susanrigetti

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.

I will tell you the secret: just jump in.

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.

That’s what the real analysis course is usually for, and why it comes after linear algebra and algebra.

I want this too. Let me know if you find anything!!

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.).

Yeah, iirc the ebook formatting made the book difficult to read.

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."

:)

guilty as charged! :)

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)