- troitsky@ualberta.ca

**Areas**

Functional Analysis & Theory of Operators

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.

Winter Term 2021Review of vector space axioms, subspaces and quotients; span; linear independence; Gram-Schmidt process; projections; methods of least squares; linear transformations and their matrix representations with respect to arbitrary bases; change of basis; eigenvectors and eigenvalues; triangularization and diagonalization; canonical forms (Schur, Jordan, spectral theorem). Prerequisite: MATH 127. (Students with MATH 102 or 125 may be admitted with consent of the Department.) Note: Credit can be obtained in at most one of MATH 225 or 227.

Winter Term 2021