For me, it’s all about consistency. It’s spending a few minutes to a few hours every day, forever, til the day I die.
I usually can squeeze in 30 minutes to an hour every day to study something (whether it’s math or something else — right now I’m studying cinematography). Sometimes that’s in 15-minute chunks if it’s a busy day. Usually it’s before bed or while I’m eating lunch or if I have extra time on the weekends while my kids are napping.
It’s all about just doing a little bit every day. That’s been successful for me.
Grab a pen and paper, open up the first book in any of the guides, and start reading. Read for 15 minutes, or 20 minutes, or whatever time you have on your lunch break or before you go to bed or while you’re using the bathroom. Do it again the next day. And the next. And the next.
That’s how I did it. There’s no brilliance involved. It’s just jumping in. The more you do, the easier it gets.
I suspect that people forget that undergraduate programs don’t really cover very much. This true not just for math, but for pretty much every other major. I mean, think about how little of physics you learn if you only take undergraduate courses!
I suggest taking another look at the list and comparing it to the required courses of the undergraduate math majors at the top 20 universities in the USA.
Real analysis, complex analysis, topology, and number theory are there (topology and number theory are both listed as electives since most math programs categorize them as such). Graph theory, functional analysis, differential geometry, probability, and statistics are almost always either electives or graduate courses.
It’s funny, because most of the things you mention as “real math” are things that many math undergraduates don’t learn (not until graduate school at least) but that physics students learn as undergraduates (differential geometry, measure theory, functional analysis, etc.).
For what it’s worth, the curriculum in this guide is modeled after the math major maps of many universities, including the one I attended (Penn). I would be curious to know what part of an undergraduate math curriculum will lead people very far astray…
In that case, I recommend starting out with Zill's Precalculus with Calculus Previews and then working through Stewart's Calculus: Early Transcendentals!
If you have a solid background in calculus, I'd recommend Zill's Advanced Engineering Mathematics, which is pretty much basic math for physicists and engineers (aka for people who need to "use it").
You cut out the middle of that paragraph, which says:
"Sadly, there is all sorts of baggage around learning it (at least in the US educational system) that is completely unnecessary and awful and prevents many people from experiencing the pure joy of mathematics. One of the lies I have heard so many people repeat is that everyone is either a “math person” or a "language person” — such a profoundly ignorant and damaging statement. Here is the truth: if you can understand the structure of literature, if you can understand the basic grammar of the English language or any other language, then you can understand the basics of the language of the universe."
Check out my physics guide: https://www.susanrigetti.com/physics. It has both the physics core curriculum AND the math essentials you need to know in order to understand the physics essentials. (And thank you!)
That being said, Axler is an excellent book. I don't know if I would replace Strang with it, but I should add it as a supplement to the next edition of this guide!
Agree that Baby Rudin is VERY difficult to study on its own. I recommend only studying it alongside the other two books I listed: Abbott's Understanding Analysis and Spivak's Calculus (which has a solutions manual). Abbott in particular is very straightforward (at least in comparison with baby Rudin haha)
Awesome!! I have it all outlined, just need to skim through the textbooks again and then type everything up. I’m putting up the philosophy list next week and then all my spare time will go into finishing the math one!
I never once in my life imagined that one of the first comments on a front-page HN post would be one that claimed that refusing service to Nazis was "spurious" and "bigoted" and that said comment was not flagged-to-oblivion.
For anyone reading this thread, please know that this is NOT the majority opinion within the tech industry - not by a long shot. We are not Nazi sympathizers, and we do not think this is normal. It's not normal.
Hey there! I don't make very much on affiliate links but I've kind of done what you want to do on my personal website. I'm a big reader so I post links to what I read and have made a specialized reading list for physics. The affiliate money is just enough each month to cover the hosting cost for the site and to buy 2-4 new books each month, so it sustains my reading (and writing) habit!
The parent comment is not correct. No, you will not be "legally complained against" (I think you mean "am I breaking the law") if you compliment your coworker's hairstyle. See this: https://www.eeoc.gov/laws/types/sexual_harassment.cfm
I usually can squeeze in 30 minutes to an hour every day to study something (whether it’s math or something else — right now I’m studying cinematography). Sometimes that’s in 15-minute chunks if it’s a busy day. Usually it’s before bed or while I’m eating lunch or if I have extra time on the weekends while my kids are napping.
It’s all about just doing a little bit every day. That’s been successful for me.