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:

• 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.
• Linear algebra - real symmetric matrices and quadratic forms, Hermitian matrices, canonical forms.
• Set Theory - cardinality.

Note: This is an HPC. It emphasises mathematical rigour and proof and develops modern algebra from an abstract viewpoint.

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Explain the fundamental concepts of advanced algebra such as groups and rings and their role in modern mathematics and applied contexts
2. Demonstrate accurate and efficient use of advanced algebraic techniques
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from advanced algebra
4. Apply problem-solving using advanced algebraic techniques applied to diverse situations in physics, engineering and other mathematical contexts

Assessment will be based on:

• Five assignments (8% each; LO 1-4)
• Mid semester exam (20%; LO 1-4)
• Final exam (40%; LO 1-4)

36 lectures and ten tutorials

A mark of 60 or more in MATH1021 or MATH1116.

MATH2021 and MATH2028 and MATH3104.