M373L Syllabus

ALGEBRAIC STRUCTURES II

Prerequisite and degree relevance: The prerequisite is M373K. M373L is strongly recommended for undergraduates contemplating graduate study in mathematics.

Course description: M373L is a continuation of M373K, covering a selection of topics in algebra chosen from field theory and linear algebra. Emphasis is on understanding theorems and proofs.

Text: Herstein, Topics in Algebra

Material to be covered: Chapters 4, 5, (sections 1-3), 6.

This includes: elementary properties of vector spaces and fields, including bases an dimension, elementary properties of linear transformations, relations to matrices, change of bases, dual spaces, characteristic roots, canonical forms, inner product spaces, normal transformations, quadratic and bilinear forms.

If time permits: topics left up to the instructor.

The Undergraduate Curriculum Committee