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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?"
amazon has lots of books and probably some on math go read like everyone else. How do you think the /. crowd gets up on the latest programming language? By running back to college? NO by reading and studying just go do it geesh
***I GOT NUTHIN***
community college -- cheap and laid-back courses that'll give you the background you want.
www.math.com has some good resources you might wanna investigate... bone up on the math and algebras then test into the undergrad courses, skipping the "bridging" courses at the University. If the bridging courses are really $495, that should save you a 1k or so...
Damn, I messed up the link. That should have been this one instead. Sorry!
i reccommend What Is Mathematics by Courant, Robbins, Stewart. This covers just about everything in modern math until the 1940's or so (and the newer version have updated sections on Fermat's last theorem). Plus there's a blurb from Albert Einstein praising the book on the back. You can't ask for much more than that.
-BlueLines
--BlueLines "The cost of living hasn't affected it's popularity." -anonymous
Look at the syllabus for courses at your favorite university web site. From there you can look up topics on the web or in books.
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 believe it's Dover anyways...they publish a really great series of math books on a variety of subjects, available at Barnes and Noble for $10-15. A real bargain if you ask me! I bought "Math for Nonmathematicians," for a refresher, but it is more of a history book--aninteresting read nonetheless. I haven't done high-level math in about 7-8 years either, so I broke out my old calculus books too. I enjoy studying number and graph theory, very useful for programmers.
Get ready to mod this -1 redundant.
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.
Check out my podcast: DreamStation.cc Video Game Show
The Teaching Company has great audio and video lectures on all subjects by reknown professors. Though they may seem a bit expensive, try requesting your local public library to order a set. I know I've ordered them for people when I worked in a library.
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Here's a link to their Science & Math courses: http://www.teachco.com/ttcstore/CoursesBySubject.
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.
Forgotten Algebra
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.
-fb Everything not expressly forbidden is now mandatory.
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.
(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".
Mathematical Atlas
Statistics Every Writer Should Know
Why is it called COMMON sense when so few people have it?
Graduate school. Take these classes at a community college:
1) Algebra
2) Trigonometry
3) Calculus
4) Differential Equations
5) Linear Algebra
6) Prob/Stat
7) Abstract Algebra
8) Numerical Methods/Analysis
Then send your applications for grad school off. If you pass those seven classes you will be a shoe in.
The middle mind speaks!
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
If you have access to the PBS-U channel on TV or can find the tapes, you might want to check out a group called "Standard Deviants" and their eponymous show.
It's basically high school curricula, at several levels, but they have a way of making some pretty dry material memorable. I was really surprised at what I retained after watching a few of their shows on physics and math. (They teach all kinds of subject matter.)
The girls are frequently cute too.
Change and Motion: Calculus Made Clear. Prof. Starbird is an exceptional instructor who illustrates insights into calculus using layman's terms. I took three calculus related courses during the course of high school and college, yet found these six tapes to be incredibly enlightening.
Be sure to buy them when they're on sale! They're $54.95 today (2 Jul 02) but retail for as high as $199.95, I believe.
Enjoy,
Helevius
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.
More physics than math, but a great place to start. If you buy the series (or tape it off PBS), you can watch it again and again until you finally learn the concepts. It opens a whole new world in math and physics. It was recorded and animated (by Pr. Blinn, no less!) in the mid-80s, and is still relevant.
-S
https://www.accountkiller.com/removal-requested
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.
Firstly sorry I'm posting here, but I should like the original requestor to read this...
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