- xic@ualberta.ca

**Areas**

Algebraic Geometry

Area between curves, techniques of integration. Applications of integration to planar areas and lengths, volumes and masses. First order ordinary differential equations: separable, linear, direction fields, Euler's method, applications. Infinite series, power series, Taylor expansions with remainder terms. Polar coordinates. Rectangular, spherical and cylindrical coordinates in 3-dimensional space. Parametric curves in the plane and space: graphing, arc length, curvature; normal binormal, tangent plane in 3- dimensional space. Volumes and surface areas of rotation. Prerequisite: MATH 100. Notes: (1) Credit can be obtained in at most one of MATH 101, 115, 118, 136, 146, 156 or SCI 100. (2) Students in all sections of this course will write a common final examination. (3) Restricted to Engineering students. Non-Engineering students who take this course will receive *3.0.

Winter Term 2021Combinatorial geometry and topology, convex sets, sets with constant width, Helly-type problems, extremal problems. Prerequisite: One of MATH 102, 125, 127, 222 or 241.

Winter Term 2021A review and some extensions of single variable complex analysis. Complex linearity and holomorphicity in several variables, Hartog's theorem, Weierstrass preparation theorem, Riemann extension theorem, Weierstrass division theorem, analytic Nullstellensatz, implicit and inverse function theorems, complex manifolds and analytic subvarieties, meromorphic maps. Prerequisite: MATH 411.

Fall Term 2020