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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.
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.
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".
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
How about a more rigorous proof.
Let x(n)=1 followed by n 6's.
Let y(n)=n 6's followed by a 4.
Theorem: x(n)/y(n)=1/4
Proof: It's true for the n=0 case.
The rest of the proof is by induction (what the original poster was thinking, but didn't really communicate well...)
To prove this, we need to show that if x(n)/y(n)=1/4, then x(n+1)/y(n+1)=1/4.
Note that x(n+1)=10*x(n)+6 (adding 6 to the end of the numerator). Further note that y(n+1)=10*y+24 (adding 6 to the beginning of the numerator. Then, x(n+1)/y(n+1) = (10*x(n)+6) / (10*y(n)+24).
Since x(n)/y(n)=1/4, y(n)=4*x(n), so this is equal to (10*x(n)+6) / (10*4*x(n)+24)
This is (10*x(n)+6) / (4*(10*x(n)+6)) = 1/4.
The poster had the right idea, contrary to some of the responses, but didn't write a very rigorous proof.
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.