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
-
>>16994033
=
>>-2

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

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

>>16994031
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.

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>>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
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
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
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.

>>17000897
>Apologies for the late reply.
No worries.

I wish you fortune and pleasure on your journey.

Nevertheless, I will warn you for a pitfall I have not yet mentioned here. One should not do 30+ prealgebra books before continuing to higher material. Try to feel for yourself when you are ready and try to take the step. This is one of the hard parts of self study since only you know your own progress.

Not only does it become incredibly boring to do that much prealgebra (or any other course for that matter); at a certain points the gains for other courses of becoming more proficient start diminishing drastically. However, this is not to erase the truth that one should really be comfortable with prealgebra before looking at college math courses.

I cannot really commend on the quality of the material you mentioned as like I said it is all incredibly subjective. As long as it covers the requirements for more advanced math and the learning style fits you it's good.

Tried and tested route (tried and tested by me):
Calculus by Thomas, with MIT lectures.
How to Prove it by Velleman
Understanding Analysis, with lectures by Marc Renault (Shippensburg University) on YouTube
Abstract Algebra by Judson, with lectures by Alvaro Lozano-Robledo (University of Connecticut) on YouTube.

Do as many questions as you possibly can and don't look at answers until you've tried your very best. None of the lectures are necessary, but I watched them out of curiousity and to reinforce certain things. Note: Lozano-Robledo's lectures cover groups only. He doesn't cover rings or fields, but the book by Judson does, so don't worry. Throw in a book on ODEs, PDEs, and number theory, and you've pretty much learnt 2 years of undergraduate mathematics (minus probability and stats but fuck probability and stats anyway). Then you can go on to something more specialised like Topology, Analytic Number Theory, and so on.

>>17000986
Right on. I'll be sure to move on to tougher material once I feel I've got the basics down. I don't know exactly why my interest in the subject reignited, but I won't let it go to waste. Thanks again, fren.

>>17001338
Shit, I forgot you need something for Linear Algebra, and if you want to learn Analytic Number Theory you'll need some Complex Analysis.

trigonometry makes me want to vomit, no i dont know what a sin wave is and i dont fucking care how it relates to a circle, and how waves can create circles, FUCK WAVES AND FUCK TRIANGLES

>>17001713
>people this retarded exist and vote
Grim.

>>17001782
Go ahead, explain to me what an angle is, explain what pure abstraction is, you won't you'll just keep manipulating symbols, like a robot, forever.

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>>17001879
>explain *concept* but NO DON'T DARE LOGICALLY CONNECT OTHER CONCEPTS AND EXPRESS IT WITH SYMBOLS!!!!

>>17001959
Nice greentext strawman, next time try actually answering the question, midwit, math will always be a fake waste of time.

>>17000450
I don’t know what to say. The book by Lagrange, including his Lecons sur le calcul des fonctions are entirely self contained and despite some odd notation here and there, it’s 100% readable and it’s actually easier than the analysis taught today because you don’t have to make giant leaps in terms of logic as you build up the theory. In modern analysis, you have to assume the axiom of infinity before you’ve done anything. It’s practically voodoo.

>>16994031
I am quite fond of Schaums Outline books for practice problems.

>>16994031
>12 BOOKS before you're allowed to learn first semester college math
I hope none of you fags fell for this.

What is the best stats/prob book that's in the goldilocks zone of not too pop sci but not too autist

>>17003518
They all kinda suck.

In theory an ideal book would be something like Springer’s Stat Labs. You use real data and leading questions to slowly introduce statistics’s tools and concepts. That book is not that easy though, you actually need to use your brain, and fill in the gaps yourself.

A lot of the books for programmers from oreilly, etc. also take this real data approach, but they are so half-assed.

I think those statistical learning books are really hard to read, like those books with Trevor Hastie, or Efron, or others as authors.

>>16994031
Are any of these books or this path in general good for someone starting to learn proofs and pure math?
Current math education is up to CS major caclulus 2 and want to eventually learn category theory and the like.

>>17003734
A lot of math books are self-contained. Even advanced ones. Just open the one with interesting title, and start reading and doing the exercises. If you find it boring, or too hard, just pick another book.

There are also a bunch of advanced math books written for idiots, engineers, biologists, and physicists with weaker backgrounds. Try those.

If you are absolutely convinced the problem is your lack of proof writing skills, or lack of problem solving skills, or lack of mathematical maturity, there are books for those.

Use your brain. Solve your excuses. Quit 4chan.

>>17003734
>Are any of these books or this path in general good for someone starting to learn proofs and pure math?
There are thousands. However, I will recommend (from **personal** experience): "Mathematical proofs: a transition to advanced mathematics"
This might not be the best book for you (since I am not you.) However, it was the book from which I learned and it contains all the essentials.

>learn category theory and the like
I think your view of pure math may be a bit skewed by internet communicators (or CS bias). Pure math is incredibly diverse and category theory is incredibly niche. 99% of its applications and even origin being completely removed from CS.

Is your main goal in math to study category theory? If so then the following should be satisfactory.

1) Study some set theory and basic proofs (just an introduciton; the book I recommended is enough for example)
2) learn from: https://arxiv.org/pdf/1803.05316
3) Study https://math.jhu.edu/~eriehl/161/context.pdf or any *other* more advanced introductory set of category notes (there are hundreds).


If you have any more concrete questions, I will be glad to assist.

so, what's the magic pill for trig. anything math wise I can learn but as soon as they introduce trig stuff in it I start shitting my pants. i think I could only ever identify sin^2x+cos^2x=1 in the wild, at most high level calc stuff and a lot of physics is basically manipulating this wave bullshit. surely someone must've written a phenomenal text that just cements this for me

>>17004751
Mileage. Exercise. Practice. You need to do the work.
You are struggling with your calculus and physics courses, because you lack the basics. Especially algebra and problem solving skills. And you also don’t want to learn.

For example: suppose you struggle with a problem > you try different things > you try using formulas and identities and other stuff you know > you ask for help from a smart friend or tutor or teacher or prof or the internet > you check the solution > you find out what you did wrong, what you didn’t know, or what you misunderstood > you try the next problem remembering what you’ve learned from the last one

That’s what a normal person would do. You instead just whine and shitpost on 4chan.

the best way to learn math is to pay some faggot phd student to teach you. go to some low income country like india or brazil and give some starving phd student some money to teach you whatever you need to learn. its very important he has to answer whatever stupid questions you may have

>>17005678
>indian "phd" "student"
>knowing things
>being able to teach them
LMAOOOOOOOOOOOO

>>16996162
based OP

>>16994733
Got any resources for learning fourier transforms, z transforms. I know laplace from taking ODE class

>>17005880
Look at the admission tests of the indian statistical institute for admission into their b.stat and b.math programmes, or the admission tests of chennai mathematical institute. Its true, most Indian phds are fake, but there are a bunch of pretty elite unis for math here. Aside from the two institutes I mentioned (these are the good ones for undergrad), theres TIFR, IISC, ICTS, which are also good for phds in math. But you probably won't get these students here to teach you cause they are too busy. Your best bet is undergrads (a select few of whom btw, by their third years have done enough self study to have almost finished a master's course worth of material). To give an idea of the progress of math education here, look at the imo results from 2024 and 2025 (India placed 4th and 7th respectively). Though calling this a progress for the overall math education is misleading, because most of these students study on their own. Maybe I should call it an increase in awareness? This is quite exciting to me and I don't mind only a small elite getting to access to a good math education, though with the current government here who knows how long this'll last. They are trying to fuck up these institutes with their zealotry and "Indian pride". They are trying to fuck the curriculum up. Want the institutes to focus on "vedic math", "Indian contributions" and all that other bullshit. Hopefully we can protect these institutes to some degree and let the professors exercise their automomy.

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>>17006249
>in a country of FUCKING BILLIONS there is a small number of actually smart people who self-educate via the internet (using Western resources) despite the shithole conditions of their country
No fucking shit. Now let's look at what percentage these people constitute of their population and compare that to any other country. Oops, it's pic related

>>17006375
I don't understand how using Western resources is a gotcha? I mean, if you are just here to hate on India, then I hate to break it to you, there are quite a few pretty good Indian mathematicians out there. But you probably won't know anyone besides tao, gowers right? I mean, I don't like India at all, despite being an Indian, but I don't see how thats relevant to what I posted. They said Indian phds have no value, and I contested by saying not if you look in the right places. I don't really care that your picrel is true, it doesn't matter to me that India is a shithole. People who spew shit like this, almost always end up being basement dwellers who have contributed nothing to society, and yet jump at the chance to say how proud they are of their country (which is to say, they are proud of other people's achievements).

>>17006414
>I don't understand how using Western resources is a gotcha?
It's not per se, but you were using a few good Indian students as an example of India being great or in the process of development when in reality it's IN SPITE of living in India that they got educated.
> I mean, if you are just here to hate on India, then I hate to break it to you, there are quite a few pretty good Indian mathematicians out there.
Once again, that's an obvious given due to multiple billion population. Only percentages matter.
>They said Indian phds have no value, and I contested by saying not if you look in the right places.
That once again is an exception to the rule. If you take a phd from a civilized Western country you have a decent semblance of a guarantee you'll be dealing with somebody basically competent and basically intelligent.
If you take a random phd in India with 99.99% chance you will get a retard who wouldn't pass a high school math test.
>People who spew shit like this, almost always end up being basement dwellers who have contributed nothing to society, and yet jump at the chance to say how proud they are of their country
Very bad guess. I'm simply stating facts here, I'm not some /pol/tard anti-jeet poster.

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>>16994031
Anna's and AI
/thread
don't even talk about math seriously in any way or even think about pursuing it until you've finished the undergrad minimum in pic rel. Why? because undergad is a bare minimum, maybe before AI and immigration you could have gotten a nice 100k excel spreadsheet job, but in terms of actual knowledge and ability undergrads are basically toddlers, you need to teach the to walk and talk before they can run or publish.
And stop fucking front loading your education, that's a fast way to burn out with almost nothing to show, that chart is so retarded and I've said that for fucking years. You need to shove the bulk mass of basic mathematics down your throat.
Pic rel is the bare minimum. It will give you a better education than the average american fat ass studying math at some shithole debt scam school meant to produce peons not mathematicians.
Maybe watch a youtube video with faggot animations if you're a stupid retard with aphantasia, but if that's the case maybe faggatory theory is more your speed anyways and you can make transgender femboy maid videos about it (only old fags will get this one).

>>16994031
"Teaching material" always shoves the stupid teacher's voices in your face. Even with books you're still subjected to this to some extent. Today you should just ask AI to teach you anything you need to learn. In fact, there's no point in learning anything anymore unless you have a goal.

>>17006441
well you misunderstood me, I even said how the government is trying to fuck the good unis up. I am just happy about some of my countrymates getting to experience good math education, and the only good thing thats happened over the decades is a rise in awareness that there is math out there thats not "hecking jee". And sorry for that last thing, guess i got worked up. If anything, I hate India more than anyone here because I actually have to live in it.

>>17006555
Absolutely. I'm from a shithole myself so I can empathize

>>17006555
ignore the chuds. thank you for free NPTEL lectures. i'm learning organic chemistry using NPTEL.

>>17006751
I am sorry, I have never had experience with that, but I looked it up, and I would recommend against using it. In general I would be cautious of anything coming out of enginnering institutes in India. You could just read books you know? I was never advocating for the good quality of education in India at large, I was just saying some students in actual good unis here are motivated enough to self educate using proper resources (BOOKS) which causes the environment in those places to be good and more opportunities for them since good professors flock to places like that.