Math 3140 Fall 26

MATH 3140: Abstract Algebra 1 (Fall 2026)

Numbers are for orientation and refer to sections with related material in the book by Gallian.

08/21: symmetries of rectangle and square, multiplication tables (1)
08/24: n-ary operations, nullary (constant) operations, algebras as models for computations
08/26: semigroups are algebras with associative multiplication, monoids are semigroups with identity, groups are monoids with inverses (2)
08/28: in groups, identity and inverses are determined by the multiplication, subalgebras, subgroups (3)
08/31: review integers mod n (see handout)
09/02: subgroups generated by a set of elements
09/04: order of elements (3), cyclic groups (4)
09/09: subgroups of cyclic groups (4)
09/11: commutative group, center of general linear group, dihedral group (3)
09/14: permutation groups, Sym X, S_n, cycle decomposition, order of permutations (5)
09/16: group homomorphisms (10)
09/18 isomorphic groups (6)
09/21: (inner) automorphism groups, Cayley's Theorem (6)

Joseph A. Gallian. Contemporary Abstract Algebra. (any edition, available electronically via the CU library)