A Mindset-Changing Book: *Algorithms to Live By: The Computer Science of Human Decisions*
How to use algorithmic thinking to make decisions in life when information is incomplete (or asymmetric)
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What Is the Essence of Learning Ability
Learning ability is not merely about memorization. It’s not about mastering the cubic formula today and the quartic formula tomorrow. Learning ability involves restructuring your cognitive framework—when you realize that the quintic equation has no general solution by radicals, you understand that the existence of solutions by radicals for lower-degree equations is merely coincidental.
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The Best Open-Source Textbook on Abstract Algebra
'Abstract Algebra: Theory and Applications,' commonly abbreviated as AATA and literally translated into Chinese as 《抽象代数：理论与应用》, is authored by Thomas W. Judson, a mathematics professor in the UK. The book aims to reduce the difficulty of learning abstract algebra. The author firmly believes that the purpose of studying abstract algebra is to discover the common patterns underlying different systems.
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Lie Groups and Lie Algebras
Differential equations with continuous symmetries that possess both group and manifold structures
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Mathematician Terence Tao’s Personal Website
This website primarily documents Terence Tao’s mathematical research progress, lectures, teaching materials, books, and other content. The material generally requires a strong mathematical background to understand, covering topics such as harmonic analysis, partial differential equations, and number theory. However, it also offers very detailed educational advice aimed at a general audience, spanning mathematics learning recommendations from elementary school through postdoctoral studies.
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