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Mathematical Sciences Institute · ANU College of Systems and Society
Algebra 1 is a foundational course in Mathematics, introducing some of the key concepts of modern algebra. The course leads on to other areas of algebra such as Galois Theory, Algebraic Topology and Algebraic Geometry. It also provides important tools for other areas such as theoretical computer science, physics, and engineering. Topics to be covered include the theory of groups and rings: - Group Theory - permutation groups; abstract groups, subgroups, cyclic and dihedral groups; homomorphisms; cosets, Lagrange's theorem, quotient groups; group actions; Sylow theory. - Ring Theory - rings and fields, polynomial rings, factorisation; homomorphisms, factor rings. Additional topics may be selected from the following: - Linear Algebra - unitary matrices, Hermitian matrices, canonical forms. - Modules - free modules, presentations, classification of finitely generated abelian groups. Note: This is an Honours Pathway Course. It emphasises mathematical rigour and proof and develops modern algebra from an abstract viewpoint.
Regular written assignments
Learning outcomes 1, 2, 3, 4
Quizzes
Learning outcomes 1, 2, 3, 4
Final exam
Learning outcomes 1, 2, 3, 4
The expected workload will consist of approximately 130 hours throughout the semester, including the following: - Face-to face component which may consist of 3 x 1 hour lecture-based classes per week and 1 x 1 hour workshop per week (workshops normally begin in Week 3), - Approximately 85 hours of self-directed study which will include preparation for lectures, assignments, and other assessment tasks.
None Preliminary Reading Algebra by Michael Artin. (Any edition is acceptable, although the 2nd edition and later are preferred.)