Ask HN: How to self-learn math?

Recommend Guesstimation by Weinstein and Adams as the first topic to master. Getting comfortable with numbers and their sizes will make everything else easier. Also, getting in the habit of doing rough explorations is an essential skill in exploring all later material.

Technical Mathematics with Calculus by Calter is a single volume that covers stuff up through calculus in a, well, technical manner.

For a more understanding way, try Elements of Mathematics by Stillwell.

If you get past Calculus, I recommend Vector Calculus, Linear Algebra, and Differential Forms by Hubbard. It gives an amazingly clear viewpoint on the higher level analysis and algebra topics, both numerically and abstractly.

For statistics, you might try something like Think Stats by Downey which emphasizes explorations with Python, real data, and Bayesian statistics.

As a faithful companion in your journey, use something like GeoGebra or Desmos to really explore the visual side of all the topics. Computers can do the tedious computations. Your task is to learn why we are doing this and how it is being done. When you get to calculus, learn what Newton's method is doing and appreciate how amazing it is.

Exactly. What’s really being referred to? Lower cost and more scheduling flexibility perhaps?

My own take on it:

Lang's books about the basics I find lovely

- Basic stuff: Basic Mathematics - Lang

- One variable Calculus: A First Course in Calculus - Lang

- Multi variable Calculus: Calculus of Several Variables - Lang

- Linear Algebra: Linear Algebra - Lang

- Number theory: An Introduction to the Theory of Numbers - Niven, Zuckerman, Montgomery

Some more advanced stuff

- Algebra: Algebra - Artin or Algebra, Chapter 0 - Aluffi

- Complex Analysis: Functions of One Complex Variable I - Conway

- Probability Basics: An Introduction to Probability Theory and its Applications I - Feller

- Real Analysis and functional analysis basics: Real Analysis - Folland

- Basic Differential Geometry: Elementary Differential Geometry - O'Neill

- Riemann Surfaces (algebraic take): Algebraic Curves - Fulton

- Differential Topology: Differential Topology - Guillemin, Pollack

- Riemann Surfaces (analytic take): Compact Riemann Surfaces, an Introduction to Contemporary Mathematics - Jost

- Modern Differential Geometry: Lectures on The Geometry of Manifolds - Nicolaescu

- Functional analysis: Fundamentals of the Theory of Operator Algebras I - Kadison, Ringrose

- Introduction to the Index Theory of which you actually have already seen some in the Riemann Surfaces books with the Riemann-Roch theorem: Index Theory with Applications to Mathematics and Physics - Bleecker, Doob Bavnbek

- Homological Algebra: An Introduction to Homological Algebra - Weibel

- Algebra for algebraic geometry: Commutative Ring Theory - Matsumura

- Soft introduction to schemes: The Geometry of Schemes - Eisenbud, Harris

- Algebraic geometry: Algebraic Geometry - Robin Hartshorne

This should get you up more or less to what was current in the '60s :)

Additional methodological note: I'm not suggesting going linearly through all these books. Well, perhaps going linearly thorough the basics would be a good idea, but after that I would follow my own interests.

The important thing is really to have pen and paper and work things out by yourself, not just reading the book. I'm not saying you should try to prove all the theorems yourself or do all the exercises, that would take an unrealistic amount of time, but you can try to think about a theorem before reading its proof to see if you have a sense of which road is more likely to lead to a proof, and then try to reproduce the proof with pen and paper after having read it to check if you actually understood it.

I'm still working on generating the MATH eBook, but the 3-in-1 book (MATH+MECH+CALC) is available here: https://gumroad.com/l/noBSmath Chapter 1 of the 3-in-1 book is essentially the same as the No Bullshit guide to Mathematics.

You can see a preview here: https://minireference.com/static/excerpts/noBSguide_v5_previ...

I found https://artofproblemsolving.com/ to be invaluable and I was at a state you were a few years ago when I found it. The online problems and the workbooks with the PDFs where awesome. I really like it tho it can be cheesy sometimes it really covers all the way through to calc very well there’s online quizzes/work problems as well as ones in the books/PDFs and it comes with a video series