I couldn't disagree more. I studied Analysis in the Uni, and even in that environment Rudin is pretty bad. For a total newcomer that book will leave you completely helpless. Also, solutions are a must have, without them you are almsot totally lost. In their absence, it is OK to ask on StackExchange or #math on EFnet.

First let's start with a few books to prep you for college-level maths:

* https://www.amazon.com/How-Study-as-Mathematics-Major-ebook/...

* https://www.amazon.com/How-Read-Proofs-Introduction-Mathemat... ; or

* https://www.amazon.com/Numbers-Proofs-Modular-Mathematics-Al... ; or

* https://www.amazon.com/How-Prove-Structured-Daniel-Velleman-... (I believe you can find solutions to the 2nd edition online)

For Single-Variable Analysis

* https://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/0...

* https://www.amazon.com/How-Why-One-Variable-Calculus/dp/1119...

* https://www.amazon.com/Mathematical-Analysis-Straightforward... (contains solutions to exercises)

* https://www.amazon.com/Understanding-Analysis-Undergraduate-... (there are solutions online for the 2nd edition)

* https://www.amazon.com/Numbers-Functions-Steps-into-Analysis... (this book is a brilliant exercise-guided approach that helps you build up your knowledge step by step + solutions are provided).

My answer to your question is math. Learn to read and write proofs. Any intro to proofs will do: those employed in discrete math, the ones in analysis, the diagram chasing ones, whatever...Working with math proofs will definitely straighten out your thinking and whip your mind into shape.

Some suggestions to get you started:

Book of Proof by Richard Hammack: https://www.people.vcu.edu/~rhammack/BookOfProof/

Discrete Math by Susanna Epp: https://www.amazon.com/Discrete-Mathematics-Applications-Sus...

Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand et al: https://www.amazon.com/Mathematical-Proofs-Transition-Advanc...

How to Think About Analysis by Lara Alcock: https://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/0...

Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers: https://www.amazon.com/Learning-Reason-Introduction-Logic-Re...

Mathematics: A Discrete Introduction by Edward Scheinerman: https://www.amazon.com/Mathematics-Discrete-Introduction-Edw...

The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs by Rafi Grinberg: https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Pr...

Linear Algebra: Step by Step by Kuldeep Singh: https://www.amazon.com/Linear-Algebra-Step-Kuldeep-Singh/dp/...

Abstract Algebra: A Student-Friendly Approach by the Dos Reis: https://www.amazon.com/Abstract-Algebra-Student-Friendly-Lau...

That's probably plenty for a start.

Are you comfortable with proving math statements? If not, How to Think About Analysis by Lara Alcock is an amazing intro to Analysis. http://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/01...