Abstract Algebra (subject)

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Abstract algebra is the study of functions (a right-unique relation, that maps everything in its domain to something) where that function has certain properties, for example, associativity, or an element (called the identity) which does nothing.

Learning Abstract Algebra

There are two styles of learning, some start at fields and work down towards rings then to 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 spaces then into 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 and explore there, heading slowly towards ring theory then to the primitives of linear algebra

Order Theory

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

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