Math
113
· Introduction
to Abstract Algebra
Solutions to the Final
Syllabus for the Final
Sections:
0-6,
7 (except for Cayley digraphs),
8-11, 13-16, 18, 26-27
The
format similar to both Midterms but about 50% longer as more material
is to be covered.
Mastery of the concepts covered in the class is expected. Pay special
attention to examples covered by Fraleigh, survey homework assignments,
test your grasp of the material by answering questions ion the Theory portion
of Exercises
that follow each section.
While
preparing for the Final you should particularly
focus on quotient structures (quotients of groups by normal subgroups,
of rings by ideals), the structure of the permutations groups (both
symmetric Sn and
alternating An),e.g.,
you should be able to determine whether given two permytations are
conjugate to each other or not, be able to determine the number of
different conjugacy classes in Sn,
be able to determine the orders of elements of Sn.
Emphasis will be also on applications of Lagrange's Theorem
and of the Fundamental
Theorem of the Theory of finitely Generated Abelian Groups.