I've recently gotten a sudden urge to learn maths from the ground up.
I have a very scattered education on math so most of it doesn't make sense to me. That's why I want to learn from the very beginning and make my way to the VERY advanced stuff.
I know this isn't going to be a walk in the park. It's going to take years and there's a chance I'll just fall behind and stop.
But at the moment I'm very determined to learn all I can and I need your help.
Where do I start. Where do I go? I found this chart on the /sci/ wiki but I'm not sure what to do with it.
Question about the chart, are all of those books or only some?
Anyone? I'm in need of some hardcore help here.
Also while we're at it, if anyone needs help learning certain types of math, they can post in this thread.
It was a bit selfish of me to just want the thread about teaching me.
I only minored in math so I dont know if I can speak to the 'very advanced' stuff.
If you're doing this for yourself I would go on Kahn Academy and just do the natural progression they've laid out. Something like Alg.1->geomtry->Alg.2->Pre Calc->all the calc courses->DEs->Linear alg.->etc. If you already understand a topic skip over it. Kahn explains maths a lot better than most textbooks will. It will give you a pretty good foundation to go explore whatever you find interesting afterwards.
I'm surprised that this isn't posted more often on this board (is there a particular reason?).
I like that it encourages studying proofs and introductory discrete Math early.
It also offers a wide variety of options to choose from. If you find yourself having trouble with a text recommended by that blog or sci, don't feel bad looking into a less rigorous text. Just return to that difficult text afterwards -- you'll have a much easier time.
Okay, so first, start with the book "Mathematics for the Non-Mathematician." It's a god-tier precalc book and you should do every single mothercunting exercise, especially since the full fucking solution manual is in the back. If you have Amazon Prime, it's like $4 new. Absolute steal.
Calculus - the border between babby-math and big-boy math. Now, you're gonna want to make some choices. You can work through that same Morris Kline's Calculus book, which is a hybrid between a calc and a mechanics (Physics I) book. But it's a doozy in terms of length so, if you want to go balls-to-the-wall, you can pick up Calculus by Michael Spivak. Kind of a meme book but it does its job. Alongside one of these calc books, you're gonna want a solid book on proofs. I'm partial towards The Book of Proof. It's made free online by the author but costs like $21 to get a solid-quality print-on-demand hardcopy on amazon. Worth it.
Analysis. Assuming you've followed my advice so far, you have several choices. Bartle or Pugh if you want to have a solid introduction to Analysis without killing yourself. Or you could choose Rudin and fuck your prostate out your tear ducts with the Math Major's equivalent of a hazing ritual. Alongside this book, work through Linear Algebra Done Right by Axler. Fucking seriously. Linear algebra is perhaps the single most useful field of modern math. Memorize that book.
After that, I don't give a fuck. You're a big boy now. Tenenbaum is good for ODEs. Ahlfors for Complex Analysis. Concrete Math is a great but extremely demanding intro to the analytic parts of discrete math. Abstract Algebra, Pinter is kind or you could do for Dummit and Foote if your idea of fun is studying a reference text cover to cover. Topology, just study Munkres.
And for functional analysis, I don't know. Riesz or Papa Rudin. (google the difference between baby and papa rudin)
Also, learn how to program. You don't have to be good. Just enough to be able to write a GUI clock
Are you just learning math without a goal? Why would you do this to yourself without some need to use it? Someday you'll wake up knowing 90% of math and realize you've accomplished nothing in the last 5 years.
a whole shitload of books won't really be useful until you patch up the basics
just get a single maths textbook like KA Stroud's 'Engineering Mathematics" and work through the whole thing. That book starts on positive and negative numbers etc and its worth going through every single exercise because you'll no doubt pick up a more intuitive feeling for how it all works instead of just being able to plug things into formulas
Here's the basic progression that you might want to take. I work a lot tutoring high school students in math, so I've worked with people on this type of thing before.
First, if you don't know it, learn high school level geometry and algebra. There are good vids on Khan academy. I can't really help you for these steps.
Next, I'd recommend reading Rotman's "A Journey Through Mathematics." It's a really good, interesting book that will help you learn and read proofs, and give you some fun anecdotes. MAKE SURE TO DO EVERY SINGLE EXERCISE (there's a little bit of calculus in the book, ignore it for now!).
While working through Rotman, you should also start learning some calculus. I recommend Keisler, since it gives you the geometric picture better than other textbooks. You can feel free to use Stewart. My recommendation is make sure you can do basic operations, derivation and integration. Make sure you can derive any function, but integration isn't as important. Pay a lot of attention to the chapter on vector calculus, it's the most important thing you'll learn.
When you finish Rotman, you'll probably not be done with calculus yet. I'd recommend the MIT OCW course materials for learning Linear Algebra at this time.
My opinion on diffy Q (ordinary differential equations): skip them. All of the textbooks are awful, and the useful information in the course comes from having a good teacher. It's supposed to be a teaser for differential geometry and more difficult DE courses (like partial differential equations), but it invariably fails. Skip it.
Next, you're ready for an intro to analysis and algebra. Do these concurrently, as well. Algebra my recommendation is Fraleigh. Analysis my recommendation is to first complete Spivak's calculus, then do Munkres' Analysis on Manifolds (this is radical, if you don't feel comfortable with that, just do Baby Rudin instead).
You're free at this point to pursue at a lot of topics. I recommend topology or complex analysis.
Thank you both for the book recommendations
I'm gonna be looking into all of them.
I really enjoy math. It looks very beautiful to me and it's sort of like a hobby at this point.
I also plan on getting a job in some sort of science so it'll most likely help me one way or another.
What I wrote is basically an easier version of the first year and a half or so of the pure/honors math curriculum at my university.
>even baby rudin is overkill
Rudin is hard, but I kind of feel like it's a necessary evil that each generation has to inflict upon the next.
You can have your own opinion, though.