/sci/ — HOW 2 TEACH YOURSELF MATH?

Consider: killing yourself puts you in a superposition of genius and retard, which cannot be resolved without finding out just how poor at math you really were. If you never sit a math exam and instead jump out of your apartment window, you will be possibly the smartest person to ever live. Schodingers retard.

>>16994031 (OP)
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>>16994033
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>>16994031 (OP)
This is highly dependent on your level of prior knowledge.
Are you at a secondary-school level or below? Then it does not really matter.
Are you at undergraduate level? Then it does matter, but the importance is on what is discussed in the work. The value of a topic is very personal and strongly related to your own mathematical *taste*, sadly as an undergraduate you lack this maturity.
Are you at a graduate level? Start with the always recommended "classics" and if they are bad, try to look for books on the topic that do suit your taste.

If you were to be more precise with your goals, I could possible introduce some books/lecture notes. However, be warned that learning is an individual experience and hence I can not provide an optimal solution.

>>16994051
Pre-Calc is my highest level.

>>16994055
What do you want to work towards? Maybe a specific application maybe a specific field? Or do you just want to get an introduction to 'college' math as a whole? If you just want to get better at pre-calc then just do Lang's "Basic mathematics" or any of the other classics suited to your taste.

If not, would you prefer a fast paced approach to the material or more handheld?
Lectures are the most extreme form of handheld, they are very slow and information sparse but highly 'illustrative' (according to students).

>>16994069
I would like to improve my math skills generally. So more along the line of college level math.

I'm certainly game for lectures. I'm out of practice a few years.

>>16994077
If you're out of practice I would recommend starting by skimming through Lang's Basic mathematics to see if you still posses the manipulation techniques required for calculus and beyond.

As to not overwhelm I will just restrict my focus to calculus.
For caclulus there is no point in reading a big book. So despite what most of /sci/ claims I will not recommend one.

You can start by watching 3B1B's video series (not very useful but hopefully convinces you of the main ideas of calculus).

A general structured course contains videos and exercises but no book. This is relatively 'fast' and straight to the point.
https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010

For another lecture series I can recommend, Professor Lenard is fine.


Easy to understand lecture notes for Calc 1-3: https://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

If you are done with calculus you must do linear algebra. Preferebly before you start calc 2.
The most important thing is to actually do the exercises. It is very easy to convince yourself that you know something but doing is a different story. Especially for computationally heavy courses like calculus.

Do stuff at your own pace, if you notice that a method is not appealing to you just change the way you're learning. There are millions of methods available for calculus and linear algebra.

If my answer was not satisfactory, feel free to ask further.

>>16994102
This makes pretty good sense to me.

If you want to give any other math advice feel free. Other users make be lurking so they could get some value from your answers I'm sure.

>>16994120
If you're doing this for yourself remember to have fun. It actually makes learning easier. I am not here to convince you of maths' beauty (this is something you must discover yourself), but making yourself suffer for no reason is not worth effort.

Never be afraid to drop a certain book or lecturer. Sometimes a slightly different approach can mean a world of difference in understanding. Try to find the way of learning that suits you best. Maybe teach your cat calculus, who knows he might be the next Euler. Don't be bound by preconceived notions of learning.

Try to actually understand **why** things are being done the way they are. Remote memorization alone will fail you at a certain point. It also makes reviewing a lot easier, since you don't need to start from scratch.

Make sure you actually understand the material before continuing. Early levels of math are build on top of each other. Not understanding now leads to problems later on.

Exercises are the best way to check understanding. Do not skip exercises, challenge yourself. However, do not waste your time on too difficult problems. Looking at solutions is fine, but try to repeat the argument yourself.

Lastly, specifically for calculus (and maybe basic linear algebra), sometimes it is not worth the effort to understand everything 100%. Move on and come back later.

>>16994031 (OP)
AOPS prealgebra -> aops intro to algebra -> hammack’s book of proof -> zeitz’s problem solving book

>>16994346
Pre-Algebra>Algebra>Post-Algebra

>>16994031 (OP)
any reason to ditch stewart for Spivak? I'm on the third chapter for stewart

>>16994588
I'd keep reading Stewart and if anything isn't clear check Spivak.

Wrath of Math Calc I series:
https://www.youtube.com/watch?v=E_BWPgEKtiw&list=PLztBpqftvzxWVDpl8oaz_Co6CW50KtGJy
Exercises:
https://www.youtube.com/watch?v=cj8fZb5CS5A&list=PLztBpqftvzxUEqGGgvL3EuIQUNcAdmVhx

Don't be intimidated by the length of the series. The Calc I series is 30 videos long but they probably average about 10 minutes each.
The exercises series is 264 videos but a lot of them are like a minute and a half and are just quadrupling down on a previous lecture. You can easily skip most of them if you feel confident you understand the procedure being tested.
It's not a replacement for a good textbook, but it is great supplementary material if you're struggling somewhere.

File: Math Question Girl.png (1.10 MB, 1523x726)

>>16994733
Awesome

>>16994127
>Never be afraid to drop a certain book or lecturer.
reposting what I said on another thread, I did exactly that with basic mathematics by serge lang because it asked for proofs and I didn't want to torture myself with that shit yet when I barely know division, I am guessing aops pre-algebra is the best alternative for someone like me?

Sometimes I wonder what the autists who were pushed into reading Rudin are out there doing. Has learning analysis improved their lives? Probably not. They probably got into some more abstract bullshit like category theory or differential geometry trying to be even more esoteric and cool and then they get jobs as community college calculus teachers.

Meanwhile the applied math chads just read stewart day one and get through calculus in 10 weeks. They just handwave everything and don't give a shit about pathological edge cases because they dont matter in the real world. They study linear algebra and combinatorics and statistics while autists are still figuring out what a dedekind cut is. They get jobs in the industry and make 8x as much money.

>>16996027
I studied applied math. Honestly it’s the same level of depressing. Just more of the same. Very few people can make a career with a math degree. Applied or not. Especially in this economy. Believe what you want though.

>>16996027
No idea why you're getting all uppity about getting filtered by undergrad math, but okay.

>>16994031 (OP)
is khan academy a good jeet?

I wouldn't bother math is extremely boring and the more advanced you get the weirder and unnecessarily complicated it gets. There are plenty of people who love doing this shit for fund. If you like overly complicated, boring repetitive tasks, get into coding and AI and get the machines to do the math for you.

>>16994033
Eat my cock, people need this advice and resources to succeed. Not everyone is an autist who likes spending his days looking at formulas.

>>16994733
This good if im still getting past college algebra and trying to get into medical school. Calculus is a prerequisite for the mcat.

>>16996027
What industry? Is the only requisite understanding calculus? Gove me an official title to look up and submit an application.

>>16996175
Calculus is the very beginning of real math. You need that + differential equations, linear algebra, statistics, combinatorics, convex optimization, and real analysis at a bare minimum.

That's what makes OP's roadmap such a trap. You spend 8 books and thousands of pages just to get to Calculus meanwhile millions of highschoolers are already applying Calculus to real world problems while you get super autistic about axioms. News flash: real math is almost never fully rigorous. That would require bertrand russell levels of mega-autism, 400 pages to prove 1+1=2.

I've never studied calculus and I'm a college graduate

>>16996192
Thank you! Im looking it has set theory and analysis before even doing one calculus problem. I know for sure plenty of medical doctors dont know how to do that. I just want to pass the mcatas and get past medical school. A basic radiologist or physician is what im going for, maybe Some research position to get into an entry level science.

>>16994102
Thanks for the advice. So single variable calculus and then linear algebra before proof writing? Exercises before a real book?

>>16994733
Is Nancy pi a good resource? She is cute and I did learn some techniques when I was going through college algebra.

>>16996120
I had an account years ago but never got started. I did like they were gamifying the learning g experience with badges and points. Have yet to try it but I'll give you advice i myself should follow. Do anything! Literally anything is better than nothing! Years i have been putting it off!

>>16996220
>So single variable calculus and then linear algebra before proof writing?
Like I told the anon I was replying to this all depends on what your goals are. if you just want to start with some university maths then yes.

If you are aiming at pure mathematics (99% of people dont), I would do a proof book before or during linear algebra. In that case you should split linear algebra into 2 parts:
1) computational (see what physics and CS covers)
2) proofs/abstraction (material in for example "Linear algebra done right").
Doing the second part after you have learned introductory proofs.

>Exercises before a real book?
Real books also contain exercises. However, the book can be incredibly overwhelming in content/scope/difficulty. Hence they can be good sources of exercises.
If you found good learning material first try to make their assigned exercises and if you feel like you don't understand yet seek out others (for example in a real book). Is that clear?

>>16996024
>aops pre-algebra is the best alternative for someone like me?
If the style of 'free' problem solving suits you, yes.
Rigour is not really important for prealgebra, you will eventually relearn everything in group theory. Prealgebra is to develop **computational** fluidity with symbols and getting familiar with abstract reasoning.

Do not stress it and just start with a book you're comfortable with and actually challenges you a bit.

>>16996192
Not to be pedantic but the last two books before Spivak in that chart actually cover some calculus and analysis.

>>16994031 (OP)
is it a traditional meme to make these hyper-autistic guides that have zero fucking practicality?

Lagrange’s theory of analytical functions is the only book you need. Thank me later.

>>16994031 (OP)
mathacademy + chatgpt to explain things you don't understand
mathacademy is pricey but it's got me to be consistent every day and i've managed to get a lot better with math

>>16999805
>just read this super advanced textbook with outdated conventions cause ughh... it's like more "real"
Again with this autism.

>>16999763
it's obvious that these guides are made by people who have never read any of these books and are not going to

This is for AstroAngela to present.

>>17000054
It ends with advanced notions but has humble beginnings (essentially high school algebra) without invoking infinities or limiting processes. The notation is standard actually. Unless you find primed function notation unusual. Anything I can help you with?

>>17000099
Yeah that seems to be a tradition almost
Dead giveaway is when they include Euclide's Le Elements lmao

>>17000099
The funniest part is that retards who were never gonna read the books actually think these guides were made by some knowledgeable people as opposed to other retards who are never gonna read these books.

>>17000241
>Anything I can help you with?
Sure, make a better guide

>>16994102
>If you're doing this for yourself remember to have fun.
I'm a college dropout and have now reacquired a hunger to learn math again. I'm basically starting from the algebra / intermediate algebra level, and working my way up from scratch. I'm 10 years out of practice, so I picked up some recommended algebra workbooks for the exercises. Most fun I've ever had in math was drilling exercise problems, getting stuck on a difficult one, and suddenly having that "eureka" moment and figuring it out. Am I doing myself a disservice my just working on practice problems without understanding how proofs work?

>>17000462
I am a bit confused about the context of your question. So I apologize in advance. You are working on prealgebra and not (abstract) algebra? I will assume the first. In this case, what are the proofs actually about? I guess things like "proving" the addition formula for sine maybe?

The point of prealgebra is to get comfortable with concepts and especially to be able to compute things with them. If *you* feel like understanding 'why' these rules are true is important then you should try the proofs.

However, it is absolutely not necessary to understand them at your level and if you continue in math you will certainly encounter them later on and probably have a better understanding as to why are as they are.

So only if you feel like the proofs matter to you, are they important, but they provide no intrinsic value (at this level).

On the other hand if you are talking about abstract algebra (college course) then the whole point is proofs so then proofs are mandatory.

>>17000482
Apologies for the late reply.
>You are working on prealgebra and not (abstract) algebra?
Yes, that's correct. However, my prealgebra skills are still good, as I'm jumping immediately into an algebra essentials book with good results so far.
>However, it is absolutely not necessary to understand them at your level and if you continue in math you will certainly encounter them later on and probably have a better understanding as to why are as they are.
Very well, I will continue to drill the basics to build a solid foundation before I continue on. Those practice workbooks I picked up are from Chris McMullan
>Algebra Essentials
>Intermediate Algebra Essentials
>Trigonometry Essentials
>Essential Calculus
I'm also going through Professor Leonard's series on precalc, but I'm going to hold off on it until my fundamentals are more solid.