View source for Abstract Algebra (subject)

{{Stub page|Needs fleshing out}}
__TOC__
==Overview==
Abstract algebra is the study of [[function|functions]] (a [[relation#Types of relation|right-unique relation]], that maps everything in its [[domain (function)|domain]] to something) where that function has certain properties, for example, associativity, or an element (called the identity) which does nothing.
* [[:Category:Abstract Algebra]] ({{PAGESINCATEGORY:Abstract Algebra|pages}} pages) - all things on this wiki categorised as belonging to abstract algebra
* [[:Category:Abstract Algebra Definitions]] ({{PAGESINCATEGORY:Abstract Algebra Definitions|pages}} pages) - all definitions
* [[:Category:Abstract Algebra Theorems, lemmas and corollaries]] ({{PAGESINCATEGORY:Abstract Algebra Theorems, lemmas and corollaries|pages}} pages)

==Learning Abstract Algebra==
There are two styles of learning, some start at [[field|fields]] and work down towards [[ring|rings]] then to [[group|groups]], the idea being that the reader is vaguely familiar with fields (via the [[real numbers]], [[integers]] so forth) and then go to more abstract structures, others go via fields towards [[vector space|vector spaces]] then into [[Linear Algebra (subject)|linear algebra]] - which is a branch of abstract algebra.

'''However I recommend that''' the reader do the other (more common in modern texts) route, that is starting at groups, then heading to rings, then fields, then vector spaces. There is a group in every field, so it isn't like the reader will never have used group properties, there are also plenty of examples. I recommend the first year, or the reader who doesn't know where to start to start with [[Group Theory (subject)|group theory]] and explore there, heading slowly towards [[Ring Theory (subject)|ring theory]] then to the primitives of [[Linear Algebra (subject)|linear algebra]]

==Order Theory==
[[Order Theory (subject)|Order theory]] doesn't involve functions on sets but other relations instead, it is debatable if this counts as abstract algebra, I include this here only as a pointer to those who expect to find it here


{{Abstract algebra navbox|plain}}
{{Group theory navbox}}
{{Ring theory navbox}}
{{Linear algebra navbox}}
[[Category:Subjects]]
[[Category:Abstract Algebra]]