I never took part in math competitions in middle or high school so I feel like I'm still pretty bad at problem solving, and it seems like a bottleneck to gaining better employment and compensation through technical interviews - how did you improve?
Discrete Math will put you in a mathematical state of mind whatever that means. Discrete Math to Real Analysis (or Abstract Algebra) is like weightlifting (and general body conditioning) to a sports discipline like classical wrestling (or soccer).
Real analysis will teach you to be an opportunistic problem solver who rock-n-rolls (street-fights) their way through problems.
Abstract algebra will turn you into a morosely formal, orderly and pedantic systematizer and generalizer.
You want to be both a formalistic thinker and a flexible one.
For intro to math try [0] Infinite Decent Into Math by Clive Newstead / John Mackey, [1] Book of Proof by Richard Hammack [2] Math Foundations of Computing by Keith Schwarz (ALL LOOK TO BE FREELY AVAILABLE)
1. Discrete Math -> Algorithms
or
2. Discrete Math -> Abstract Algebra
or
3. Discrete Math -> Real Analysis
Discrete Math will put you in a mathematical state of mind whatever that means. Discrete Math to Real Analysis (or Abstract Algebra) is like weightlifting (and general body conditioning) to a sports discipline like classical wrestling (or soccer).
Real analysis will teach you to be an opportunistic problem solver who rock-n-rolls (street-fights) their way through problems.
Abstract algebra will turn you into a morosely formal, orderly and pedantic systematizer and generalizer.
You want to be both a formalistic thinker and a flexible one.
For intro to math try [0] Infinite Decent Into Math by Clive Newstead / John Mackey, [1] Book of Proof by Richard Hammack [2] Math Foundations of Computing by Keith Schwarz (ALL LOOK TO BE FREELY AVAILABLE)
[0] http://www.math.cmu.edu/~jmackey/151_128/infdes.pdf
[1] https://www.people.vcu.edu/~rhammack/BookOfProof/
[2] https://web.stanford.edu/class/cs103/notes/Mathematical%20Fo...