I am in a career that is quite mathematical – volume graphics / medical imaging. However I have not formally studied any mathematics since the age of 16 (I’m 43 now). I’ve generally managed to “muddle through” and I have a decent working knowledge of a number of areas that are beyond high school maths.
But I really want to fill the gaps in my knowledge more comprehensively. I would like to at least be able to look up mathematical concepts on wolfram, or heck, Wikipedia, and understand the terminology and proofs.
Now of course there are many, many options for distance / online learning now, and that’s my issue – I don’t want to sign up for an A-level maths course at a college, and then find there are actually far superior free or cheap online options. At this point in my career it doesn’t matter at all about obtaining any kind of certificate / diploma, only that I genuinely improve my understanding of advanced mathematics.
(Oh, and in case anyone is worried about someone with a poor maths background working in medical imaging…my job does not involve needing to write or understand equations. I’m more on the user experience side of things. It would just be nice to understand better what’s going on “under the hood”.)
Those are often not the best places to look when you’re trying to learn about or understand a new mathematical topic.
But as for where you should look, well, that depends. What specific areas of mathematics are you interested in learning? At what level? Are you more interested in learning about mathematics, or in learning to do mathematics? Skills or intuitive understanding? Neat ideas or deep theory or practical (or impractical) applications? Do you learn math better from books, or videos, or guided exercises?
Yes to the first two, calculus is where the wheels start to come off.
I can derive that y = x² has gradient 2x. But the typical differential equation goes over my head, let alone the kinds of operations then performed on those equations.
I used purplemath a lot when I was still working. I did a lot of math programming and it was a good refresher for various things. Note: It’s not just algebra.
All good questions, but alas, I think I am at the point right now of not even knowing what I don’t know.
I think I would like to start with enough pure mathematics that I could understand this level of terminology. And yes, I would prefer guided exercises where I need to do some work and can check my answers.
In order to solve differential equations, you must know how to solve integrals, and that’s much harder to learn than derivation. Derivation depends on some basic rules, and working with these rules algorithmically will always lead to success. Integrating almost always requires some intuition and guesswork which you can only learn by a lot of practice.
ETA: in my first semester studying electrical engineering, besides the regular math courses we had a (voluntary) special seminar where we did nothing but solving integrals.
And that’s a good example of why I wouldn’t use Wikipedia to learn about math concepts. Most of what’s on that Wikipedia page would be way over the head of probably most people who would need to work with normal distributions, let alone anyone who was looking them up because they had no idea, or only a vague one, of what a normal distribution is. For such people, a very basic introduction like this would be a better place to start.
You might look into the Schaum’s Outline series of books on various areas of math.
The MIT Open Courseware series is quite good, but it helps if you know just what you’re looking for. I hear the Khan academy is great for teaching math, and there is so much content you can probably get up to speed on whatever topic you like, on your own.
If you’d like to work in a more guided way, with e.g. a tutor, a local community college might be really helpful. Maybe take a math course or two there, and take advantage of one-on-one teaching they may offer. (I’ve helped serveral students as a tutor under such circumstances.)
From the example you gave, it is clear you want to learn calculus and learn what an integral is (it is actually the area between the curve in question and the x axis). In the distribution example, the integrals cannot generally be solved analytically (the Wiki actually says that) and must be calculated numerically. So it looks what you want is something that goes into the theory but does not concentrate on actual computation.
Then there are the differential equations, which is a difficult topic in itself. Again, nearly all DEs cannot be solved analytically and numerical solutions are needed.
As an update, I am working through Khan academy right now.
From the responses, and my previous intuition, it seems that calculus is the main gap in my maths education, so I am working through courses on differentiation and integration.
It’s starting out easy, but I’m going through it all anyway to ensure I have no holes.
After I (hopefully) have calculus in the bag, I might be better placed to understand what I need to study next. As I say, right now, I can’t “read” calculus, so whenever I look up any maths topic, as soon as dx shows up, I’m lost. After I understand calculus I should know better what I don’t know
