There are two aspects to “knowing” calculus. You can know the mechanics of calculus – taking derivatives, doing integrals, solving related problems, etc. To me, that’s the easy part of calculus and it can be mastered without understanding the underlying theory. To fully know calculus requires understanding all the fundamentals, learning theorems, and, yes, doing proofs. For that, having some math maturity and intuition would be helpful. I had no problems with the mechanics of calculus as an undergrad and did well in the courses. But, to be honest, I didn’t master all the intricacies of the subject until I had to teach it years later! My point is to not fret about all the details if you have a basic working knowledge, unless you’re planning to contribute to the field.
Neat!
I have Martin Gardner’s updated version, and would submit that it is well worth it. I also happen to love Martin Gardner, so there you go. Either way, it’s a great book.
You’re much better than me. It takes me quite some time to come up with percentages. I hate and am terrible at math and it has slightly hampered by own progress as a scientist. To me, math is just not logical (Yes, I realize how ridiculous that may sound to most of you). For example, there is some mystical process in which mathematicians can do some kind of reverse distributive property; that is, they can convert (4 x 50) + (4 x 3x) to 212 - 162x and then take 212 - 162x and turn it back to (4 x 50) + (4 x 3). The math is probably wrong but the concept is similar. There weren’t even any goddamned rules to do the process, either! I hate math, I hate math, I hate math, I HATE IT!
“Innumeracy” is like “illiteracy” - a weak ability with to comprehend math concepts or reason with numbers, due to a lack of exposure or formal education.
Totally unrelated to innumeracy, there is a learning disability related to math. It is called dyscalculia. You can google it, we’ve had some discussions of it recently as well so if you search dycalculia you can find old threads. If you frequently transpose numbers when you write them down, always orient a map to the way you are facing, have trouble distinguishing “left” and “right,” and have problems learning and recalling physical sequences like dance steps, you might be dyscalculic.
Hmmm…sounds like I might be wrong in having this new term I just learned thanks to you all–“dyscalculia.” What you’re saying (transposing numbers, having to orient maps, etc.) I don’t have any problem with. So maybe it’s not that.
I will definitely check the references that **Thudlow Boink **and Magelin mentioned. Maybe I am not beyond hope after all.
Maybe I just need a better grounding int he fundamentals.
But let me also say how very much I appreciate all the responses. You have clearly given this matter some thought on my behalf and took the time to offer your insights and helpful approaches as well as some anecdotes. I wish I could shake all of your hands and say “thanks” in person.
The blind spot could be sums of series and limits.
Let’s pretend that we have a curve like the top of a hill. If you want to approximate the slope at a certain point on the curve, you could pick two points on the curve, connect them with a line, and find the slope. To get more accurate, you could slide the points closer to the point you’re interested in. And again, and again, getting more and more accurate.
The derivative formula comes from limit formulas. It find the limit of the slope of your estimation line, as the distance between the points approaches 0.
Now what if you wanted to find the area under the curve? Well, you could draw a rectangle under the curve, and its area would just give a rough estimation. So you could draw 2 rectangles and their area would fit better, and be more accurate. Or 3 and be even closer to the actual value. 4 is even better.
The integration formulas is just the sum of the area of those rectangles, if you drew an infinite number of them.
Here is a good link from NYT on calulus . It is part of a series written by Steven Strogatz (professor for applied maths at Cornell) , with some great other articles also.
Maybe I’ve misread, but it seems to me that this is what the OP has problem with. The “mechanic” part of calculus, the part that can be done by a computer, basically. To me that’s not math, and having trouble with it doesn’t imply that someone is bad at math, just that they’re uncomfortable with symbol manipulation.
This is true. I never learn as much about a subject as when I have to teach it. Some things I even gained a better understanding of (by which I mean, I was able to link them with other things in my mind) while I was in front of a class.
It does sound to me like your problem lies with the algebra. That’s perfectly understandable, since the hardest thing about calculus is the algebra.
Look at a calculus example problem: almost every step is algebra, geometry, or trig, until you take a derivative or integrate. When dealing with word problems, the concepts of calculus come into play before the equations, they let you know whether you’re supposed to find a rate of change, or an area under a curve. It’s the algebra, geometry and trig that let you find relationships between variables, and manipulate those variables, in order to come up with the equations you need.