what does the word "Abstract" mean in Abstract Algebra?
What is the exact word meaning of "Abstract" used for Abstract Algebra?
I find many meanings of this word from the dictionary but just want to be sure the actually meaning for "Abstract Algebra"
- DavidLv 79 years agoFavorite Answer
it means "general", the opposite of "specific", or "concrete". "abstract algebra" is purely theoretical algebra, in as full generality as the theory (and logic) will allow.
this is to distinguish it from "high-school algebra" where algebraic rules of specific number systems are used, and often applied to "real-life scenarios" (the dreaded "word problems"). typically, the number systems explored in "algebra" are limited to the integers and the rational numbers (fractions), although some exposure to "algebraic real numbers" (in particular square roots) is often given.
also, in college curriculums, "abstract algebra" is also distinguished from "linear algebra", although there is *some* overlap. linear algebra assumes one has a field structure + an abelian group structure, which makes for a rich theory, with many applications. abstract algebra typically deals with the simpler structures of groups and rings (in a sense, it is "more general" than linear algebra, because of the fewer number of rules (axioms)).
- Anonymous4 years ago
If it really is a misspelling of "yak", then i imagine of the animal it truly is form of equivalent to water buffalo. If it really is a verbal interjection, then i imagine that's some thing like "Yuck!"