The course introduces the most important structures in abstract algebra.
ones which are common to all algebraic structures are emphasized, such
as homomorphisms, isomorphisms and quotient objects. Group theory, which
has many applications in physics and chemistry, takes up more than half
the course. For example, groups are used to classify elementary
particles and to study the symmetries of crystals. Group theory is also
used in most forms of geometry. The rest of the course is about ring
theory; as important examples of rings we study fields and polynomial
rings over fields.