Manish Patnaik

Associate Professor, Faculty of Science - Mathematics & Statistical Sciences

Contact

Associate Professor, Faculty of Science - Mathematics & Statistical Sciences
Email
patnaik@ualberta.ca

Overview

Research

Areas

Automorphic Forms, Loop Groups

Courses

MATH 411 - Honors Complex Variables

Complex number system. Analytic functions. Cauchy's Integral theorem and formula. Applications including the maximum modulus principle, Taylor expansion and Laurent expansion. Harmonic functions. The residue theorem with applications; calculus of residues, argument principle, and Rouche's theorem. Basics of analytic continuation. Additional topics at the instructor's discretion such as: Normal families, The Riemann mapping Theorem, Picard's Theorem. Prerequisite: MATH 314 or 317. Notes: (1) This course is primarily for Honors students in Mathematics or Physics. (2) Offered in alternate years. It may be offered in intervening years if demand is sufficient.

Fall Term 2020
MATH 447 - Elementary Topology

General point-set topology. Compactness, Tychonoff's tbeorem, connectedness. Metric spaces, completeness, Baire's theorem. Urysohn's lemma. Topological manifolds. Homotopy theory, fundamental group, covering spaces. Prerequisite : MATH 216 or 217. Corequisites: MATH 328. Offered in alternate years. It may be offered in intervening years if demand is sufficient.

Winter Term 2021

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