MHB Should You Memorize All Theorems in Abstract Algebra?

AI Thread Summary
Abstract algebra is recognized for its vast array of examples, applications, and interconnected concepts, making it a unique mathematical field. The discussion highlights the challenge of memorizing numerous theorems while understanding and proving them. A key concern is whether complete recall is necessary for mastery. Recommendations for learning resources include Herstein's "Abstract Algebra," Dummit and Foote's graduate-level text, Fraleigh's "A First Course in Abstract Algebra," and Gallian's "Contemporary Abstract Algebra." These texts are noted for their effectiveness in building a solid foundation in abstract algebra.
alyafey22
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I am reading at the moment about abstract algebra. It is a very interesting field. I was amazed by the number of examples, applications and related concepts. Never seen something similar in any other mathematical field. I saw lots and lots of theorems and I was wondering whether I should remember all of them. I can prove and understand most of them and define most of the concepts involved but my concern is whether I should be able to recall all of these stuff ?

PS : how did you learn about abstract algebra and what is the best approach to master it ?
 
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