What then? One option is Saunders Mac Lane and Garrett Birkhoff’s Algebra (3rd edition, AMS Chelsea, 1999). So suppose you want more than you’ll get from Beardon or perhaps you already have some - possibly fragmentary, possibly half-remembered - knowledge of algebra, and want to go up a level in sophistication and detail. and I think is particularly suitable for self-study. ![]() ![]() Its presentation of even quite complex ideas is typically exemplary, both in giving motivation, and in explaining official definitions, presenting the proofs etc, and all often written with a light touch. This is Paolo Aluffi’s Algebra: Chapter 0 (American Mathematical Society, 2009). But the treatment is quite brisk, and I think there is now a better option, taking quite a similar approach, but in a rather more engaging way. This is a distant and slightly more advanced descendant of their famous A Survey of Modern Algebra (which originally dates back to 1941), and is notable for the way it weaves into the story categorial ideas, with a fairly light hand and in an illuminating way. ![]()
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