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by openknot
1612 days ago
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For books on strong fundamentals, you can try the Art of Problem Solving series [0]. They suggest a curriculum to start with prealgebra, move to algebra, then counting & probability, then geometry, then precalculus, and finally to calculus (though a regular calculus book like Thomas Calculus/Stewart Calculus/even Spivak/Apostol would work fine). The main advantage of these books are its focus on building intuition by visualizing shapes or immediately rephrasing notation (e.g. 4/2 is better understood as 4*(1/2), which better explains why you should avoid cases where you divide by zero; I also found their exponent rules easier to understand, because it encourages visualization instead of just memorizing the rules). The downside is that they're time-consuming due to a large number of exercises (I'm currently still trying to slowly work through them when I can, but if you need higher-level math in the short-term, it's probably better to start there). They're also not a free resource. For free lecture videos, I've found Professor Leonard's lectures to be excellent, and equivalent to lectures at a university classroom [1]. [0] https://artofproblemsolving.com/store/recommendations [1] https://www.youtube.com/c/ProfessorLeonard/playlists |
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