MATH3010 Operations Research

Prerequisite(s): MATH 2014 Linear Programming and Networks, MATH 3009 Optimisation.

Description: Characteristics of large-scale real-life decision problems. Typical models of industry, trade and finance. The need for optimisation. Basic measure theory (measurable space and measure space, the Lebesgue integral), basic linear algebra (eigenvalues and eigenvectors, singular value decomposition), basic probability theory (random vectors, covariance matrix).Estimation theory (linear and nonlinear estimators) Principal Component Analysis. Theory of optimal data estimation. Error analysis. Modelling: Basics of modelling. Modelling methodology. Model generation and management.

Coordinator: Associate Professor Regina Burachik

MATH3017 Decision Science

Prerequisite(s): A basic understanding of elementary probability and matrices

Description: Fundamental concepts of decision analysis, utility, risk analysis, Bayesian statistics, game theory, Markov decision processes and optimisation. The value of sampling information and optimal sample sizes, given sampling costs, and the economics of terminal decision problems.

Coordinator Professor Jerzy Filar

MATH3019 Investment Science

Prerequisite(s): MATH 1055 Calculus 2, MATH 2014 Linear Programming and Networks.

Description: Deterministic cash flow streams: present and future values, fixed income securities, term structure of interest rate. Single period random cash flows: mean-variance portfolio theory, general principle of pricing. Derivative securities: forward and futures, models of asset dynamics, basic option theory, Black-Scholes equation. General cash flow streams: optimal portfolio growth, general investment evaluation.

Coordinator: Professor Vladimir Gaitsgory

MATH3026 Applied Functional Analysis

Prerequisite(s): MATH 2025 Real and Complex Analysis, MATH 3025 Differential Equations 2.

Classical Abstract spaces in Modern Functional Analysis:

• Topological spaces (convergence, continuity, weak topology, and compactness results) ,
• Metric spaces (Complete metric spaces, Baire Category Theorem, Arzela-Ascoli Theorem, Holder-Minkowski's Inequalities),
• Normed Vector spaces,
• Space of Lebesgue Measurable Functions,
• Hilbert spaces

Fundamental Theorems of Analysis:

• Hahn-Banach Theorem,
• Uniform Boundedness Theorem,
• The Open Mapping Theorem.

Dual Spaces:

• Weak and Weak* topology
• Riesz's Representation Theorem,
• Closed Graph Theorem,
• Adjoint Operators in Hilbert spaces,
• Lp spaces.

Differential Calculus in Normed Vector Spaces:

• Differentiability of functionals (Gateaux and Frechet differentiability)
• Minimization of Differentiable functionals (optimality conditions for constrained optimization)
• Gateaux differentiable convex functionals
• Lower Semicontinuous Functionals and Convexity.

Text book/s: Kurdila, AJ & Zabarankin, M 2005, Convex Funtional Ananlysis, Bikause

Coordinator: Associate Professor Regina Burachik

MATH3030 Multivariate Statistical Analysis

Prerequisite(s): MATH 1056 Linear Algebra, MATH 1036 Statistical Methods.

The linear model; the multivariate normal distribution; convariance matrices; Hotelling's T - squared; principal components; Flury test, discriminant analysis; factor analysis.

Coordinator: Associate Professor Irene Hudson