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Options for Adults with Renewed Interest in Math?
Internet Ninja asks: "After only doing mathematics in high school level and in my first year of University, I've suddenly developed an interest in mathematics. Since that was now almost 10 years ago I'm a little rusty. Anything past pythagoras is a little tough for me :) but I know I could get back up to speed quickly. I could probably steal my daughters math textbooks and start reading but I'm wondering if there is a better way. I considered a part-time University paper at US$495 each and you need to do two as bridging courses in order to even start on undergraduate courses. A bit pricey when you have a home and family to look after as well. Another option was a night courses but I'm kept pretty busy with work. Does anyone have any advice or good resources?"
community college -- cheap and laid-back courses that'll give you the background you want.
2) If you don't have grey hairs, you can probably pass for a student with a little creative wardrobe work.
Given premises 1) and 2) above... well, do the math.
(The best part? You don't even have to show up for the exams!)
"I could probably steal my daughters..."
To answer your question I need to know more about this... what grade is she in? How old is she?
Brunette, red head, blonde? Please, I would love to help you but you're not giving me much to go on...
dmarien
Personally, I was in a similar bind a few months ago. A co-worker was going to school for CIS and I read over his shoulder while he did his homework. More came back to me in those few months while watching him work and helping each other out than if I'd read the book by myself.
Learning works better with two people.
http://mathworld.wolfram.com/
This isn't completely what you want, but it is a very good reference site for mathematics, from the fine people who brought us Mathematica. And it's free, and as we all know, free is good.
-twb
I have found that doing these USAMTS competition problems have pushed me forward a lot this past year of my high school career (not to mention an honorable mention finish). Try it and see what you learn. For those high schoolers out there, its a nice competition to get into, the only thing you pay is postage to send your answers in.
I'm the Devil the Windows users warned you about.
Here are a couple of other ways to use your local university:
(1) You can register as an official auditor. That means you can go to lecture, and usually take exams and have them graded. You won't be able to use the lab, if there is one. This gives you a more official status, and makes it easier to get your exams graded, and so on.
(2) You can enroll in summer school. A lot of universities have summer sessions that are open to everyone who is over 18, or who has a high school diploma, or who has permission from their high school principal. They charge full rate but you get 6-10 weeks of intensive academic whoop-ass.
It's up to you whether you can go the independent study + book route. That works fine for math, but it's a personal character thing whether you can discipline yourself to do it.
Web sites, et cetera, are hokum. A good book is much much better. Just go down to your college bookstore and browse some. If your math is at high school level, browse the "freshmen bonehead math" books.
It sounds like the real problem is going to be creating a space in your life to work on the math every damn day. Math is hard and takes a lot of sweat. Learning calculus is like, say, running a 10k race -- you are not going to get there with an earnest attitude or even just by buying the magic equipment. You get there by training every day for weeks or months.
And similarly (speaking as a big math geek and a horrible runner who can barely make 10k) -- don't worry one bit about other people you encounter who are way better than you. When I see some elite runner go by me, I just congratulate myself that I'm on the same path as them, propelling my fat geek ass under my own muscle power. It's okay to be a newbie, especially at something tough. Just get in the game and stay in the game.
Yes, I second the importance of asking yourself this question.
I have an intensive classic liberal arts education. Calculus directly from Newton and Leibniz, for example. This is great for understanding what the calculus really is, but very poor for doing the kind of calculus that people do as a practical matter.
The thing to understand in science and, yes, even math today, is that these have become almost completely technical fields -- that is "technical" in the sense of "technique". To be functional at all working in any of these fields requires the acquisition of a great amount of particular knowledge and technique that is not at all about a deep comprehension of the subject matter in general. A lot of my fellow alums find this out the hard way if they continue on to graduate school in a science, even though they tend to be accepted to the best schools. They have a lot of catch-up to do about the nitty-gritty stuff. On the other hand, their deeper comprehension serves them well as students and working scientists not infrequently.
The point is that if you want to just really get into math because you want to know more about it, then you should not try to duplicate what someone does who is studying it for professional purposes. You should approach it from another angle; then, if you choose, supplement your general knowledge by beginning to acquire proficiency in the specific. You'll also have a better idea of what interests you before you go the distance by learning much of the minutae necessary to even have a decent comprehension of actual contemporay work done in these fields.
The people doing this stuff for a living (or are students until they discover that they can't find a job and do this stuff for a living) will snobbishly dismiss a liberal arts approach to these subjects as being a waste of time or as some sort of pretense of learning that's not really there. Ignore them. They can't see the forest for the trees, and they shouldn't. That's not their job. For you, it's probably more fun to first examine and think about the forest before you start getting intimate with the trees.
I wonder if you have education versus career reversed?
I mean, I can think of very few professional degree programs that even get into multivar calculus. At my university, that's quite an optional endeavor for anyone but math majors!
Lots of science majors take calculus, but it's brief calculus.
Now, I'm in something like the same boat as the original poster. I was good with language, never with math. I failed every math endeavor I attempted, scraping through college on a liberal arts degree by barely passing the algebra requirement. That was then. At the age of 35, I discovered a new interest in learning math for its own sake, and am now doing a part-time program at a university majoring in math!
If I had to do this for "career" reasons, I'd not be able to. It's only because it's education for its own sake that I can even face it. I'm hoping to retire as a math professor someday. I don't want to teach NOW, but as a gray, when the business world doesn't suit me anymore, hopefully I can still work as an educator!
-fb Everything not expressly forbidden is now mandatory.
I'm a math prof at a small private college. My students who have taken courses at community colleges repeatedly tell me that the classes are so much better at our school than at community colleges. At small private colleges, your math courses are taught by real, professional mathematicians with Ph.Ds. The Ph.D. is not always directly relevant, but it does give your professor the authority to look far ahead of your current coursework and tell you what is relevant and what is not.
Community college professors are usually masters (or less) degree instructors, perhaps working part time teaching while also doing other jobs. They have far fewer rigorous evaluations of their teaching, and they do absolutely no real mathematics research, so they don't really know what mathematics is actually important and what isn't.
Professors at big universities also have Ph.Ds and do research, of course, but they are paid primarily to conduct research and teach graduate students; undergrads are the lowest priority for them.
(Also in response to all of the comments/flames below)
A *huge* part of which is "better" depends entirely on the instructor. I've seen fantastic University professors, and fantastic college Instructors.
One thing is for sure though: College will be cheaper, and University will have more depth. I'm sorry to all the flaming college advocates, but in general you simply will not find hard-core mathematicians working at a community college.
If you want basic multivariable calculus, maybe a little bit of algebra.. yes, college is they way to go. If you are serious about a deep study of mathematics... you simply cannot beat training with people who are ACTUALLY ACTIVELY DOING IT. University professors, as part of their jobs, are required to engage in active research in their field of study. The same is not generally true of college instructors.
I'm *not* putting down colleges by ANY stretch of the imagination. I'm just saying that colleges tend to focus more on "pratical mathematics" (e.g. "here is the math you need to be an engineering tech"...) whereas a University math department will focus on "theoretical mathematics" (I feel silly typing that.. but you get the point). It really just comes down to what you're interested in learning, and what you want to do with that knowledge.
In any case, good luck to you and welcome to the wonderful world of mathematics!
I am a math professor at a liberal arts university and we have a "non-traditional" student (he hates it when I call him that) who went back to school for reasons like the one you mention. However, he has is doing it full time; he was a fairly successful consultant/businessman and took early retirement. Sounds like you don't have that option.
If you have a fairly week background in mathematics, you are going to need to "go to school". By this I do not mean that you have to register for a class. I mean that you need to be around people who are learning mathematics and talk with them - a lot. Students will typically tell you that they learn most of their mathematics not from the classroom setting, but talking with other students. Especially at the early levels, learning mathematics is very similar to learning a foreign language; to really learn it you must surround yourself with people who speak the language.
Our non-traditional student has learned this lesson well. For all intents and purposes, he lives in the math lounge across from the department. He even does non-math homework there just so he can be around when someone comes in to study math. He also gets the bonus the faculty come in and talk to him when they need a break. We don't always talk about the material he his studying; sometimes we talk about something that was in the news or something we are working on. But whatever we talk about increases his math vocabulary and exposes him to the important concepts in mathematics.
If all you do is night classes, you will not get this, even if you go to some of the best teaching schools in the country. And you certainly won't get this from reading books. So what is there to do? Many good liberal arts universities have math clubs that are intended to "popularize mathematics" and draw in new majors to the department.
A lot of times, these clubs pull in speakers to talk about jobs in mathematics. However, these clubs also farm for Putnam contestants (the big undergraduate mathematics competition) and hence sometimes work on problems. Putnam problems can often be understood with very little mathematics (though their solution is far from simple).
So, if you have a liberal arts university in your area, you might want to check if they have a math club (And whether it actually does math, or is just a social club). These typically meet in the evening and would give yourself an opportunity to surround yourself with other people learning math. This is not a substitute for learning math, however. You will still need to start either reading or taking night courses in order to learn the basic "grammar".
I take it that you're interested in math itself, not necessaarily interested in pursuing a degree in math. Trying to learn most things through formal education is like trying to paint a barn with a brush that only has 10% of its bristles. You'll get it done eventually, but boy is it inefficient.
One of the few advangates that formal education provides, at least in terms of learning, is the step-by-step programmed nature of it. If you're trying to learn something and you don't know how to approach it or what to study, then formal instruction can work. However when you know what it is you should be studying and learning, then formal schooling is usually a hinderance because you can learn things more quickly and more thoroughly on your own, assuming of course that you have some degree of discipline. The forced nature of formal education is its other advantage, and it is a dubious one at that.
Formal education is geared towards the stupid and lazy. For someone who is intelligent and industrious it usually gets in the way more than anything else.
Primary and secondary school spends twelve years teaching those of average intelligence what those whose IQ ranges in the top 10% can easily learn in six. I should know because when I was in sixth grade my "achievemnt" test scores were on par with most college students. My IQ is about 130, or in the top 10%. Of course my teachers all thought I was much brighter, but then they're not used to dealing with someone like me and are, by and large, not too far above the 50% percentile themselves.
College courses are better in that the instructors aren't there to babysit anyone. Also anyone who is either stupid or lazy doesn't usually stick around for long. The pace of study and depth in which the subject is explored can vary greatly however. There have been courses I've had to work pretty hard at, of course those have almost always been the ones that were worth taking.
But anyway, my point is don't spend money to take a course when independent discipline and effort will get you farther in your pursuit of knowledge. Spend money on courses only when they are required for some other purpose independent of learning, such as a job. Don't rely on them as your sole or even primary form of education. Rely on yourself and you'll always be ahead of curve.
Lee
Muslim community leaders warn of backlash from tomorrow morning's terrorist attack.
Ask [your daughters] to teach you.
This is the best advice so far, because it will help you and your daughters. One of the things I learned while I was a math tutor was that I didn't know dick about math until I started tutoring. Sure, I had made it to Calculus, and I could keep up at that level, but I didn't know math. It has been said that the best way to really learn something is to try and tech it to someone else, and I've found that it really is true.
Having your daughters teach you the math they're studying will help you relearn the things you've forgotten (or maybe even teach you new things, depending on where they are at), but it will help them even more through the increased understanding they will gain by trying to teach these concepts to someone else, and perhaps as your memory is refreshed you can teach them concepts that don't seem to be presented to them otherwise (the way Kramer's Rule is presented currently is a prime example of this. It is more much more difficult to understand the mechanics of it with the current method, even though (or maybe because) it is more consistent with matrix mechanics).
A better understanding of math can only open more and better opportunities to them, which is a noble pursuit for any parent. Also, the time spent will help strengthen the bonds between you.
So, don't steal their books, ask them to teach you. This is by far the most beneficial solution for all involved.
Under capitalism man exploits man. Under communism it's the other way around.
Computers have made it much easier to experiment with mathematical ideas, and experimenting helps you learn better. I'd suggest buying a copy of Mathematica and one of the companion books. It will do you more good than college courses until you're back in the swing of things.
For the more adventuresome, I'd try J from JSoftware. It's terser, and more intellectually challenging, but it's free and also has advantages over Mathematica in some respects. Ken Iverson has some on-line papers that make a good companion (one of which comes with the J distribution).
A local community college is your best bet. You can pay for classes "a la carte".
Here's a good starting point:
You need algebra to start....without algebra you can't do anything. After that:
Calculus I & Calculus II: Integration and differentiation.
Statistics: Very important...means, medians, confidence intervals...etc.
Like computer science? Take discrete math. This is extremely important if you want to understand the "digital" world, and the foundations of logic...truth tables etc.
That should be plenty to keep you busy. Calc III and differential equations are really hard-core engineering maths. I was an EE major before switching to CS...let's just say that Diff EQs, helped me make the switch.
Have fun and good luck!
-ted
May I recomend Dover Publications?
They republish paperback versions of classics (Newton, Einstein, Fermi, etc...), as well as titles such as Problem Solving Through Recreational Mathematics , and 100 Great Problems of Elementary Mathematics. The beauty of Dover is their price. Many books are under $10.
Also recommended for self study are the Schaum's Outlines series from McGraw-Hill.