Geometry

LECTURER : CC Remsing

Prerequisites

Linear algebra, Advanced calculus, Transformation geometry, Differential geometry.

Description

Undergraduate mathematics today rests on two foundations : calculus and linear algebra. A perfect sequel to calculus and linear algebra is Lie theory (i.e. the theory of Lie groups, Lie algebras and their applications). The naive approach to Lie theory is due to J. von NEUMANN (1929).

"Lie theory today has become the subject that all mathematicians ought to know something about". (J. Stillwell)

Topics

Geometry of complex numbers and quaternions, transformation groups, generalized rotation groups, the exponential map, the tangent space, structure of Lie algebras, the matrix logarithm, topology (of matrix Lie groups), simply connected Lie groups.

Textbook

"Naive Lie Theory" by Stillwell (Springer, 2008).

Tutorials

ONE tutorial per week.

Tests/Exams

TWO tests and ONE final examination.