This course will introduce to the basics of Actuarial Mathematics. The first level course consists of the following topics: basic theory of interest (we develop formulae needed in the rest of actuarial science), equation of value, concept of annuities, amortization, sinking funds, bonds, life tables, life annuities, life insurance, multi-life insurance, evaluation of pension plans.
This course will introduce to the basics of Life Contingencies Actuarial Mathematics. The Level II course consist of the following topics: insurance annuities, life tables, life annuities, life insurance, multi-life insurance, evaluation of pension plans.
This course requires extensive usage of probability and statistics theory, calculus, functional analysis.
Our primary goal is to study the scope and methods of game theory. We mainly focus on games arising in economics and business, although general games will be considered with applications to other fields.
Game theory is about the strategies adopted by agents (e.g. consumers, firms or governments) when there are competing interests or ends and the outcomes depend on the actions chosen by all of the participants. Our time together is designed to develop a view of the concepts and problems studied by game theorists. You should also learn a set of analytical skills reflecting game theory’s main themes.
The course is modular in structure. There are 7 modules in all.
Despite the wide range of mathematical topics touched upon, this course is intended for anyone who has completed beginning calculus. As we enter the 21st century, it becomes essential for students to be experienced in the use of software such as Maple. If you have never heard of CAS (Computer Algebra Systems) or Maple before, or if you have been using Maple for years but would like to expand your knowledge of its capabilities, this course is for you!
The course teaches you how to use Maple to explore calculus and study mathematical models. We will use Maple for calculus in one variable and two variables, and for graphing functions, curves and surfaces. We will learn how to model physical systems and use Maple to solve them and visualize and animate their solutions. The course will also strengthen your programming skills. We will write a lot of simple programs involving loops, functions, arrays, lists and sets.
This course was designed for students who are interested in mathematical modelling and believe that usefulness of mathematics lies in its application to practical situation. The course was prepared in such manner that students with backgrounds in fundamental algebra can understand and learn the ideas of the course.
The modular structure of the course allows students a freedom in choosing how to present the material in their research and presentations.
There are three modules:
The following criteria were used to determine which topics to include into the modules.
So, utility theory, difference equations and population growth, bonds and shares are included into the first and third modules.
Also, mathematical models in Music, models and patterns in plane geometry, models and ppatterns in Art and Architecture will be offered to students in the module 2. They enliven the course and help students to appreciate variety and beauty of models in our life.
This course covers the basics of the mathematical modeling method with regard to the solution of some geophysical tasks. In particular, we will consider the models and methods of magnetotellurics, thermodynamics of lakes and pollution transport. We will discuss the basic steps of the mathematical modeling process and propose different approaches for discrete models constructing.
Course will focus on the study of both classical and modern numerical methods for solving the equations of mathematical physics. We will consider boundary-value and initial-boundary-value problems for the advection-diffusion, Poisson and non-stationary heat equations.
This course focuses on the connection between real life problems and making decision. Students will learn how to model real life problems, formulate real life problems and study of the quantitative methods for decision making, in particular the application of mathematical and statistical models in the analysis of problems related to economic and business. The main topic includes probability and decision-making analysis, analysis under uncertain conditions, theory of portfolio: The Markowitz and Tobin portfolio theories.
Course aim is to teach students to construct models and make decision.