Help Me Get My Math Back? 467
nwm writes "I am trying to refresh my math skills back to the point that I can take college-level statistics and calculus courses. I took everything through AP calculus in high school, had my butt kicked by college calculus, and dropped out shortly thereafter. Twenty+ years later, I need to take a few math courses to wrap up a degree. I've dug around some and found a few sites with useful information, but I'm hoping the Slashdot crowd can offer some good resources — sites, books, programs, online tutors, etc. I really don't want to have to take a series of algebra-geometry-trig 'pre-college' level courses (each at full cost and each a semester long) just to warm my brain up; I'd much rather find some resources, review, cram, and take the placement test with some confidence. Any suggestions?"
Why? (Score:5, Insightful)
If you're job hunting, your time would be better spent making yourself relevant to current employers or starting a consulting business than trying to match your calc and trig skills with a recent grad and get a degree.
A degree is a nice "filter" when hiring new applicants, since it proves that they were able to deal with BS for at least 4 years, however with 20 years of actual job experience, you'll do much better off trying to differentiate yourself from the recent grads than you will if you try to "look better on paper."
That said, if you want to do this just because it's "unfinished business" lots of community colleges have entire departments dedicated to getting us old folks "up to speed". Just stop by and talk to someone.
Hard work should do the trick (Score:4, Insightful)
Most text books have practice questions for each chapter, and some answers in the back. Why not just work through some of those on your own? Math is the kind of subject that you can only learn by doing problems, so I don't think there's any shortcuts. But I suppose if you work on problems, it's nice to have a teacher to help if you get stuck, but perhaps a reasonable substitute would be forums.
A Bit of Advice and a Few Suggestions (Score:5, Insightful)
What you're mostly going to find in these replies are codices. Not teaching. Not knowledge. You're going to get information sources. What you do with those sources, that will be the teaching, the learning and the progress. No one's going to help you get your math back but you. You're going to get static nonliving information and it's going to be up to you to bring that alive. Frankly, on your part it's going to require the will of a volcano otherwise I suggest a tutor or precalculus class.
The course I can refer you to echos my sentiments [mit.edu]:
This material could conceivably be studied by a student on his or her own, but this seldom works out. Students tend to get stuck on something, and, having no goad to keep them going, they try to get past it with decreasing energy, and ultimately develop mental blocks against going on. Having an organized course prevents this by forcing them to face obstacles like exams and assignments.
If you attempt this and get stuck, as is almost inevitable, you could try emailing us and we can try to unstick you.
Did you catch that last part? You're going to need help. Whether it's bribing your nerdy friends with cases of beer or Star Wars Galaxy Series Five collectible card packs (*cough* *cough*) you are going to need guidance at certain points in time. Don't be afraid to ask those around you or -- and I recommend this only in dire cases -- dressing up like a student and rolling into your local university asking to see the precalc professor for help.
Your codex might be Wikipedia [wikipedia.org]. Your codex might be Wolfram's MathWorld [wolfram.com]. My codex sits three feet in front of my face as I type this. My codex (and this is purely personal) Bronshtein et al's Handbook of Mathematics [amazon.com]. The binding is acceptable. The paper is not the greatest. The content is priceless. This is not a teaching device. This is my starting point. If I were you my ending point would be at my college's library pouring over all calculus textbooks. The great thing about this starting point is that I like how it lays out all the starting points leading up to that starting point in case I need to start backwards. Another great thing about this particular resource is that it has nearly everything imaginable and is well organized. The bad thing is that it costs $71.97. I think I paid $60 for mine but either way it's not free like Wikipedia.
I don't know where you are comfortable starting from but if I were you I would simply research what your learning institutions pre requisites are and spend your free time now acquiring their books and notes in order to make sure you have them covered. All of my old University of Minnesota syllabuses are online [umn.edu] although I cannot find the Math department equivalent (aside from the registration listings).
If you could name your courses, I'd suggest books like The Annotated Turing [theannotatedturing.com] which has been a page turner for me and actually starts with basic set theory to work up to automata. I'm guessing you're aiming for more Multivariable and Diff Eq type stuff. Let us know what the courses are and perhaps more human readable works can be suggested that aren't as laboriously mind numbing as reading a codex would be.
Motivation (Score:5, Insightful)
Sigh... (Score:3, Insightful)
I find it profoundly unsatisfying that you have to ask this question.
It's not your fault; it's the structure of the educational system. You are clearly not interested in mathematics, since you just want to cram and pass some test. You don't specify exactly for what you need mathematics, but I'm guessing it's for some other thing, possibly something computer related.
It's a big lie that you'll ever use calculus for anything except for specialised degrees (and if you were to use it for anything you personally would want to do in your future, you would already be interested in it). It's also profoundly strange that calculus seems to be pinnacle of mathematical education if you're not going to go on to study something like mathematics itself or physics.
To put my frustration another way, why doesn't anybody ever ask similar questions for sculpture, or Schaum's Outlines on Basket Weaving or all the other myriad useless things we humans do for our edification? Why is western society obsessed with mathematics, deluded into thinking it's useful in general, and why are people so stressed over learning this useless and dryly-presented subject? Why aren't you required to achieve a certain level of chess expertise before you can complete a computer science degree? A lot of early computer science was concerned with chess playing, let us not forget!
It's pointless. It's pointless to cram for exams about subjects you don't care about in order to satisfy requirements you don't genuinely need.
My recommendation is, are you really interested in learning this stuff? If so, just spend hours and hours in your local university library in the math section browsing books you're interested in. If you're not really interested, go grab some Schaum's Outlines or the Complete Idiot's guide or whatever, and use that to pass whatever bureaucratic and pointless requirement your educational institute imposes before you're allowed to study what you really want to study.
Re:If you can't handle calculus, science isnt for (Score:4, Insightful)
Newtonian physics (Score:2, Insightful)
I remember Newtonian mechanics as the best applied calculus class. If you didn't like calculus as math, maybe this will work out better for you. It links math with more physical (useful?) phenomena.
If not, I don't have a clue what would help you, since I found college calculus much better than AP high school stuff.
Re:If you can't handle calculus, science isnt for (Score:5, Insightful)
Really... No business getting a degree in ANYTHING? That's a rather closed and inappropriate (IMO) view. If he's worked in a field for years that doesn't require he use any algebra how's he supposed to keep up with his skills other than doing algebra problems in his spare time? He never indicated the degree he's completing was heavily math-biased or math-dependent. Stats and Calc may be akin to gen-eds.
When you paint such ridiculously broad statements you risk your own image before anyone else's.
Still, if you can't even pass calculus then there's something wrong. And that's not even the problem- he's looking for help preparing for the placement test. If he's let his skills deteriorate so far that he forgets algebra, then he has no business getting a degree in anything.
Re:Always without a calculator. (Score:5, Insightful)
"Bombed back to the stone age" is best regarded as just an expression. The iron age is here to stay, no matter how much civilization declines. Even if we forget how to smelt iron ore, there would be billions of tons of refined iron lying around in abandoned machinery, buildings, and such.
Re:If you can't handle calculus, science isnt for (Score:2, Insightful)
It's the same deal as people who say others can't learn to do art. Their skill makes them feel special and if someone else can learn to do it also, their specialness is threatened.
And saying that someone should not be awarded a degree because they don't know algebra is extremely arrogant and ignorant. There's a reason why they TEACH algebra in colleges.
Re:If you can't handle calculus, science isnt for (Score:2, Insightful)
Re:If you can't handle calculus, science isnt for (Score:5, Insightful)
No matter what kind of scientist you plan to be, your knowledge of calculus will be essential. You'll never use statistics
This has to be about the worst piece of advice about a science education I've ever seen. Like anything, it depends. Calculus is extraordinarily useful to someone in physics, but less so in biology. Statistics is insanely important in an experimental science (actually it's insanely important in just about any science I can think of). Hell, statistics should be a mandatory class taught in High School. It's far more applicable to everyday life than trig is.
Re:If you can't handle calculus, science isnt for (Score:5, Insightful)
They want you to pass calculus for a reason. No matter what kind of scientist you plan to be, your knowledge of calculus will be essential. You'll never use statistics but you will need to use calculus every day.
Are you wooshing me here?
Having an understanding of what a derivative or integral of a function is a good insight to have, no doubt.
But I would argue that statistics is much more broadly applicable, and extremely important for a clear understanding of scientific discourse and all the 'facts' that the poster will encounter.
In reply to the original query, what you're going to need to do is a lot of problems. You need to look at this like getting in shape--you can't do it overnight.
I returned to college after about 5 years off and needed to take placement exams myself. Turned out the test allowed using a Ti-89. I cheated myself out of really 'placing' myself by being able to approximate/calculate all the multiple choice answers and placed highly.
After a few attempts in the classes I was placed in, in the end, I re-took precal and calculus.
I could have avoided that if I had actually done a large volume of problems rather than skimming some books and looking at the answers and deciding that it was 'easy enough'.
Never look at the answers of problems until you try them. Once you know the right answer, you convince yourself the problem was easy and that you didn't need to do it. This will fuck you over in the end.
Find an approach to doing math that makes it enjoyable for you. One thing that helped me a lot was getting a large whiteboard. I find I enjoy doing math more pacing back in front of a board and whatever else comes along with doing work on a board rather than a piece of lined paper. Chalk would have been better.
Lastly, ignore the assholes here who are going to berate you for not knowing what they think is simple, obvious knowledge. Math is rife with 'tricks' and non-intuitive methods to solving problems that come through experience. Someone who had a good experience with math through school and went straight into college is not going to understand your position.
Good luck to you, and if you really want this, do problems and problems and more problems. Put on some music you love and shred through a book or two. Get help at local colleges. Bribe a friend to help you study, or just hire a tutor.
Otherwise, you're going to end up doing it by taking the classes (as I did). One way or another, you have to do the work.
Practice, practice, practice (Score:3, Insightful)
The parent is absolutely right. You need practice. Actually, you need what Anders Ericcson calls 'deliberate practice'. Solve every example in the book as follows:
Write down the problem. Close the book and try to solve the problem. If you got it right, go on to the next problem. If you didn't get it, look at how the example is solved. Close the book and try again until you get it right. Repeat until you have solved every example in the text.
Check out this article: http://www.conestogac.on.ca/~bcoons/readings.html [conestogac.on.ca]
BTW, Jamie Escalante, http://en.wikipedia.org/wiki/Jaime_Escalante [wikipedia.org], just died. He was the real life teacher who proved that you can teach calculus to just about anybody. They made the movie 'Stand and Deliver' about his life. Ability is highly over-rated. Most people can, as Escalante proved, learn math to quite a high level of accomplishment.
Most people think math is some magic thing that some people just can't get. They are wrong. Almost everyone is wired to learn math. If you are missing some important skills, go back to the level where you were good and start from there. John Mighton points out that most people discover that they have no math ability the same year they have a bad math teacher. ;-)
If you want, you can learn math as long as you practice, practice, practice.
Re:If you can't handle calculus, science isnt for (Score:5, Insightful)
I do a lot of molecular biology. I've never thought of it as like the humanities at all. It's always seemed a lot more like computer programming to me.
Re:Sigh... (Score:5, Insightful)
Why is western society obsessed with mathematics, deluded into thinking it's useful in general, and why are people so stressed over learning this useless and dryly-presented subject?
Essentially because:
1) Everyone should learn logic and disciplined thought. Otherwise you'll end up with adults who can't read instruction manuals, have an attention span of 5 year olds and can't see their own mistakes and contradictions due to disorganized thought processes and hubris. Math can have a humbling effect on people.
2) Proper mathematics is used constantly by good electrical engineers, physicists and mathematicians. If you want a good engineer, you have to teach him math from childhood. And since you can't have a grade school for scientists and another one for everyone else, everyone has to learn math.
3) Math greatly contributes to keep idiots out of the sciences, med school and other important professions.
Re:Sigh... (Score:3, Insightful)
I find it profoundly unsatisfying that you have to ask this question.
You are probably just put off by the title of this post. "Help Me Get My Math Back" is a presumptuous start to be sure, but his actual question is fine.
And his actual question is not what you addressed at all. He's just asking if you know of any place that has the information he needs in a format that is convenient to him. Your response is just a depressing and pointless toil at windmills.
Re:Sigh... (Score:2, Insightful)
1) Everyone should learn logic and disciplined thought.
They could learn those from taking courses in logic. Taking math courses isn't necessary for that.
2) Proper mathematics is used constantly by good electrical engineers, physicists and mathematicians.
But very few people out of the general population go into those fields. And I would leave out "because mathematicians use it" as a reason for studying mathematics. :)
3) Math greatly contributes to keep idiots out of the sciences, med school and other important professions.
You're right. By becoming math majors, those idiots are kept out of those important professions. Generally, from what I've seen in my own experience as a math professor, the best students do not major in math. Other math professors I've talked with have the same opinion. The best students I've had all went into physics, chemistry, or engineering. The ones who went on to major in math were among the weakest students; they went into math precisely because they weren't good enough for those other fields (and admitted it to me).
Re:If you can't handle calculus, science isnt for (Score:2, Insightful)
In sociology, and psychology some scientists build models for phenomena and those models are sometimes mathematical. I am a CS scientist but I work on building such models (models for human behaviors) and most of those models are mathematical.
Re:If you can't handle calculus, science isnt for (Score:2, Insightful)
Wow. Don't hate on it just because you thought "hey I'm 'good with computers' and this major says Computer in it" and got burned by math expectations. If you don't love math, you have no business being in CS. Computer Science is a of field mathematics, not an engineering program where you learn to fix and build computers!
For (potential) CS freshmen, I recommend going through the classic SICP video lectures [mit.edu]. It's very appropriate how Sussman says over and over things to the effect of "we don't care how this would actually work, we're studying the theory." If that doesn't excite you, or you think functional programming is stupid and inconvenient, or if you can't follow a word he's saying, for your own good switch to a different major because it only gets harder and more theoretical. That course was given to freshmen. Clearly you weren't a good fit for CS, but that's because you couldn't handle the math, not because it was bullshit you'd never use.
It's really alarming to me how hostile a lot of posters are to academia. A bachelor's degree isn't a fast-track to get into a career, it's a period of academic study. You really have no business claiming that you completed four years of post-secondary study without some basic understanding of math- and calculus is really, really basic.
Re:If you can't handle calculus, science isnt for (Score:3, Insightful)
Re:If you can't handle calculus, science isnt for (Score:5, Insightful)
When someone suggested my skills were due to a magical innate ability, I'd get ticked off and tell them no, everybody has the innate ability. My skills, in fact, came from many hours of tedious practice, doing the same thing over and over until I got it right.
I don't think it has to be one or the other. I've never been able to draw worth shit. I probably could learn if I really wanted to, but even as a kid my skills were mediocre at best. Rational thinking and separating out bullshit from what's real I've always been very good at, even as a kid.
I think there most certainly are innate talents. The idea that "anyone can do it" might be true if we all had infinite patience, time, and motivation. We don't of course, so we gravitate towards things which we develop at with less effort. If you work at subject A and get half as far as the average person, but work at subject B and get twice as far.. which one do you think most people will pick?
It's not magic, it's just how our brains are wired.
Re:If you can't handle calculus, science isnt for (Score:5, Insightful)
Parts of biology are getting insanely mathematical. Very recently, say the last five to ten years, there has been a large influx of mathematicians into biology. They use stochastic analysis to model various processes such as transmission of genes to offspring and growth of cell populations.
A decent fraction of the PhD students in my department (maths) are involved in biology.
Re:Engineering Math by Stroud (Score:1, Insightful)
*cough*
Stroud - Engineering Mathematics 5th Edition [btjunkie.org]
*cough*
Stroud - Advanced Engineering Mathematics 4th Edition [btjunkie.org]
*cough*
Terrible cough I have.
Re:If you can't handle calculus, science isnt for (Score:3, Insightful)
Unfortunately, the problem with economics is that it has TOO MUCH math in it. Or rather, it has too much math misuse.
There should be a large amount of statistics, but little calculus. That's because we're dealing with human beings and their obstinate free will. So much of modern economics is about making assumptions so that you can start applying some math to the problem. But the assumptions are often unwarranted, like micro's assumption of "perfect knowledge" that can only exist in a fantasy land.
Yes, you're going to have to do a shitload of math to get a degree in economics. But you shouldn't have to. Economics is not a hard science like physics, and should not be treated as such.