Hi all, long time lurker, finally registering to ask a question.
I’m a middle aged guy and have always felt a bit of regret that I never studied math more than I did. The last time I took a formal class was in high school, and that was Algebra II.
Beyond that level, what’s most important for an adult to know? Calculus? Statistics? How do I go about getting a good grasp of the right subject–self study, or take a class? What kind of textbooks? I’d like your opinion!
I’d suggest statistics or geometry. These are both relevant to real life. To me, calculus hasn’t been relevant for anything until I started working on my Ph.D. And people who have Ph.D.s tell me they didn’t use calculus at all after they got their degree. Geometry might be more interesting if you are interested in mechanical stuff, woodworking, hands-on activities like that. Statistics are more focused on reading and interpreting information. Another fun class might be logic.
As far as independent study vs. taking a class, I think that depends on your personal style and schedule. For me, a class would be better if I were just getting into math for the first time in a long while. After that, I might be able to study independently but I’d definitely need the class as a jump start.
I have always regretted that I never studied statistics. I don’t know what they mean by regression or chi-squared that they throw around. I do know about mean and standard deviation because those terms are really from probablility, which I do know something about.
Of course, statistics is not mathematics, actually. (You want to start a fight; tell a statistician that it is.) I can only answer in terms of what interested me. I loved HS geometry but that isn’t taught any more (more’s the pity). I can’t say I much cared HS algebra for calculus in college, although I have a much better appreciation of the latter after I taught it a few times and understood what it was really about. It is about reasoning with infinitesimals, which point of view is generally supressed as it is usually taught. What I really fell in love with was modern algebra, but that is definitely not for beginners.
I would say basic statistics. Anybody who reads the news or sees commercials would benefit from an understanding that the statements “2% of cyclists are involved in road accidents” and “2% of people involved in road accidents are cyclists” are not equivalent. Statistics are not “damned lies”, if you understand them.
Statistics and basic finance are probably the two most important things for the guy on the street to know. Beyond that, everything starts to be a little more specialized.
No matter what, though, you’re going to need calculus to get started. The material itself will be useful in the other classes you take later, but the skills you pick up from doing lots of calculus problems will help you a lot more. You will need a pretty solid background in algebra and geometry, though, so consider taking some time to refresh those in your mind. At this point, you should definitely look to take a class if you can. Take a look at what your local community college offers.
First of all, congratulations. Learning math is a great way to keep your mind sharp. I’ve actually done this myself; I bought a textbook and got through algebra and trig. Someday, I want to tackle calculus too.
One or two things. First off, I second the people telling you to learn stats. VERY useful. Secondly, you might want to get a good algebra/trig textbook and get through that before you take on calculus. There’s nothing particularly mystical about calc, but as others here have noted, you need to have your algebra down before you can get it. If you start calculus, and you can understand the logic behind it despite the complexity, then you’re good enough at algebra to continue. Otherwise, back up a bit and concentrate on the more basic stuff. Don’t get discouraged–Math is one of those subjects where you absolutely have to master the fundamentals to get the more complex stuff. Keep at it, and you’ll get there sooner or later.
I’ll dig up my old textbook and give you the title and Amazon link. I went from sucking at algebra to helping others with their algebra homework on messageboards using this book, so I’d definitely recommend it.
I’ve always thought of math as a road map. It’s a network of interconnecting ideas with many ways to get to the same place. For example, is 35=7*5 or =40-5? Well, either, depends on what you’re trying to do. So far, some have suggested learning “how to get to” those places you visit most often (algebra, stats) but if you’re going to go driving through a foreign land, why not take the scenic route? Go for Calculus! You’ll never need it in real life, I promise you, but the concepts are excellent and appreciably “beautiful” in their own right to make them worth studying.
I’ve a degree in Mathematics and have only ever used statistics outside of class. There are plenty of books out there that are easy to get through and just enough to give you a taste. I’d recommend a few, but I’m not at home right now.
If you’re just looking at it from a practical standpoint, for what you can actually use in your everyday life, I agree that statistics is the most useful area to study. You could start with a popular-level book, like The Complete Idiot’s Guide to Statistics, Statistics for Dummies, or The Cartoon Guide to Statistics, and then, if you want more, take a class or work your way through a textbook. (And though it won’t teach you how to do statistics yourself, the classic How to Lie With Statistics will open your eyes to the ways other people use and mis-use statistics.)
At an even more basic level, books like The Only Math Book You’ll Ever Need or All the Math You’ll Ever Need might be what you’re looking for, or they might not. I haven’t read them, but it looks like they won’t teach you much actual math (not much beyond basic arithmetic), but rather, they’ll tell you how to use math, to apply it in real-world contexts. You may learn a lot of practical stuff, but it’s not what a mathematician would think of as math.
On the other hand, if you’re interested in math for its own sake, because you think it’s fun or fascinating, my recommendations would be completely different.
One last recommendation: John Allan Paulos’s book Innumeracy makes a good case for why it’s important for the average adult to be comfortable with mathematical thinking.
If you want one math book that will give you all the basics and quite a bit more, I recommend Allyn J Washington’s Basic Technical Math with Calculus. It’s expensive but worth it; it takes you from how to count, literally, to integral and differential calculus and statistics and all sorts of other things. I had it when I was in college and I am still kicking myself that I managed to loose track of it. I’m going to buy another copy.
As for what you need? The average person needs to know money math, especially the workings of compound interest, even more than statistics, in my opinion. If you are doing any sort of construction, even just building a deck, you need trigonometry. Algebra is very useful in all sorts of places.
FWIW, this is the algebra/trig textbook I used. It’s pretty big, and it will keep you occupied for a good long time, but when you make your way through, you will be ready for calculus.
Try to find a couple of math messageboards to help you through the more confusing problems too. They’re all over the place.
In learning math there’s an ongoing dispute on whether you should learn more theory or do more rote practice. The answer is simple. You have to do BOTH to get it right. That might sound like an incredibly obvious point, maybe even a waste of pixels, but you wouldn’t believe how many math teachers still don’t get it. Especially the ones who emphasize theory. Many wasted hours, many sad children and parents as a result.
Second, look into Stanford University’s distance learning program is probably worth looking into. You could probably find it in seconds via Google.
Finally (As they say, there are three types of people. Those who can count and those who can’t - Had to sneak a math joke in here ) consider http://tutorvista.com/ - unlimited tutoring via phone and internet for about $100 a month. But if your religion doesn’t allow for outsourcing don’t bother.