| Module Objective: To give an introduction to modern Algebra. Linear Algebra: vector spaces; linear dependence and independence; basis and dimension; linear maps and connections with matrix algebra. Group Theory: notion of a group; examples of groups including permutation groups, symmetry groups, matrix groups, cyclic groups; subgroups; orders of groups and elements; Lagrange's Theorem; homomorphisms and isomorphisms. Parallels between group theory and linear algebra. Consideration of how algebra could be taught in a second level classroom. |