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?"
Re:Why? (Score:3, Interesting)
If you haven't needed a degree or calculus in 20 years, why bother now?
In case you haven't realised it, there is a recession going on, a -lot- of people are either unemployed, their spouse is unemployed or they need a way to secure their job. Rather than doing the rational thing of looking at productivity, most businesses hire and pay based on education. If his wife lost her job and he was expecting the income, the only way he can get a raise to keep up his standard of living might be through a degree.
Most degrees are completely useless when done for a raise, but, money is money.
Re:If you can't handle calculus, science isnt for (Score:5, Interesting)
Oh bullshit. Those are both overt and ridiculous generalizations. First off, many scientists use statistics every day (at the least, much more than "never"). Second, not all scientists use calculus "every day", and many use it almost never.
As a calculus teacher, I can tell you this: you need skills in symbolic manipulation. Your algebra needs to be rock solid before you attempt college level calculus. In my experience, you need dozens of hours of practice before you get it. Buy an algebra textbook, and do every odd problem in every section until you are reliably getting everything right. My experience = flunked high school math and went back to college 10 years later, and am now working towards a PhD in math.
Re:Why? (Score:3, Interesting)
FWIW, it's much more profitable to go into consulting and do/manage whatever it is that you're good at and happy doing, than try to maintain a dead-end job as one of the "cogs." Businesses are much happier to pay someone a good rate for services that they need, when they need them, as long as the consultant will happily vanish when the need vanishes.
Re:If you can't handle calculus, science isnt for (Score:4, Interesting)
I would mod you up if I had any points. Sad as it may seem calculus was where I *learned* trig. For me, trig is one of those subjects that you beat your head against for months and years and one day *POOF* it makes sense. My first semester of college level calculus was were I learned trig. The second time I took that first semester of calculus - man I got it.
Don't forget to brush up on the basics - algebra, trig, analytical geometry as well as your calculus.
goes looking for an old text book just to tinker around with it.......
Re:If you can't handle calculus, science isnt for (Score:3, Interesting)
You'll never use statistics but you will need to use calculus every day.
Statistics is great for figuring out when you're being lied to, so go ahead and learn it or prepare for a lifetime of being easily manipulated with real-sounding BS.
Re:If you can't handle calculus, science isnt for (Score:3, Interesting)
As a calculus teacher, I can tell you this: you need skills in symbolic manipulation. Your algebra needs to be rock solid before you attempt college level calculus. In my experience, you need dozens of hours of practice before you get it. Buy an algebra textbook, and do every odd problem in every section until you are reliably getting everything right.
I couldn't agree more. My better students are invariably the ones who can do basic algebra in their sleep. Those who struggle are those who never learned high school algebra (or god forbid, arithmetic) well.
Re:If you can't handle calculus, science isnt for (Score:3, Interesting)
Re:If you can't handle calculus, science isnt for (Score:5, Interesting)
That has to be one of the most useless statements I've read on Slashdot. Statistics is one of the most applicable branches of mathematics; it does the best job of allowing us to model our observations of events, since we understand 0% of the world around us well enough to say with 100% confidence what the outcome of a certain event will be.
Not only is it an extremely important field, it's an extremely understudied and undervalued one. I avoided statistics until I began my master's degree, and if there was anything about my educational career I could change it would be taking an intro to statistics course in my undergraduate years, or even AP Statistics while in high school because of how applicable it is to everything.
Re:If you can't handle calculus, science isnt for (Score:1, Interesting)
I would add - get a college physics text. There's almost no better way to get some algebra/trig/basic calc practice than to work on physics problems. I remember thinking that my Physics 1 class at the University level was really just an algebra/trig class in disguise. Helps to get some practice.
An interesting thing to note about calculators - in my math department Calc classes, we weren't allowed to use any calculators, but because of this, basically all the problems they gave use used 'perfect' angles - i.e. angles that corresponded to the small table of trig values we were expected to memorize - 0, Pi/6, Pi/4, Pi/3, Pi/2 (and the other angles around the rest of the circle which are really just those angles reflected across an axis).
In the calc class, since you could use a calculator, they could somewhat randomize angular values, because you could use your calculator to calculate sin(23 deg), arcTan(47 deg), etc. Actually, a lot of the problems in Physics didn't even care about concrete values - the answers were more about deriving the correct formula to find an answer, and you just left x or y or whatever as the symbolic parameter values (which is also an important lesson in mathematical thinking - formulas which solve a problem are usually more interesting than concrete numerical answers - because once you have the formula, you just plug in your values, and it spits out an answer [though as a comp sci major I might have been a little biased - that's how I tend to think anyhow: people solve problems, computers calculate answers]).
Re:Sigh... (Score:3, Interesting)
In a similar thread on Slashdot, someone posted a link to A Mathematician's Lament [maa.org], by Paul Lockhart, which I found persuasive and very moving.
I'm in a position similar to that of the original poster. I've gone back to school, after years of low-paid jobs, hoping to work towards a CS degree. I had to admit I wouldn't be able to do it -- I've found the programming and networking courses very easy, but the calculus courses I took required ten times as much study as everything else put together, and I was still doing poorly.
Yet, outside the formal coursework, I found calculus very interesting. I kept getting the sense that the course material was all but irrelevant to the subject itself. In fact, the texts go to great length to avoid discussing subjects, particularly the concept of the infinitesimal, that have some problematic aspects, but happen to be critical to the discovery and development of calculus, and are much more intuitively clear. Annoyingly, the textbook I was using kept saying that Leibnizian notation (dx/dy) was "suggestive," but never explained how or why. It was like watching a movie from the '50s, in which the characters are talking about sex, but so indirectly that it's hard to understand what they're saying.
My hope, at this point, is that I can learn enough of mathematical reasoning on my own, without going to through the pointless drudgery of math courses, to be an effective programmer.
Re:If you can't handle calculus, science isnt for (Score:3, Interesting)
It's the same deal as people who say others can't learn to do art.
Speaking as a former art major (which is why I'm a truck driver now, BTW), people who say that really used to piss me off. Sure, some folks have a huge natural artistic talent but the rest of us have to learn how to do art. 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.
There are a lot of jerk answers here (Score:4, Interesting)
Anyway, I commend you on your efforts to get back into mathematics. I started taking mathematics courses well after I received my B.A. (in Philosophy) and my friends and colleagues gave me no shortage of grief over this. I don't complain when they want to spend their free time painting or water skiing, and yet-- they seem to think there's something wrong with a grown man studying mathematics. The best advice I can give you is: ignore them. Mathematics is a fulfilling and beautiful subject. At the risk of sounding like a stoner, it will open your mind to new possibilities.
You already have the important part: motivation. But motivation is not quite enough. Until you understand the weird (or I should say, counterintuitive) ways of mathematics, you really need a teacher. This is worth the money. I was in your same position about five years ago, and what I did was: start at precalculus. I signed up for a summer course in precalc and trig at the local Uni (UMass Lowell, in case anyone is wondering...), and then I worked my way through calculus, stats, discrete math, set theory, algorithms, and formal languages. I threw in a physics course for kicks, and I found that it reinforced my calculus immensely.
Remember: math is hard. But not for the reason you think. It's hard because you need to change the way you think. The problem sets are essential, because they make you understand what assumptions can be kept, and which must be thrown away. You will be a better person for it. Once you change the way you think, math is easy. It sounds trite, I know, but it is very true.
Also, Bach helps during homework.
Good luck, and do not let your friends and family discourage you. I personally believe that if you are not challenging yourself, you are not living. I would do it again in a heart beat.
Re:If you can't handle calculus, science isnt for (Score:3, Interesting)
I'm a Computer Scientist/Software Engineer (I dropped out of the research end a few years ago - my current job is R&D in the commercial realm so I'm not sure what to call myself), before that I was a land surveyor. My parents owned that business and I started work there when I was 12 (apparently that is legal for your own kids - they payed me minimum wage so at 12 I was the richest kid in school and was happy :)). As a Computing researcher I can't say I did much calculus at all. Most everything was heavily discrete math. Lots and lots and lots and lots of discrete math.
I have, however, used calculus a few times as a land surveyor even though they are less likely than a computing professional too.
We had done a topographic map of a local gas depot's containment pits for their tanks. At the time some new regulations for the pit had passed and (I'm going to botch these numbers - fine details like that were too long ago) they had to go from 105% the volume to 115% the volume and they wanted to know what their current containment was. Most surveyors know very well how to draw topo's and with software how to calculate volumes and such, this was before said tools were widespread. So I basically did an integral to calculate the "area under the curve" with the curve being a close approximation of the contours (which were smooth and a spline was highly accurate). They ended up with ~90% of the volume contained (I know it was around that - I recall a little over 10% spill over). After me redoing my numbers (still in college - who am I to contradict a licensed engineer who designed the thing) I realized the person had simply made the containment pit "square" - that is the side sloped to the bottom at around a 45 degree angle and a several hundred foot long pit dropped about 3 foot from one end to the other. The engineer took the highest point on the burm, the lowest point in the pit, and the dimensions around the outside of the pit and calculated a volume. I had less than a .5% error from his numbers from the one we produced if I used that method.
After calling their head engineer and telling her what we found she went back to the person who originally did that and asked - I was correct. I had also submitted a full accounting of how I came to my conclusion on the area. They asked me to calculate how much more needed cut, I did so, they signed off and built it, and I'm still not sure how that makes me feel. I was a college student and not *remotely* qualified to do that. I figure they had me do it for the same reasons the person screwed up - it was cheap. They payed my parents 50 dollars an hour for me to do that, their staff drew it up, and their engineer signed it. It was good money for me (they gave that financial part of the job to me) and no liability on us - we were clear we were not able to do that or sign off on it and had it in writing. In that sense I'm OK with it, in another I hope the other parts of the system were done better than that was originally. They just lucked out that I could do what they wanted and had enough knowledge to do so
I'm lucky enough to both have had the correct schooling and ability to apply that - since then I've learned a great deal and know I inferred the correct things. Yet, I really shouldn't have been put in that position, but it at least gives me an amusing story I guess. Indeed, as I have aged since then I have become more and more aware of how truly lucky they were that I still know I did a working design. I clearly recall long phone conversations where I kept saying I was still in school and they didn't care.
Then, none of this helps the OP. I do not know the answer to his/her question. Calculus was always a struggle for me due to dyslexia and an insistence on memorizing forms (thats about like demanding an armless person catch a football with their hands). I never once had the issues they stated - I was in graduate level math (graph theory and formal languages/computability) before I made it through calc II. It took
Schuam's Outline and Lisp (Score:2, Interesting)
I have the same idea as you. I took the AP courses in high school and got my butt kicked in college. I hit Math 401, aka Differential Equations, and it hit back. I didn't have a solid understanding of the basics to really tackle diffq.
Years later, I was influenced by several things:
First was Neal Stephenson's Boroque Cycle. That novel brought home the idea that math was a tool invented to solve problems and expanded minds. The second was my growing fascination with Lisp -- specifically, MIT Scheme / SCIP. By the time I started watching the first lecture, the introduction was already echoing what I felt about calculus, that software engineering dealt with idealized machinery, much the same way calculus was tool that gives us leverage.
I chose the Schuam's Outline for Calculus and started some self-study. I had also taken AP Physics, and the teacher more or less ignored our nominal textbook and used the Schuam's Outline for Physics. Although I was able to follow the derivations on the blackboard, I retained none of it. We were assigned problems out of the Schuam's Outline, meant to be two problems per week, all handed at the end of each half-semester. There were no fancy pictures, no chatty text to wade through. It was straight up physics concepts, how the math worked, and condensed down to its essentials. And lots of problems to practice on.
Of course, I procrastinated on the assignments. The day it was due, I spent every spare break time doing as many of those problems as I could. I wasn't able to complete all of them in time, but the sheer pressure of attempting that many within a short amount of time got me to really understand the concepts and how to work the math. I had no trouble with college-level physics taught to engineering students, just the calculus that powers it.
When I picked up the Schuam's Outline for Calculus, the material was much like that for physics. The concepts were not taught from first principles so much as showing you *how* to use the tools first, then later, *why* those tools worked. I was quickly able to get a handle on basic stuff that I had been vague on -- the Chain Rule, for example. I realized there were really two parts to calculus: Describing the problem (setting up the problem) in the language of math, and then symbolic manipulation. I could generally do the first part OK, considering that I've been writing software for ten years now. The latter part was where I was more hazy on, since I simply didn't know the tool. In structuring the "how to" before the "why this works", I could dive into solving my problems, then satisfy my curiosity later.
Good luck.