Chap1 -- Why Abstract Algebra ?

So the first difference between the elementary and the more advanced course in algebra is that, whereas earlier we concentrated on "technique", we will now develop that branch of mathematics called "algebra" -- in a systematic way.

Ideas and general principles will take precedence over problem solving.

人类对 “代数” 的认识,长期以来一直处于一个 “解方程” 的状态 -- 数学家们互相约战,出题,看谁在规定时间内解的多,胜者就可以拿奖金。

“抽象” 也是一个相对的概念。 One person's abstract is another's bread and butter.

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