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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?"
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.
I guarantee you will go back to hating math after taking a single class.
But seriously university classes in math tend to be rather boring because they tend to reduce even complicated fields into a few formulas that can be memorized and a few problem types for which you can memorize which formula to use.
Also they tend to assign a lot of dull homework.
So classes seem to be geared towards those that cant understand math but are willing to tackle it with brute memorization.
Or maybe i just went to a bad university.
Some colleges have courses on TV. In Portland, PCC (Portland Community College) they have 'telecourses' on Math. Unfortunately, I failed to keep up on the class. However, if I get renewed interest in taking the course I can fire up the PCC channel and watch it.
I imagine this is available in SOME other areas too. It's worth a view and doesn't cost you anything.
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.
Mathematics is one of those fields where there's a huge variety of topics covered by a single label. What does "math" mean to you, and what are you interested in?
If you're interested in calculus (differential equations, dynamic systems, chaos, etc.), you would probably be best served by getting a current university calculus book and Maple/MathLab/Mathematica/whatever and working through it. The software handles the mechanical aspects of the process and you'll probably find the material easier to pick up than before.
Same thing if you're interested in number theory (cryptology, matrices, etc.) If you get an introductory text designed to work with one of these programs it will handle the mechanical grunt work and allow you to focus on the concepts.
If your interest is precalculus (algebra, trig, etc.), you may be better off working through the problems by hand. You want the software to be a tool, not a crutch, and one of the main reasons for the usual introductory sequence (up through PDQ) is just to train the students how to reliably perform the necessary work.
For every complex problem there is an answer that is clear, simple, and wrong. -- H L Mencken
hey, here's an idea: try working some math problems. there are tons of resources on the web from math contests that were originally given to high school students all the way up through graduate students. try working some of them - you can often find elegant solutions published right along the problems after you have tried to solve them. here's a couple of links to good problem repositories:
/ pr oblemarchive.html
/ pu tnam/index.html
n .h tml
http://www.unl.edu/amc/a-activities/a7-problems
http://www.unl.edu/amc/a-activities/a7-problems
and to order copies of easier (though still very interesting) exams:
http://www.unl.edu/amc/d-publication/publicatio
good luck,
jeff.
But the math you should do is dependent upon what you want to do with it later. To take a trivial example supporting my point, I was really pissed off at the education I'd gotten previously when I worked my way through Book I of Euclid's Elements and came to the Pythogorean Theorem. Suddenly, I understood it in a much deeper way. Did it matter that much in regards to that algebra I had done earlier in high school? Nope, not really.
Or take irrational numbers. They are presented to students in the most prosaic fashion, and many students (not math majors or mathematicians, of course -- remember, I'm using rudimentary examples) would simply say "uh, they're numbers whose decimals go on forever? Oh, wait, they're numbers whose decimals go on forever without anything repeating?" That's literally true, and means nothing. When you stumble upon the incommensurability of the diagonal of a square to its side in the context of Euclidean geometry, such a thing is dumbfoundingly counter-intuitive.
This type of thing repeats itself as you work your way deeper into any discipline. The top people tend to better acquaint themselves with deep, fundamental ideas as necessary. It's hard to do truly original work without doing so. But today's scientists are not trained, really, for doing truly original work, and they shouldn't be. Those that want to and have the aptitude will achieve that deeper level of comprehension on their own. Everyone else will do their much more technical, incremental work. And that is, in fact, the overwhelming majority of the progress made in science and mathematics. The big stuff gets all the glory, but its the little stuff that accounts for most of the work and enables the big stuff to be discovered. This is why although I greatly personally prefer deep comprehension over facility with technique, I don't advocate that this is the proper pedagogical approach for all students.
The poster that asked the question needs to ask what he's looking for in his approach to mathematics. You know as well as I do that introductory calculus texts are more an attempt to manage to acquaint the student with calculus and then teach a variety of techniques that are likely to be of use in particular fields. If you're not working in those fields, if you're never going to use calculus either for technical purposes or as a working mathematician, you probably don't need most of those techniques. Much of this comes and goes as different technical approaches are fashionable. It just simply isn't the case that all the techniques that a student is taught in college calculus courses are essential to their understanding of the subject matter. That can't be true, as which techniques are taught change over time.
Obviously, there's a core facility with both concepts and technique that is necessary for any resonable level of comprehension. I was not disputing that. That's why, in fact, I went to a liberal arts college very unlike yours (which is every one other than mine), where actually doing the mathematical work, of say, Lobechevsky, is considered essential and where a gloss in a math survey course is rightly considered for the most part a waste of the liberal art student's time. You're right: you don't learn a subject like math by reading about it.
This is such utter and complete FUD it is nuts.
From personal observations and anecdotal evidence I can safely say that community college courses on the whole are far better then four-year university courses. The professors who teach them take a genuine interest in your success as well as a compasionate atitude towards individual students.
I attend a top US university and I can safely say the mathematics department here hasn't done any cutting edge research aside from the weekly acid trip. One of my good friends is going down the path towards becoming a math professor to stay near the young girls and the good drugs. I'd be surprised if it wasn't the same at other so-called "top schools".
-davidu
# Hack the planet, it's important.
In truth, almost all American higher eduation is now vocational education. Your attitude and comment demonstrate this. It's the only thing most people can imagine that an education could be for.
The problem is that since what they want is a vocational education, and what the economy needs is a vocational education, it's interesting that we're not doing a very good job providing one. This is because of the supposed continued commitment to a "liberal education" by most American undergraduate schools. The result is the worst of both worlds: watered down liberal arts classes that teach little and make the students resentful that they are required to take them; and too few vocationally relevant classes, often with a poor degree of contemporary technical relevancy. This is why there's been a junior/community college revolution going on in this country for about twenty years -- they're meeting the demand that the universities aren't.
Obviously, since I went to an extreme liberal arts school I believe in the ideal of a liberal education. But as a practical matter, vocational education is essential. Ideally, it'd probably make me happy if everyone did what I did, and then do a year or so of undergraduate preparatory work in a particular field, then continue on to a graduate school in that field. For the people that wouldn't have gotten an advanced degree, or don't want that much schooling, you could still do what I did but put vocational schooling and experience beginning in parallel like they do in Europe. But I don't really expect everyone to do what I did, and I'm certain it's not appropriate for everyone. What degree of a sort of liberal education is for "everyone"? Well, we started down this road before and where we're arrived is not satisfactory. I think I'd prefer to find a way to get as much as possible of this done in primary and secondary school, extending schooling to year-around and adding another year; then sending people on to vocational, liberal, or professional educations.
It's actually a pretty modern thing to think of "education" as being a vocational education. What you needed to know to work in a vocation, you learned in apprenticeship or some other such institution. America has a particular problem with all this, though, since we have a very egalitarian ideal that wants to give all citizens some sort of a liberal education, while our relentless practicality also demands that we teach people to do their jobs. The two things are in many ways disharmonious.