Options for Adults with Renewed Interest in Math? 633
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?"
Don't buy from amazon (Score:1, Insightful)
Find a university. Show up. Have a seat. (Score:5, Insightful)
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 dont know where you are (Score:3, Insightful)
Where are you going with it? (Score:3, Insightful)
Do you want this for information's sake, or do you want to plan a career out of it?
These questions are important because if you are doing it for education's sake, the first time you look into a college-level Multivariable Calculus book might result in a little voice giving you a sudden desperate need to close the book and never open it again.
Course, if you plan to make a career out of it, the above situation will probably still occur, but you'll at least have a strong reason to ignore that little voice and give it a serious try.
-Matt
As Euclid said... (Score:2, Insightful)
Either that, or don't bother. Quite seriously, I doubt you'll be able to learn much whatever you do -- mathematics is a subject which people find incredibly hard to pick up late in life.
Tutor (Score:3, Insightful)
The problem is time (Score:2, Insightful)
I am a family man (two kids) and trying to get anything done with a family to take care of too has been very tough for me. So, slowly I realize I will eventually end up as yet another mathematician-wannabe... |sigh|
Recommendations? Get a family, skip the intellectual masturbation. When you're approaching forty years you will thank me. No algorithm beats a bed-time story.
Depends on the depth (Score:3, Insightful)
If you are hoping to learn enough to publish papers or contribute to the advancement of math, then I recommend taking the effort and getting a degree in mathematics (unless you are really, really good at math.
If you just want to have some fun with mathematical recreations. Scientific American released some great books with math problems, as well I know of a few others if you want them.
If you want to have some real fun and learn classical mathematics (no applied stuff), there's always Euclid's Elements and Mathematica Principia. But these books are definitely not for the faint of heart either.
If you want to learn math with a more applied edge, you can take night courses, or get a few good books on modern calculus or mathematics.
If you want to learn statistics, I feel really sorry for you.
If you want to learn comp sci related math, there are some fantastic books out there that will help (if you want details, just reply).
There is just so many areas to go into when you decide to mathematics again. It is hard to help you out with exactly what to do. I am taking a degree in math right now, but I can understand that with children that would be a difficult and strenuous challenge. Even though, I think it would be great to have another mathematician contributing to the body of math that exists.
The only suggestion I really have that may be quite helpful is to see if you can talk with any of the pure mathematics professors at the university or college near you. They might be able to help you find your niche in mathematics, and even provide you with some other alternatives not mentioned here.
Re:Find a university. Show up. Have a seat. (Score:5, Insightful)
(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.
Re:Where are you going with it? (Score:5, Insightful)
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.
Re:Go buy a book (Score:2, Insightful)
I think programming/development/etc are differenct since you can actually apply those concepts in the real world, but from the sounds of the original poster, the amount of math he'll actually use is minimal . . . sounds like he wants to learn it for the sake of learning, and more power to him for that, but without some sort of application/repetition, it'll be real hard to learn it . . . which is why I think a college classroom is probably the best way for him to go . . . and like many others have posted, community college is a good option . . .
Re:Re-learning (Score:5, Insightful)
Let x' = 10x + 6. This essentially adds a '6' to the end of the numerator.
Let y' = 10y + 24. This essentially adds a '6' to the start of the denominator.
Then x'/y' = (10x + 6) / (10y + 24) = (10x + 6) / (40x + 24) = 1/4 [(10x + 6)/(10x + 4)] = 1/4.
Re:Where are you going with it? (Score:2, Insightful)
Courses cost money, knowledge only dedication. (Score:4, Insightful)
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
Excellent Advice! (Score:5, Insightful)
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.
Applied Math (Score:1, Insightful)
All of this being said, a bigger point remains: SCREW MATH BOOKS! They are references and references ONLY. You're never going to learn much unless you go and get your hands dirty with what you're learning. In so far as books and community colleges are concerned, this means homework/quizzes/tests, the academic answer to "exercises". However, this sucks all of the life out of math and explains why I was originally despised/feared math, routinely failed math classes, and was headed to graduate school as a music composition student and not a MATH guy. However, one day (probably much like you), I realized that math in its application was an uber-powerful language. If it is not true that much of the world performs itself in the language of mathematics, it is at least true that much of what the world performs can be understood by describing it in the language of mathematics. We do it all the time, and this is kind of why we made up the language in the first place. This observation motivates my final endorsement: don't simply study math because it's cool. Find a field that you're interested in like weather prediction, fluid flow, predator-prey relationships, economics, investing, astronomy, etc. and study the math in the context of that interest. I think that you'll find the pursuit more organic and rewarding. For example, it is one thing to solve an ordinary differential equation in a homework exercise, but it is quite another to then use your solution to reveal how species populations destabilize when ecologies are destroyed, be able to predict if it will rain tomorrow at your house, or retire on the merit of your stock portfolio that you based around a simple differential model (good luck with that one!) Applied math explorations like this are available to tenured professors all the way down to high school students, and you can slide up the scale as you become more mathematically sophisticated.
P.S. Once again SCREW MATH BOOKS. What you really need is software like Maple or Mathematica or whatever would be useful to you. After you get to the point where you could push through any computation with pencil and paper if the power went out and you absolutely had to, it is better to unload some of the "tougher" computations onto a computer so that you can enjoy more of the forest and less of the trees. Enjoy!!
Some really good advice here (Score:3, Insightful)
1. You say you have developed an interest in math. Does that mean you like the idea of yourself knowing a lot of math or you are interested in a field that you want to know more of.
2. If it is the first one, then pay lots of money to learn lots of math that you will never use and halfway thru give up. At least you won't have regrets.
3. If it's the other one, then you know what fields of mathematics that you need to study in order to further understand the subject that you are interested in. Find the things that don't make sense or topics that don't make sense and make a list of subjects that you need to learn. You can go the local university library and read some of the books there which will lead you to other question and so on. That will be the true fun way of doing it.
Have fun! (Mathematical recreations) (Score:3, Insightful)
There are lots of "mathematical recreations" and "math puzzles" that are fun to try solving, in the same way that it can be fun solving other puzzles. And sometimes you may see a variation on that puzzle that's fun (and truly new). Not all of them are truly critical from the point of view of furthering the advancement of mathematics, but they help develop the mind, and if your purpose is to have fun, start now!
For example, I learned about the ``four fours'' problem as a kid (using exactly 4 fours, create legal mathematical expressions to compute 0, 1, 2, 3, etc.). Recently I created a definitive list of answers for the four fours problem [dwheeler.com]. I also played with various really weird bases [dwheeler.com]. Will these change the universe? No. But in the process I learned more than I knew before, and I enjoyed the process.
If nothing else, if you enjoy the process, you're more likely to continue doing it.