Hey, /sci/. I have a weird and open-ended question, so please

>>8065182
On on khan academy and MIT open courseware they have some really good shit that will help you out. I know some other ones that I'll get back to you on.

>>8065182
Math grad student from standford here.

I was in the same boat when I was younger.

I dont think you messed up. I think its just a common pathway that many people follow. Going from mindless plug-and-chug A+ to realizing the power behind it and developing a genuine interest for deeper understanding

>>8065243
So its not so much you cheated yourself out of understanding as opposed to a natural and common developmental stage

Thanks for the responses, guys

>>8065238
I'll definitely check those out, thanks!
Which OCW course would be good to start with? Single Variable Calculus?

>>8065241
Which book is Stewart's book? Is it referring to "Calculus" or "Calculus: Early Transcendentals"? I'm looking through the Spivak calculus book, and it looks really complex, but I'll try my best when I get to that point.
Thanks for the guide!

>>8065243
>>8065249
That makes me feel a lot better, thanks. I'll try my best!

Also, does anyone know if there are any online communities where I can quickly ask a question I had? I know that there are forums, but are there any beginner math-oriented chat rooms or IRC channels where I can ask questions to people who know more about math than me?

I dropped out of school at sixteen. Walked out in the middle of a basic geometry class. Am now 31, going back to school with a newfound passion for math. Aced every class I've taken so far.

You'll be fine, anon.

>>8065273
stewart's book is calculus: early transcendentals

he split his book "calculus" into two, of which early transcendentals covers single variable derivative calculus & basic series/sequences. the second book does multivariate calculus in a similar format as the single variate curriculum (i.e. he focuses on the mechanics over the proofs/rigor)

the reason why you do stewart first is that he provides you with the mechanics of calculus. you don't want to be struggling with the basic mechanics of calculus while also having to do the heavy lifting in proofs/analysis

this is why people generally suggest stewart before spivak/rudin to most students, unless they are profoundly autistic

>>8065285
this is not true

The early transcendentals edition is the first half of his full calculus book. It covers from basics of functions, single variate derivative calculus, single variate integral calculus, polar/parametric calculus, sequences, series, basic ODEs. Calling this a "condensed" version isn't true. It's a truncated version from the full single variate-multivariate text.

>>8065285
>>8065287
>>8065292
Alright, I'll take a look at transcendentals then, thanks again guys

>>8065314
there are many pdfs online of his full calculus book

personally i would recommend doing both parts of his text, since multivariate calculus is an important part of many many domains

>>8065321
I was thinking of doing early transcendentals and then going to the spivak book.

Would it be a better idea for a beginner to do the full stewart calculus book first?

I realized that nobody really addressed the
> I feel like I learn best when I have someone to ask questions and get clarifications from

I think that most people feel the same and that there's no real solution here. The transition from a math student to a mathematician is one where you can self-study essentially as well as study from an instructor. This is because there is far more material in mathematics than there are potential instructors available to you at any given time.

>>8065322

To be honest, I haven't covered the Spivak book. Looking at the table of contents, and considering my personal experience, I would recommend going through all of stewart first.

People loathe stewart since he basically just gives students the "plug-and-chug" recipe without much intuition, but like I said, it's typically difficult to understand the proofs if you don't even understand the mechanics (assuming you have the opportunity to distinguish between the two).

Keep in mind that a first year uni undergrad going into math/phys/chem/eng will typically cover all of stewart's two books, yet essentially no student beyond a mathematics student will go over the proof/analysis behind calculus (i.e. spivak/rudin). So when asking "is it a better idea for a beginner to do the full stewart book first", I'd have to say yes.

>>8065314
Reading stewart is a good way to get back into snoresville

Most analysis textbooks are for beginners and assume very little.
Spivaks book is streets ahead Stewart. Especially if you actually like math and aren't just doing it so you know how to calculate a derivative.
Pugh is a bit harder but has amazing explanations.
If you can through the first chapter of any of the analysis books (the one on the real number axioms, which you should recognize for the most part anyway), its only a couple steps to understand epsilon-N proofs then epsilon-delta. After that the rest of analysis is a breeze.
And then You can explain why things like lHopitals and fundamental theorem of calculus work

>>8065322
Doing Stewarts and then Spivak is just doubling your work with little benefit imo.
Spivak plans to show you how to apply the theorems as well.

>>8065331
Alright, thanks for clarifying that for me.

I'll spend time covering the entire Calculus book, and then slowly work through more advanced books.

Guys, what about discrete mathematics, probability, and statistics? What are the best textbooks for those topics?

>>8065323
>self-study
Yes, this is a big problem I have. Do you have any tips on improving my capacity to self-study? When reading about a new topic, I find myself losing focus a lot