A mathematics analysis textbook specifically written for teaching purposes. This book also abandons the traditional “definition > proof > example” format, instead presenting the background, motivation, thought process (including drafts of calculations), and examples of theorems in detail to help readers understand why the proofs are constructed that way.
This book, however, is intended for those who genuinely love mathematics. Rather than mechanically teaching the definitions of theorems, how to prove them, and then solve exercises, it guides readers to understand why these definitions are formulated the way they are and to comprehend the concrete significance of structures in abstract algebra.
How to use algorithmic thinking to make decisions in life when information is incomplete (or asymmetric)
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.
'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.