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Options for Adults with Renewed Interest in Math?
Posted by
Cliff
on Tue Jul 02, 2002 02:59 PM
from the back-to-school dept.
from the back-to-school dept.
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?"
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Science and Math For Adults? 489 comments
Peter Trepan writes "Like most Americans, I made it through high-school and college without a thorough understanding of major scientific and mathematical concepts. I'm trying to remedy this situation both for personal betterment and so I can supplement my *own* kids' education. The problem is, most textbooks are not designed to convey an understanding of the subject, but to squeeze in all the 'facts' required by state law. I'm looking for books that don't just tell me an equation or a concept works, but also explain *why*. Would you please list books that have helped you gain a greater understanding of the basic concepts of algebra, chemistry, calculus, physics, and other core areas of science?" This is similar to an earlier question, but with a broader focus.
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2 words (Score:4, Informative)
Re:2 words (Score:5, Informative)
Parent
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!)
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.
Parent
Blending in (Score:3, Funny)
2) If you don't have grey hairs, you can probably pass for a student with a little creative wardrobe work.
Here's some pointers on blending in:
GMD
I dont know where you are (Score:3, Insightful)
Small private colleges are WAY better (Score:5, Informative)
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.
Parent
Re:Small private colleges are WAY better (Score:3, Interesting)
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
Re:I dont know where you are (Score:5, Informative)
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!
Parent
I need more information! (Score:4, Funny)
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...
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
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.
Parent
Re:Where are you going with it? (Score:3, Informative)
Yeah, "a lot" is two words. I conflate them to one quite often, since I think of it as a single word. I'm not the only one. It'll probably eventually appear in the OED. I'm a language pragmatist, not a proscriptivist.
Re:Where are you going with it? (Score:3, Interesting)
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.
Re:Where are you going with it? (Score:3, Interesting)
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.
Re:Where are you going with it? (Score:4, Informative)
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 [mcgraw-hill.com] series from McGraw-Hill.
Parent
Re:Where are you going with it? (Score:4, Interesting)
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!
Parent
Re-learning (Score:5, Interesting)
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.
Re:Re-learning (Score:3, Funny)
Just make sure the person knows what they're doing. At university I saw someone take the fraction
16
----
64
Cross out the sixes and end up with
1
---
4
The scary thing is it actually worked!
Re:Re-learning (Score:4, Interesting)
166
___
664
as well as
16666
_____
66664
work, as I would suspect any number of sixes on either end will.
Parent
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.
Parent
Re:Re-learning (Score:4, Informative)
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.
Parent
Re:Re-learning (Score:3, Interesting)
Exists x, y, n such that nx = y.
Let x' = 10x + a, y' = 10y + b.
Then...
where this particular set is n = 4, a = 6, b = 4.
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.
Parent
Just read some books (Score:3, Informative)
-BlueLines
Re:Just read some books (Score:3, Informative)
It proved to be so useful even after I've entered and graduated from university, and beyond.
Tutor (Score:3, Insightful)
For free... (Score:5, Informative)
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.
Whatever you do... (Score:3, Funny)
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.
dont worry (Score:3, Interesting)
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.
Math Competition Problems (Score:4, Informative)
Community Colleges (Score:3, Informative)
As an undergraduate I had a minor in mathematics. I've been out of school for a few years and was interested in taking the GRE. In order to prepare for the quantitative section of the GRE I enrolled in a 5 week summer evening math course at my local community college. The course was titled "college algebra", it was basically stuff you should already know coming out of high school. However, it was wonderful. A perfect refresher for somebody who hasn't writen a proof or solved a quadratic since college. I enjoyed the experience so much that I'm enrolling in more classes this fall. I have found that community colleges are wonderful resources, but more importantly tuition is dirt cheap. $67.00 a credit hour here. I can't stress this enough, tuition doesn't get any cheaper than that anywhere in the US.
Where are you starting? (Score:3, Interesting)
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.
try some problems (Score:3, Interesting)
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.
Book Recommendation! (Score:3, Informative)
Barron's
0812019432
Apologies if you're beyond this, but it is EXCELLENT if you're thinking of going to a
college level algebra class. Takes a few weeks
to work through. You'll be ready for intermediate
algebra or precalc when done.
Advice from a math professor (Score:4, Informative)
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".
Three Sites to Start With (Score:3, Informative)
Mathematical Atlas [niu.edu]
Statistics Every Writer Should Know [robertniles.com]
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
Get Mathematica...or something similar (Score:4, Informative)
For the more adventuresome, I'd try J from JSoftware [jsoftware.com]. 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).
It all depends on the application (Score:4, Informative)
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
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.
The Mechanical Universe -- Goodstein (Score:3, Informative)
-S
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.
Re:Go buy a book (Score:2, Interesting)
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.
Re:Go buy a book (Score:3)
This is true, but it is due to the difficult nature of the material being presented. There is a huge difference between reading *and deeply understanding* "George Washington was the first president of the US", and "A Function F from A to B is called continuous on a set A if and only for every open set C in F(A) ( a subset of B ) the inverse image of C under F is open in A."
The first is a simple statement of fact, the second is simply a definition. To understand the first takes almost no effort. To understand the second, you have to know and understand the definition of Set, Open set, Function, Domain, Range, Inverse Image, and Subset. You also have to put these concepts together in a new way and form some sort of picture in your mind of something it's impossible to take a picture of.
I'm not bagging on history, and I know that there are much more difficult concepts than my example.
The point is that you can't "read" a math book. If you want to get anything out of it you have to take time to understand every subtle concept. Every sentence depends critically on almost every previous sentence in not just that book, but every book that came before. I took a graduate class in real analysis my senior year, and our book was about the size of The Catcher in the Rye. We got through about a third of it in the entire year. I spent a week understanding a single page from the book at times.
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.
This is the point of that thing called "learning". High school is one thing, but at college level, the point is that you are presented with concepts and you take those and apply them to new ideas in new ways. I know you are just doing it out of personal interest, rather than for a degree or something, but if you do want to take a step past books about math for the lay person, it does take a certain level of commitment.
Math for me is something that would have to be taught in a classroom not from a book.
A classroom setting might help somewhat in some areas, but even then it requires quite a bit of work to wrap your head around some of the concepts. Having other people to discuss it with makes a huge difference, but there is no way around spending time wrestling with some very abstract concepts.
...another idea... (Score:3, Interesting)
I imagine this is available in SOME other areas too. It's worth a view and doesn't cost you anything.
Re:Go buy a book (Score:3, Informative)
It provides a very intelligent of the whole topic of Mathematics, from the point of view of an adult reader wanting to learn more. The author goes into a lot of the interesting historical and cultural background behind the math.
It's truly a book that belongs in everyone's library.
Re:Mathematics (Score:2, Informative)
Re:I had problems (Score:3, Informative)
Mathematics, at least pure mathematics, is more of a mindset that a knowledge set. It is incredibly hard to learn the mathematical way of thinking from books alone, that said once this mindset is acquired the books are the only thing you'll need.
My advice would be to find yourself a mentor who's willing to assist you in acquiring this mindset, you'll probably be succesful asking around the various maths newsgroups.
You need to be able to interact in real time with this person occasionally, but there is no reason not to do this over IM or IRC.
As for what to learn / which books to read Calculus by Micheal Spivak is an excellent book, it brings in rigour gently and covers all of the main points of analysis. Covering its contents alone would set you up for a college / uni course, though you might also what to get a basic grip of [say] group theory and a very basic idea of sets [doesn't have to be above the venn diagram level]
One word of warning do not let a physicist, on engineer or anyone else who 'thinks' they know maths teach you maths, find a mathematician