COURSE NAME AND CODE:  Introductory Linear Algebra and Analytic Geometry (MATH 1141)

LEVEL: I

SEMESTER: I

Students will carry out a research project in groups of no more than four, under the close supervision of one or more faculty members. Each student should have a distinct, well-defined role in the project. The group will report its findings in the form of a written thesis, and each student in the group will be required to make an oral presentation on their role in the work.

Stochastic processes: definition and classification; modeling with stochastic processes, Markov chains and applications; theoretical aspects  of stochastic simulation; counting processes and applications; queues  and applications; practical aspects of stochastic simulation.

Partial differential equations and classifications; well-posed problems,  classical solutions, initial and boundary value problems; first order linear  and quasi-linear partial differential equations; method of characteristics; conservation laws; classification of general second order operators; the wave equation, D’Alembert method of solution; Laplace’s equation, the maximum principle; the heat equation; separation of variables; boundary  value problems and Sturm-Liouville theory.

Metric spaces, examples; continuity; completeness; topological spaces;  Hausdorff spaces; connectedness.

Review of Macroeconomics; Characteristics of the various types of  investments used to fund financial security programmes; traditional  techniques of financial analysis used in selecting and managing

 nvestment portfolios.

 The course builds on the material in courses MS28D and MS38H,  introducing further tools and techniques of asset/liability management, general product design, as well as issues of pricing and valuation and  asset management.

Review of earlier statistical work; individual risk theory; other frequency distributors; mixed distributions; stoploss insurance; ruin theory.

Multiple life functions, multiple decrement model; insurance models  including expenses; nonforfeiture, benefits and dividends; valuation theory for pension plans.