however, they're your
best bet at finding a guide and no matter how difficult they are you want to
read them through.

~~~
eru
And even mathematical textbooks require lots of work to understand.

~~~
tjarratt
I shudder to think how many hours I spent poring over textbooks and lecture
notes just so I could have the "AHA" moment that comes along with dealing with
abstract entities.

------
chegra
Oddly enough that he should mention this, but last week or so I was thinking,
"my how I have lost some of my mathematical prowess".

There was a room of 4 males and 10 females, now there was 5 other guys who
were to be paired with someone in that room. What is the probability that the
pairs would be as follows (MM,MM,MM,MF,MF) where M=Males and F=Females.

This was a real life problem I create for myself to determine the bias by the
selector. I struggled to work it out by pen and paper. This was a problem 8
years ago it wouldn't take a minute to do, most of the work would be in
punching numbers in the calculator. Eventually, I said when I go home I will
program it up. Between the time it took for a friend to restart her computer,
I had whipped up a simulation. This is something I wouldn't have been able to
do 8 years ago.

So in a sense, I call it a skills exchange. I lose some skills and gain some
skills. I'm sure with practice I would be back up to par, the same goes for
this guy.

~~~
light3
Is the answer: 4x3x2x10x9 / (14x13x12x11x10) * 5! Is there some easier way to
solve this?

~~~
ohmygodel
You need to divide by 3! and 2!. One way to look at it is that every selection
of five from the 4M and 10F is equally likely. There are \binom{14}{5} (i.e.
14 choose 5) such selections. Of these, \binom{4}{3} * \binom{10}{2} have
exactly 3M and 2F. Therefore, the probability is \binom{4}{3} * \binom{10}{2}
/ \binom{14}{5}, or (4 * 3 * 2 * 10 * 9) 5! / (3! 2! (14 * 13 * 12 * 11 * 10))
= 10 * 9/(13 * 11 * 7) = 0.08991...

~~~
light3
Ahh indeed, I thought there were 5!=120 ways to order 3M and 2F, but
apparently there are only 5!/(2!3!) = 10 ways:
{MMMFF,MMFFM,MFFMM,FFMMM,FMMMF,MFMMF,MMFMF,FMMFM,MFMFM,FMFMM}. I made the
mistake of thinking you can distinguish between individual males/females.

------
cheez
Teach your kids (or someone else's)

~~~
abbasmehdi
Exactly! Teach anyone and explain the concepts to them. Go your local
community college and volunteer at the math clinic, even better go to a local
high school that's not been doing very well. Public school systems can use all
the help they can get.

I went from sucky math guy to an awesome math guy in just 1 year - just
because I was tutoring.

------
deskamess
I wanted to brush up on my math with a goal of shoring up fundamentals and
understanding probability and statistics (not just formulaic solving). I was
not sure where to start, so I have decided to start by practicing the
fundamentals. Addition and so on. Khan Academy has that covered. As of today
they have 'practices' that go from basic addition all the way through simple
differentiation. Most important, if you run into problems with an exercise
set, they have video links to the topic you are practicing. Once you have
watched the video and understand the concepts, you can come back to the
practice set. (RUPPPL - read understand practice practice practice loop)

You should be able to run through the set without much effort, but I think
there is value in doing these simpler exercises. It establishes routine and
steeps the mind for greater challenges.

I will likely add some permutation & combination stuff to my 'course work'
before I go on to my eventual goal of understanding prob & stats. Getting
exercise for these higher level topics will be a challenge.

~~~
tricky
This is EXACTLY what I'm doing and it seems to be working out great. Finding
exercise for the higher level topics is a bit more challenging, but there is a
lot out there. The thinkstats book is great if you're a programmer:

<http://www.greenteapress.com/thinkstats/html/index.html>

I've also been studying a berkely stats course on itunes u and working the
exams/notes from this class:

<https://netfiles.uiuc.edu/fenghong/www/STAT100/>

I'm also reading a lot about financial analysis and risk assessment to fiddle
around with real-world applications of the things I'm learning.

it's a hell of a journey.

------
codelion
The best way to study math is to fight it ... <http://abstrusegoose.com/353>

------
sudont
Similarly burned-out, I'm having trouble caring about design: learning about
how it interacts with other disciplines and practicing the skill on these
issues, rather than just practicing design itself, is essential. Design, like
math, is a problem-solving application and there's definitely a "feel" that
can be lost.

These solutions can definitely be abstracted out to other areas, but really--
what part of math can't?

------
nextparadigms
Try www.khanacademy.org

------
CallMeV
Like all things at which you have to work hard to gain ability, the original
poster has but one course: the hardest one. To delve into those tiresome,
brain-aching problems at which he once balked in school - the ones where he
found that he had to put in a real effort.

And he will have to accept lots of failures before he can start to claim lots
of successes. With nobody to mark his efforts down for not showing sufficient
workings, however, admitting to failure can come a lot more easily when you
only have your own self as teacher and student.

------
parfe
Grab a Calculus book and solve some random problems. It can get fairly
entertaining. Solving how much rocket fuel you need to reach orbit or how fast
a conical object will drain or the angle you need to fire a canon ball into a
castle wall or something. I haven't found much use for Calculus though in
regular life.

On a side note, we've been arguing about 48÷2(9+3) at the office today. There
is a correct answer, of course, but also an argument (that some think is
reasonable) against that answer.

~~~
e03179
48÷2(9+3) = 2

~~~
nlco
not quite, 48÷(2(9+3)) = 2, but 48÷2(9+3) = 288

to clarify: PEMDAS is the order of operations. so parenthesis first: 48÷2(9+3)
= 48÷2(12) then multiplication and division (they have the same precedence):
48÷2(12) = 24*12 = 288

for another reference: <http://www.google.com/search?q=48%C3%B72(9%2B3)>

~~~
sga
Best bet is to replace x÷y by x*(1/y) as division is not commutative while
multiplication is commutative. Therefore 48÷2(9+3) => 48(1/(2(9+3)) => 2

~~~
wging
You've still failed to correctly apply associativity, unfortunately. You're
treating 2(9+3) as a single unit, but ÷ appears before the implicit
multiplication between 2 and (9+3) and so should get evaluated first. The
division should get simplified first with its immediate operands, 48 and 2.
This yields (48÷2) * (9+3).

~~~
nostrademons
It's funny, the top Google result for [juxtaposition precedence] is exactly
this question, posted on the PhysicsForum boards. 2 is actually leading 288 by
a hair there.

<http://www.physicsforums.com/showthread.php?p=3235154>

Anyway, the answer depends completely on whether you believe that
multiplication by juxtaposition has the same precedence as multiplication by
explicit symbol. There're good reasons to believe it doesn't, eg. the first
post on that linked thread, but whatever the answer, it's entirely based on
typographical convention. I don't work in the community that cares, so I don't
really have an opinion, other than to point out it's not as cut-and-dried as
virtually ever poster here believes.

In the community that I do work, people who write parsers, things like this
have to be explicitly specified. That's why I maintain that the correct answer
is "syntax error".

~~~
parfe
the real answer is that thw juxtaposition rules are made up on the spit by
people trying to rationilze their incorrect answer . there is not and never
had been a n "implit mulitplication" rule in the irder if operations.

sent frim my drunk phone

~~~
nostrademons
They did, however, cite sources (possibly made up almost on the spot), which
is more than anyone on this thread has done.

------
projectileboy
This topic comes up from time to time on HN. Here's what I did to dive back
into mathematics: <http://news.ycombinator.com/item?id=108924>

------
ciopte7
Check out this blog for a lot of free resources <http://hbpms.blogspot.com/>

------
32ftpersecond
see: G H Hardy's "A Mathematician's Apology"

------
michaelochurch
I don't think you lose "good at math" if you're actually good at math. Being
actually good at math, as I'd define it, means you understand problem solving
and logical reasoning. It's not about computational techniques. Most math
professors have to review linear algebra and the calculus sequence before they
can teach their first undergraduate class.

It's like this: if you study a language intensely for a year, you'll have a
good understanding of it after that year. If you stop using it, the grammar
will remain with you but your vocabulary will fade over time. If, however, you
travel back to that country, it'll only take you a couple weeks to regain took
you a year the first time around. Math is a language, and what you lose is
vocabulary, not the language itself.

I'm 27 and have been out of school for 5 years. I couldn't do integration by
parts without consulting a textbook, and I'd probably do poorly on a Calc-3
final if I had to take it closed-book, right now, in the alloted time. But I
also know where to look when I need to review calculus or linear algebra.
There's a huge difference between "rusty" and lost skills.

For "rusty", you just need to study again. It starts out hard and gets easier
as you regain the skills. It's actually fun, at least for me, to revisit
familiar friends like set theory. And I'm still learning new things (although
not at as fast a rate as when I was in school) even though I've been out of
school for half a decade.

------
pitdesi
I'd recommend going through Khan academy and starting from the basics:
<http://www.khanacademy.org/#browse>

