How to self study pure math - a step-by-step guide

Good introduction for the starting topics with consistent related topics in mathematics, I believe that would help to build s good solid foundation for each single concepts to be well-linked. Thank you.❤❤🎉🎉

Thank you very much.
The problem for students today is not having enough resources, it's having too many resources - which, if you think about it, is just like not having any resources at all.
When the signal that you are searching for is hidden in a cacaphony of incomprehensible noise, you might as well be deaf.
Your insight is extremely valuable.

I used to just do a thousand of questions and make tons of mistakes. I literally just bash my head on the wall without thinking the consequences. So just plain cowboy tactics.

Can you please make extensive lists for studying math as a physicists

hi an excellent self study guide, ever thought of doing one for Mathematical Statistics or A.I. Mathematics

Bruh that is so much math by second year 😭 I majored in eee and we only take up to diff eq, calc 3, and linear alg. Math majors are crazy haha

I just can't wrap my head around math, it feels like my brain was not made for it at all. No matter how hard I try to understand I just can't find any meaning in it
and it makes me feel so stupid

i just search up (topic name) math sorcerer and get whatever book he recommends

Not going to do this, but this video is gold for everyone wanting to learn math on their own. hella valuable resources. Thanks a lot!

I want to read the book Differential Geometry Please suggest me books that I should read before(Please Note I have already read calculus)

Not sure why I’m watching this as I’m an anthropologist, but it seems neat. I have high respect for anyone who puts in the work to study (whether in a university or on their own) such difficult things. Or really anything for that matter.

Hello. What's the title of the book behind " Self Study"? Thank you.

Thank you very much. How about partial differential equations?

Where are abstract algebra, probability theory and number theory? These are important fields in pure mathematics. What's wrong with studying determinants in linear algebra presented in the book you are referencing?

What a treasure did I just find?

Can you suggest resources to learn ODEs and PDEs as well?

buen contenido, quizas pueda aprender algo.

Following this map, will I learn in any of these books multivariable calculus? If yes, will it be as rigurous as the real analysis book?

please dive deeper, show us how you learn(the learning and thinking process, what you think about the content you read, what question will you ask while reading it as so on) for a sub-topic in any book. that will help a lot

Sorry but this video is bullshit.
The only thing that helped me passing my IT math exams was to
1. get help from tutors
2. do as many exercises with solutions as possible and only then fall back to theory when I did not understand something

Videos are helpful but dont fool yourself: all math guys did a million exercises and had good tutoring

ChatGPT as a private tutor revived me;

-> not one single book and most lectures helped me understand the concepts.
The reason why is that they dont mention 50% of the information they have but don't mention specifically which you need for understanding the assignments.

Passive learning is extremely slow and all the exercises in books are not part of the content but out of context (thus being difficult to solve and often have no solutions).

Thank you so much for this video !!

I will return here when I complete LinAlg by Sheldon Axler and Analysis 1 by Terry Tao!!

Can you learn complex analysis directly from serge lang without reading any other book on complex analysis

Linear algebra is not concerned with general maps between vector spaces, but with linear maps between them.

Linear maps are also not defined as maps between vector spaces... They are defined as vector space homomorphisms.

Why does every other comment start with "as a [...]" 😂

There is an argument in the comment section about which is the best introductory and self study book for Calculus. Some say Spivak's is the best but it's the worst in terms of being the introductory book on Calculus. However, in my opinion Louis Leithold's two book namely Before Calculus & TCWAG are the best introductory and self study book of all time.
Louis Leithold is the G.O.A.T🐐.

Wish there was a similar outline for Statistics

I love when they include numerous examples. When I was learning math, the teacher always showed us the easy examples, but would give us the challenging ones. Like, I get it, but you can't just show us how to do A, B, and get C, but tell us to do our own problems that require us to get from A to E.

In your description box at complex analysis Wesleyan University playlist is not working???

is it possible to make this video any more boring? I don't think so. That's why mathematician have that "special reputation"

Is calculus, technically speaking, a sub-topic of any of those subjects? I ask because I've seen books on Vector Calculus and I wonder if that can be treated as a chapters of a very comprehensive linear algebra course.

Bruh, I don't even do maths....however, i love this video purely because I know I can study pure math if I wanted to, and here are the resources.

How many years would it take to learn half or all of it for an average person 35+ y.o.?

Just read a book start to finish.
Every math book basically starts with axioms and definitions then grows on that

What should I learn to succeed in statistics ?

as a cabbage, i am green

Totally agree with
@giochiqobava3467. I always hated most of those books "great for self-study" havingexcercises without solutions. A tutor at university said: "at some point you're supposed to just know whether solutions are right or wrong."

I always thought this was so silly. If I knew all the solutions all along - why would I even have to do the excercises? Why can't these smart guys writing the books figure this out?

I know this video has been out for a while but what do you recommend for ODEs?

Thank you :)

Some suggestions for other topics:

(modern) Algebraic logic: J.M. Font, An Introduction to Abstract Algebraic Logic
Universal Algebra: Clifford Bergman, Universal Algebra: Fundamentals and Selected Topics
Category Theory: Tom Leinster, Category Theory; Emily Riehl, Category Theory; William Lawvere & Stephen Schanuel, Conceptual Mathematics

This is why I wasn't in advanced placement math-

I simply can't follow the subject and start daydreaming...

If you don't mind 12$ per month subscription, then Perlego has a great library of scientific text books on all subjects including Mathematics. Actually, mathematics alone has over 10 thousand text books available, many of them written in 2022 alone, but there are many classics from 70s and 80s as well. Truly an endless well of academic resources. You are also not bound to it, so if you don't like it just cancel it any month you like and you won't be charged anything extra.

Thank you for bringing all this together, true hero! Your voice is wonderfully relaxing too!

I must add that NPTEL courses, which are delivered by good professors from IIT , NIT , CMI and other fantastic institutes , are also brilliant and knowledgeable source for Pure maths and engineering subjects

What book you sugest to learn probability

I used to be one of the better math/science people I knew. at least among my peers. However, since graduating high school, all my friends are studying math and science while I study outdoor leadership which is an arts degree and has no required math courses which made me sad. However, outside of just going and getting another degree, I didn't have a strong grasp for how best to learn these things. Thank-you so much