Ask HN: How to self-learn math?

https://www.amazon.com/Maths-Students-Survival-Self-Help-Eng...

By starting code so young, I had years of experience before college, serious enough to work part time developing on commercial products.

I was cocky, thought CS 101 was a joke, and it mostly was. But it didn’t take long before vast areas of theory and practice I wasn’t even aware of became part of the classes.

At the end of an undergrad degree you don’t master all these new concepts, but you do become aware of them, you practice them enough to know where to dig later in your career.

I just see it as very unlikely that most jobs will make it easy to establish this same broad foundation, and it’s a powerful thing.

Surely for a few people it may not make a difference, but even for geniuses who turn out to have wildly successful careers, who’s to say it wouldn’t have enabled more insights or productivity?

And some introductory mathematical logic.

From this you can immediately move to Analysis on the real line (up to Reimann integrals)

Linear Algebra is also something you can start (Kenneth Hoffman and Ray Kunze https://www.amazon.com/Linear-Algebra-Kunze-Hoffman/dp/93325...)

Once you are comfortable with Riemann Integrals, you can start attacking Complex Variables (John Conway has excellent springer texts: Functions of One Complex Variable Vol 1 and 2)

Some texts you should look at after you understand basic set theory:

Analysis:

1. [Michael_Spivak]_Calculus - good book for introduction to real analysis

2. [johnsonbaugh,pfaffenberger]_Foundations_of_Mathematical_Analysis - Dover publications

3. [Vladimir_A._Zorich]_Mathematical_Analysis_I - well written but less known. Recommend checking it out.

4. [Gerald_B._Folland]_Real_Analysis_Modern_techniques_and_their_applications - My top pick, but a tough read.

5. [Rudin_Walter]_Principles_of_Mathematical_Analysis - classic book

Linear Algebra:

1. [David_Lay]_Linear_Algebra_and_Its_Applications -

2. [Friedberg,Insel,Spence]_Linear_algebra - Undergraduate level text

3. [Hoffman,Kunze]_Linear_Algebra_2nd_edition - Graduate level text. My top pick.

4. [Gilbert_Strang]_Introduction_to_Linear_Algebra - Undergraduate level linear algebra. Same guy has MIT OCW lectures.

5. [Peter_D._Lax]_Linear_Algebra_and_Its_Applications

Complex Variables/Complex Analysis:

1. [John_Conway]_Functions_of_One_Complex_Variable_I - My top pick

2. [Lars_Ahlfors]_Complex_Analysis_(Third_Edition) - Classic. Not a big fan though.

research as much as you can about the problem until you understand it well enough to explain it to someone else

when you come across new concepts, research them.. recurse ;p

if you like to program then try to write your own implementations of concepts as you learn them

if you are unfamiliar with programming i would recommend trying it, you get to build this math you are learning and when complete you can develop intuitions by manipulating: constants, methods, models,..; as well as being a great learning aide.. debuggers as standins for instructors

read original works: books,papers,..; where ideas are branched from

the engineered complexity of the state of the art can obfuscate underlying concepts, and seeing how they were first formed can illuminate their present state

these initial works can be very approachable because they often contain new concepts that need to be defined within them, whereas a paper referencing that initial work will often consider the concepts well known to anyone intending to read them and omit comprehensive description

i think what is most important is that you research whatever is interesting to you

(o) https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_m...