51–60 of 231 posts
This book is fantastic and pretty much takes you through an entire undergrad mathematics course: https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...
One thing that worked for me was to have a community of fellow mathematicians to study with. There's a lot of cultural stuff that is kind of hard to osmose from books, such as for example, how to pronounce things that you read. Mathematical notation is meant to be read out loud. It's shorthand for English, or whatever your natural language is. You should be comfortable seeing a sigma sign and thinking in your head, "…
That is also part of the loosely defined term, “mathematical maturity.” When you’ve reached it, you can generally grasp the basics of unfamiliar math quickly. Failing that, you can find out what you need to study to understand it and do so on your own. You don’t typically obtain that kind of maturity until graduate school, maybe upper undergrad if you’re quite good.
People complain a lot that books and presentations don't do everything and that mathematics has a bad "user experience". They may have a point, but the complaining alone won't fix it and will leave most people still feeling like frustrated outsiders.
There's a set of basics that you will want no matter which direction you go: calculus/real analysis, linear algebra, differential equations/dynamical systems, and sets, groups, rings, and lattices. Calculus: learn to extract qualitative information about a function (it goes up here, has a maximum there, goes down there, oscillates with an increasing period, goes to this value at infinity...) and to numerically comput…
Any suggested reading on rings and lattices? I took a lot of math classes in undergrad but was never exposed to these concepts.
I know there are textbooks on the topic, and probably lots of people who deal with lattices a lot. But my own experience seems to be that wikipedia puts more emphasis on lattices and things like universal algebra than actually happens in math.
I had math through some introductory calculus when I was an undergrad 20 years ago, but I let my skills lapse. But I want to understand enough math so that I can do some more complex electronics projects and some statistics / ML / intelligence analysis. This level of math, as I recall, is more or less the math core of the undergrad engineering program I dropped out of in favor of a philosophy degree (cause I am dumb…
If we are talking about content you can find plenty of advice here or elsewhere. But do yourself a favor and pay a tutor and/or find a study group. As in writing, dancing, etc. you cannot evaluate your own work good enough. You will not improve your math watching youtube videos and reading books. You need to produce stuff that pass the "sniff test" to your colleagues.
You will not become good at math watching youtube videos and reading books. That depends on exactly what you mean by "become good at math". If you're talking about "becoming a mathematician" and doing original research in pure math, then you're probably right. But if one means "learning existing math well enough to apply it to a problem", I would argue that one can learn this stuff just using books, videos, etc. At l…
https://www.theatlantic.com/education/archive/2014/03/5-year...
Math is not linear, So why do we teach math in hierarchical steps? - https://prezi.com/aww2hjfyil0u/math-is-not-linear/
http://ocw.mit.edu/resources/res-18-001-calculus-online-text... highly recommended for Calculus
Here's my personal opinion about how you should approach this. It's all well and good to want to cover undergraduate math courses. When you are actually enrolled in a university, you will have enough inertia and motivation to complete the courses. However, when you are self-studying you are doing it all on your own. It's hard to be as thorough and cover everything. And so I ask, what really is your goal here? You don…
It's an incredible resource with great introductions to each topic and examples that are easy to follow and try for yourself.
It is really hard to truly self-study in mathematics. Going through the opencourseware and reading textbooks (working as many exercises as you can, of course) will get you only so far. It is important to have someone (ideally with a PhD-level education in mathematics) who you can meet with to guide your study, correct mistakes and answer questions.
Textbooks and lectures will teach you what math is. The concepts, the different proof methods can all come from a book.
The value from an instructor is that they'll give you feedback on the _how_ of math. A halfway decent professor will edit your proof just like an English professor will -- from the level of word choice all the way to the method you constructed and presented your argument. And, just as importantly, they'll tell you when you fucked up and didn't notice.
Earlier quoted context omitted.
Any suggested reading on rings and lattices? I took a lot of math classes in undergrad but was never exposed to these concepts.
Lattices (the algebraic structure) seem to exist only on Wikipedia in the sense that the only time I've seen lattices every mentioned in my standard undergrad education is once for a proof of the Stone-Weierstrauss theorem. I know there are textbooks on the topic, and probably lots of people who deal with lattices a lot. But my own experience seems to be that wikipedia puts more emphasis on lattices and things like u…