How would you design a program for an adult trying to learn all the Math he missed?

In My Humble Opinion
1

If you had an adult who wished to learn mathematics from head to toe, on his own, how should he go about it? Knowing only basic arithmetic, and a smattering of algebra, where and how should he start? And when I say learn math, I mean learn all of the fundamentals, algebra, geometry, trigonometry, pre-calc, calc 1&2, linear algebra, and diff equations, etc. And when I say learn, I mean learn it. Not simply knowing how to solve the problems, but understanding the why behind it, the odd bits of number theory and basic epistemology that every teacher desperately hopes the students will somehow “get” during around jr. high.

Where should he start? Are there any specific books you could recommend?

2

What are the time and money constraints? Going back to college, or at least taking a few classes, is probably the best way.

3

No time constraints.
I do not see how money would be a problem, I said self-taught, no college.

4

Hmmm. I personally, if I were in this situation, would start scouring the web for math tutorials. The last time I looked for such a thing, I even stumbled across some interactive ones: questions were shown, you tapped in your answer and hit ‘enter’ and it’d tell you right away if you were right or wrong. (However, I don’t think any of those could tell you why it was wrong, which is something a person could do for you, and knowing why something didn’t work can be as important as knowing why something does work.)

The good thing about this approach is that it’s easy to mix-and-match: if one place does a really good job of explaining X, but glosses over Y, you can wander to a different spot that picks up the slack, so to speak.

For reference books, I’d head over to the local college/university and browse through their math textbooks, and perhaps seeing of one of the professors can give you a reccomendation.

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5

I learned most of the math that I’ve taught and tutored in high school and college by working the problems in text books and doing so repeatedly until they were practically etched into my brain.

Just start with practically any college level remedial math text.

It’s just basic math and will take you by the hand step by step.

Read each chapter and make sure you understand what you’ve read. Take your time, work every example, every problem in the book. Several times if necessary!

Make a goal for yourself, something reasonable, like say a chapter per week. When you finish one chapter/text, go to the next, and so on until.~.there’s no guarantee that you’ll ever be another Einstein, but who knows?

I’ve seen that little bulb go off in people’s head many times.
You know the one where, “it makes sense now.” Usually it’s some little something that’s been missed or an approach that’s from a different perspective.

I am talking about a long term committment. If that’s what you’re interested in. I don’t know of any “crash courses” in advanced mathematics.

Remember, not everyone see’s math the same. To most it’s a problem…to some it’s a solution, to a few- it’s just math. If you find yourself stumped try working it backwards or apply a different scenario, something will ultimately make sense, provided you’ve understood what you’ve done up to this point. Be honest, don’t lie to yourself and claim to understand, when you don’t. Simply plugging in numbers with success won’t cut it.

I can’t tell you the number of folks I’ve known that did great in math classes BUT w/out a calculator they were absolutely lost. Nothing like a pencil and paper…granted there comes a time when it becomes almost necessary and that’s fine but until then. Even worse, next semester, they wouldn’t have a clue.

Also get the solutions manuals for the books, try not to rely on them though. Make sure they give explanations in addition to the answers. They will be well worth their cost. Try a used college bookstore. You can get obsolete books often for just a few dollars especially in the summer. I bet if you go to one and explain what’s up, you may just get all you want for free.

good luck

6

What? I never said it was for me!
cough:rolleyes:

I am just terrified that I will end up going through all of these subjects and find at the end that I know how to do it all, but I do not understand it. I would know that steps, but not real reasons.
Richard Feynman wrote about this many years ago.
http://feep.org/articles/feynman.html

7

"What? I never said it was for me!
cough "

well, uh, then…nevermind :o

8

I taught myself algebra I & part of geometry just from the books, and it would seem that if getting textbooks and working through them would be enough to teach someone - but they would need to do the problems, not all, but a fair selection of the problems to ensure that they could do them, and that they could apply them. (Most math textbooks have application questions & word problems which would ensure that you could use the stuff you’ve learned - not just repeat it, the way the kids in the Feynman article seemed to.)

One thing for me about math is that I could understand the what and the how - but the why (the truly understanding it) always showed up a few classes later. Intentionally - the books would say things like “the proof of <insert concept here> is beyond the scope of this book. But we can still apply this in problems like ______.” And, strangely, I have the type of personality that’s ok with that. And once I’d hit the class where the concept was in the scope of the lesson, and the whys were explained, it would illuminate the why of what I did years earlier. Which is one of the fun parts of math. To me at least.

9

Everyone starts by going through the motions, but at some point, the moment of understanding will come. Just stick in there.

10

There are books out there (Algebra Unplugged and How To Ace Calculus are a couple that I’m familiar with, if remember the titles correctly) that attempt to explain the concepts behind a subject like Algebra or Calculus in a reader-friendly way that would supplement a regular textbook and/or course in the subject. Browse the real-life or on-line bookstores, or look for recommendations on other math-related websites.

11

try math.com at
Math.com Lifelong Learning

they have learning programs, books, tutorials, etc.
if “your friend” :wink: or whoever is interested