ABSTRACT ALGEBRA
Instructor: John
Rey D. Domingo
WEEK 1-2: PRELIMINARY TOPICS
A. Modular Arithmetic
B. Functions
C. Equivalence Relations
WEEK 3-4: GROUPS
A. Binary operations
B. Groups
C. Elementary Properties of Groups
WEEK 5-6: SUBGROUPS
A. Order of a Group and Order of an
Element
B. Subgroups
C. Cyclic Subgroups
WEEK 7-8 CYCLIC GROUPS
A. Definition and Properties of Cyclic
Groups
B. Finite Cyclic Groups
WEEK 10-11: PERMUTATION GROUPS
A. Permutations and the Symmetric Groups
B. Orbits and Cycles
C. Properties of Permutations
WEEK 12: COSETS AND
LAGRANGE’STHEOREM
A. Cosets
B. Lagrange’s Theorem
WEEK 13: ISOMORPHISMS
A. Isomorphisms
B. Automorphisms
WEEK 14-15: NORMAL SUBGROUPS
AND FACTOR GROUPS
A. Normal Subgroup
B. Factor Groups
WEEK 16: GROUP HOMOMORPHISM
A. Group Homorphisms
B. Properties of Homomorphisms
WEEK 17: INTRODUCTION TO RINGS
A. Definition and Examples of Rings
B. Properties of Rings
C. Subrings