- volker.runde@ualberta.ca

**Areas**

Functional Analysis & Abstract Harmonic Analysis

Sets and functions. Induction. Axiomatic introduction of the real numbers. Sequences and series. Continuity and properties of continuous functions. Differentiation. Riemann integral. Prerequisite: One of MATH 101, 115, 136, 146, 156 or SCI 100. Note: This course may not be taken for credit if credit has already been obtained in MATH 118. Credit can only be obtained in one of MATH 216 and MATH 314.

Fall Term 2020Axiomatic development of the real number system. Topology of Rn. Sequences, limits and continuity. Multi-variable calculus: differentiation and integration, including integration in spherical and polar coordinates. The differential and the chain rule. Taylor's Formula, maxima and minima. Introduction to vector field theory. Prerequisites: One of MATH 102, 125 or 127, and either MATH 118 or MATH 216. Notes: (1) MATH 216 may be accepted as corequisite with consent of the Department. (2) Engineering students will receive a weight of 4.0 units for this course.

Fall Term 2020Implicit function theorem. Transformations of multiple integrals. Line integrals, theorems of Green, Gauss and Stokes. Sequences and series of functions. Uniform convergence. Prerequisite: MATH 217.

Winter Term 2021Locally convex spaces, weak topologies and duality in Banach spaces, weak compactness in Banach spaces, structure of classical Banach spaces, local structures, infinite-dimensional geometry of Banach spaces and applications. Prerequisite: MATH 516. Corequisite: MATH 447 or consent of Department.

Winter Term 2021