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Science and Math For Adults?
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.
The solution that most math texts take then is to give you *lots* of problems/drills so that the mechanics get ingrained, allowing the insight to come later.
When I screwed up my second year calculus course *really* badly (like 6% on the midterm...) I used a Schaum's Outline to get back on track (and eventually ace the final). It's main benefit is *heaps* of problems to work through. That made me a convert to the problems approach to math teaching.
The key is to do all the problems, in order.
That said, I can't really recommend one math text over another, just so long as there are lots of problems, and hopefully a solution key in the back for at least half the excercises.
The problem is, most textbooks are designed to be companion references, with all the 'facts' squeezed in so the teacher can spend time helping everyone understand the concepts etc. The two work together.
Simple answer is, you need to take adult education classes. I left college barely half-way through, and ended up taking night classes- intro to calculus was one; another was an intensive Economics class. I found them worthwhile; I probably would have enjoyed the class more if I wasn't young enough to be most of the other student's kid(you would fit in FAR better, from the sounds of it.)
Without the classes, you don't get the benefits of peer learning, in-class interaction("Did everybody get that?" [blank stares] "Heh, ok, let me explain it a different way...") the discipline that testing creates, nor the resource of having a Really Smart Person(professor) to go to when you need help. There are also other benefits- making friends(you're probably all in similar 'boats' so to speak, so people socialize pretty readily), and networking. My old boss decided to do part-time classes for an MBA, and got a lot of networking out of it(granted, those were business classes, more prone to networking activities, but you get the idea).
Please help metamoderate.
...and very little from the books.
I suppose it depends on the type of learner you are, but frankly, I imagine seeing and using the information being delivered to me. Rather than simply "knowing" the things I learned, I understood them and used what I learned to add more peices to the puzzle I call "reality."
In more simple terms, everything you (should have) learned should be assimilated into the way you operate within your environment. Ever heard "you use it or you lose it"? There's a lot of truth to that.
Rather than try to get what you missed from books, perhaps it's time to make a much more grand display by going back to school. It doesn't have to be thought of as "remedial" but rather as a "brush-up" or simply continuing education. If you show your children that learning only ends when you die, their minds will be open for life with the expectation that they can grow and improve themselves at any point in their lives... not just during the beginning phases. By the time they reach it, "middle aged" will be 50-something anyway.
Best advice? Go back to school and pay attention this time.
On the topic of calculus, don't learn anything past calculus I (well, bits of calculus II are useful). The rest is completely useless and you'll forget about it all in a couple of years anyway because of its uselessness. If you want something that's useful go for discrete math and/or the good bits of linear algebra. Your comment is completely offbase. Actually, Linear Algebra is about as important as Calculus in many scientific/engineering disciplines.
More importantly, you claim that anything more advanced will be forgotten, but the later courses often serve to reinforce earlier material. For example a course on Fourrier theory reinforces both Linear Algebra and Calculus.
Most math departments have a course somewhere after the introductory sequence which teaches basic proof techniques often by studying the definition of numerical systems from logical axioms.
These basic proof techniques are the very basis of mathematics. The reason so many people get through high school with little understanding of math is that they are never forced to do any proofs outside of Geometry.
In short, if you cannot prove anything, you know practically nothing about mathematics.
http://yetanotherpoliticalrant.blogspot.com
Calculus is INCREDIBLY important, and from a philosopical point of view it might even be dangerous. :)
Imagine a field of mathematics that explicitly has at it's underpinnings the hypothesis that as you break up a line into smaller segments, eventually if you make each segment have no length, they still all add up to a lenght.
Philosopy aside, it's an INCREDIBLE tool for particular applications. Need the area of a sphere, no problem. A cone, still no problem. An oddly shaped object that looks like a art-deco running shoe? BIG problem, that is unless you use calculus.
I just wanted to reply concerning the cost issue. If you find something you think will work, and can learn easily from it, it's worth the price. You'd be surprised what a good foundation of scientific principles can do for you, at work and at home.
It's not only the facts you know about things; those give you the ability to carry on a discussion with a specialist in any given field. It's also the process of discovery and fact-checking. Every time you work a problem, or follow the progression of a historical great discovery, you teach yourself how to apply your natural curiosity in a productive way. Invaluable.
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