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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?"
well, I read a lot. I do mean a lot. I graduated w/a degree in History. You can learn a ton from reading books about History but books about Math are more difficult to learn from IMHO.
I never had difficulty learning the examples. I could do any problem pretty much that relied on the examples in the book. When I needed to apply something else that wasn't taught to the T in the book I had a bit of a hard time w/that.
Math for me is something that would have to be taught in a classroom not from a book.
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 agree, community colleges are the way to go. I'm not sure about the "none of the liberalism" comment though as I went from being a conservative christian to a liberal democrat after attending community college in VA for a few years. I see this as an added bonus but I doubt the original poster would agree. :-)
Though I'm not in the same situation as you, SOSMath is a GREAT reference that I've used many times to "remember" things such as how to solve differential equations and matrix multiplication properties. good luck!
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.
Regardless of your experiences, there are some decent community colleges around. Why would he want to pay the huge prices on large universities to take some math classes when his obvious intent is learning for the sake of learning?
Is your browser retarded?
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!
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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.
Rather, you should begin your study of mathematics by reading the Ancient mathematicians. Begin with Euclid. In reading the Elements, you'll quickly discover that Euclid has presented a complete science (from self-evident first principles to logical conclusions) that includes truths about geometry (continuous quantity), number (discrete quantity), even the foundations of algebra (Elements, Book II). The Elements culminates with the constrution of the Five Perfect (or Platonic) Solids, the proofs of which are marvelous to behold.
In reading Euclid you'll not only create a rock-solid mathematical foundation for yourself, but you'll also:
After you've finished with Euclid, move on to Apollonius' Conics, a beautiful work, a thousand times more complete and wonderful in its treatment of conic sections than you'll find in any modern analytic geometry textbook. You may also want to look at works by guys like Archimedes, whose early work on the infinite inspired the Classical develompent of the Calculus.
With this firm foundation, you'll be able to read and understand the mathematics of Descartes, whose treatment of geometry (notably the solution of the four-line locus) was key in the development of algebraic notation. And if you stick with it, you can probably read Newton's Principia, Leibniz, and other later Classical mathematicians. I'd stay away from 20th century mathematics, at least at first. There's lots more joy for the amateur mathematician in reading and understanding these Ancient and Classical works than there is in trying to decipher some of the work that has been done recently (within the past 100 years).
Whatever you do, read original works. They are infinitely more understandable than textbooks and other secondary sources. Find someone or a small group of people to discuss them with. Ask each other what each author is doing, what assumptions he has made, what he thinks he has proven (if anything). Memorize proofs, especially with Euclid.
There is lots more that you can do, just with the authors I've named here, but at the very least, even if you ultimately decide to take a college course or something, get yourself a copy of Euclid's Elements. It's a singularly wonderful work, and you'll be very glad you did.
Belloc
I got more rhymes than Jamaica got Mangoes.
You should start by looking at every single function in the header file "math.h" in ANSI C (Appendix B of Kernigan & Ritchie) and for each of them ask yourself "what exactly does this function do?"
Then you need some math programs. You only really need one from each of two categories. You need one serious number crunching program, and one serious algebra program.
For number crunching, I recommend "Octave" (which is free but hard to compile correctly unless there is already a binary for your platform), "Matlab" (which will run you several hundreds of dollars but you can probably get a used copy with a want ad or an auction site), or a spreadsheet with a sufficient coverage of library functions, such as Excel. I recommend them in that order.
In addition to a number cruncher, you will want a computer algebra system (which will also do calculus and "higher" math): Maple, Matlab, and Macsyma; again, I recommend them in that order.
I agree with you there on the community college thing. I took all my calculus courses at a community college and I learned a lot more from my professors there then I did at the University when I took diff eq. The small classroom sizes and the ability to reach professors much more easily makes CC a real plus. I came into college not knowing what I wanted to do and really disliking math, and now I'm a Electrical Engineering major!
Good luck at whatever you do.
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.
I was an undergraduate math major (graduated 5 years ago). I was excellent at it, but unfortunately in the "real world" there is little opportunity to use abstract mathematics.
So of course it's easy to miss out on doing math unless you have the time and patience for doing it in your "spare time". Even then, there are certain hurdles that I'd like to overcome. Perhaps some of you can help.
I can also confidently say that it is nearly impossible to really learn advanced math (beyond 3rd year undergraduate) from books alone. The major problem is that math is a very highly compressed field. The notation is usually different from book to book, and the notation is extremely terse. There is rarely any reasonable prose describing why or what motivated a step along the way. Combine this with difficult ideas, and you find that having someone who can help explain why and how to go forward is infinitely more helpful than going alone.
with beginning undergraduate topics like calculus or differential equations, you have comparatively expansive textbooks to describe what and why and how the math was developed along with how it works. It's also usually very applied mathematics. There are plenty of example "real world" problems where you can see how they work. Try that with n-sphere packing or coding theory and it just doesn't work.
However getting access to teachers for advanced courses (beyond 2nd year undergrad) is usually very hard. First, they aren't taught except at universities, (even the small colleges rarely have more than 3 or 4 courses for post 3rd year undergrad) then second they have 1 section and sometimes only tought every other year or every 3rd semester or whatever.
So it's actually hard to even find a place and time to do things like knot theory, algebraic topology, or complex variable analysis.
Has anyone else who has an undergraduate math major been able to go on to do more math other than as a graduate student? I'd love to hear some suggestions as to how to do it.
I was going to take a number theory course at UC berkeley summer session, but it was too much time commitment (commute to berkeley and back, plus 2 hrs lecture 4 times a week)
Has anyone been successful at finding a mentor outside of these channels?
thanks if you can help
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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.