161–170 of 182 posts
I wrote this guide to help from 0 to advanced math. I hope it helps. https://juandavidcampolargo.substack.com/p/juan-davids-newsl...
An extraordinarily accomplished mathematician replied, when I asked him what books to study, “You don’t solve problems by reading, you solve problems by thinking.” Thinking (hard) is the key, the practice of mathematics requires and unlocks a level of clarity far beyond ordinary everyday thinking.
Try mulling over simple facts which even children know, like the Pythagorean Theorem or the Quadratic Formula, and see if you could explain them so clearly and convincingly that any reasonable person would immediately and plainly see that they must be true.
Learning is spiral. You will almost never understand everything there is to know about a subject, but you will learn more as you return to that subject as you’ve grown and matured, and have acquired more knowledge, skills, and perspective.
You may find this resource useful. It was written by Susan Rigetti (née Fowler) [1]: So You Want to Study Mathematics… https://www.susanrigetti.com/math She also wrote: So You Want to Learn Physics… https://www.susanrigetti.com/physics [1] https://en.wikipedia.org/wiki/Susan_Fowler
> So You Want to Study Mathematics…
> https://www.susanrigetti.com/math
HN discussion here: https://news.ycombinator.com/item?id=30591177
I prefer traditional textbooks, so I've always been turned off by suggestions to use Kahn Academy. My preferred math resource is OpenStax, an open-source textbook publisher. The books only go up through calc 3, so if you're beyond that level, you will need to find a different resource.
I generally agree, as videos tend to take a long time to convey information. Have you actually worked through the OpenStax books?
I’m in a very similar position. I didn’t go to uni and somehow found myself in a programming career. In a few weeks I’ll be sitting A-level (UK advanced high school) Mathematics exams for the same reasons as you. I’m 32 years old. I’ve found having formal exams to study for very motivating, and humbling. I thought I knew things I’d read in books, but it turns out I just recognised them when I came across the same top…
I don't understand, why are you taking high school exams? Is it entry requirements for university?
Check out Barbara Oakley’s Coursera course called Learning How To Learn. It turns out exams are actually an excellent tool for learning, more so than learning without assessment.
A side effect has been that having a deadline and a measurable outcome has been incredibly motivating. I’d have probably been distracted by side projects if I hadn’t committed to the exams.
And yes, it’s accepted for uni entrance here. STEM courses at top unis will expect A-level grades in maths/science subjects, even for mature students with industry experience.
I was a C student in high school. I never took a math class beyond basic algebra. I started from Khan Academy's first exercise when I was 33 years old. It seems silly looking back that I was solving problems on the number line as an adult. At that time, around 10 years ago, Khan Academy had excellent coverage through trigonometry and single variable calculus. Once I reached that point I went to my local community col…
If you want something more hi-tech there is Khan Academy of course.
Earlier quoted context omitted.
I don't think it is, because I'm talking about a marketplace where goods and services can be exchanged for a price as being a filter for quality; otherwise known as capitalism.
If you assume price=quality and therefore always buy the most expensive one, you’re not participating in price discovery and they can just raise it, producing Veblen goods.
I think just having a price tag at all incentivizes a marketplace where the best lessons compete. Now how one determines that quality though...lots of different heuristics and I have a few thoughts on how it could be done better but reviews, especially negative ones do a fairly decent job of assessing for qualities.
My apologies if it was not clear what I meant earlier.
„A single book is enough to learn mathematics: Riley, Hobson, Bence: Mathematical Methods for Physics and Engineering: A Comprehensive Guide It has a whopping 1300 pages, but it has everything you need.
And if that is not enough for you get Cahill: Physical Mathematics This will give you advanced topics like differential forms, path integrals, renormalization group, chaos and string theory.“