This course introduces students to key concepts and techniques in advanced algebra. Topics will be taken from contemporary research areas in Algebra.

Possible topics include:

Algebraic number theory, Analytic number theory, Algebraic geometry and scheme theory, Sheaf theory, Derived and Triangulated categories, Algebraic curves and Riemann surfaces

Note: This is an HPC. It emphasizes mathematical rigour and proof and continues the development of 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 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:

• Assignment 1 (20%; LO 1-4)
• Assignment 2 (20%; LO 1-4)
• Assignment 3 (20%; LO 1-4)
• Take home exam (40%; LO 1-4)

36 lectures plus tutorial by arrangement.

Prerequisite:  MATH3345: Algebra 2

This course introduces students to key concepts and techniques in advanced algebra.