Fundamental Courses

CSM210: QUEUING THEORY

Lecturer Alexandra V. Krainikov, Associate Prof., Ph.D.

Basic concepts of queuing theory, Poisson processes and Markov property, single queuing systems and queuing networks as models for computers, computer systems and computer networks performance evaluation, numerical solution of queuing models.

1. Introduction and Overview

2. Mathematical Preliminaries (Probability Theory Review, Moment Generating Function, Laplace transforms)*

3. The Poisson Process. The Markov Property

4. Discrete and Continues Markov Chains

5. Single Queuing Systems. The M/M/1 Queuing System

6. Little's Law. Reversibility and Burke's Theorem

7. Transient Solution of the M/M/1

8. The M/M/m Queuing System. A loss System. The Central Server CPU Model

9. TheM/G/1 Queuing System

10. Network of Queues. Open Queuing Networks. Local Balance

11. Closed Queuing Networks

12. Numerical Solution of Queuing Models. Closed Networks: Convolution Algorithm

13. Approach for Large Markovian Queuing Networks

14. Simulation of Communication Networks

1. Thomas D.Robertazzi, Computer Networks and Systems: Queuing Theory and

Performance Evaluation. Springer-Verlag New York Inc., 1990

2. Dimitri Bertsekas, Robert Gallager, Data Networks, Prentice-Hall International Inc.,

1987,

CSM220: DECISION THEORY

Lecturer Dmitri V. TCoulikov, Associate Prof., Ph.D..

Introductory course on the theory and applications of Decision Analysis. Elective course that gives students access to up-to-date information on modern decision analysis techniques at a level that could be easily understood by those without strong mathematical background. The intended participants are students who want to learn more about decision making under uncertainty and tools that can be used to support it. Some familiarity with basic statistical concepts, probability, and probability distributions would be helpful. After having taken the course the students must be able to understand and develop basic decision models, evaluate these models using decision support software, interpret the results, and communicate them to non-analytical decision makers. Emphasis is on good model formulation, analysis and use of decision-making techniques in Engineering, Operations Research and Systems Analysis. Includes formulation of risk problems and probabilistic risk assessment. Graphical methods and computer software uses decision trees and influence diagrams.

6. Assessment of subjective probability

9. Using computer software for Decision Analysis

Course Text

1. Kneale T. Marshall and Robert M. Oliver. "Decision Making and Forecasting (With Emphasis on Model Building and Policy Analysis)." McGraw-Hill, Inc., 1995, ISBN 0-07-048027-3

CSM230: GRAPH THEORY

Lecturer Dmitri V. Koulikov, Associate Prof, Ph.D..

The course provides a systematic review of solution techniques and problems that have formulations in terms of flows in networks. The development of efficient algorithms to achieve optimal solutions for problems defined on graphs and network is an important theme in this course. Related problems for which no efficient algorithms are known are introduced as well.

1. Introduction: definitions of graphs and networks

2. Complexity of algorithms

3. Formulation of problems as network flow problems

4. Shortest path algorithms and applications

5. The Ford-Fulkerson algorithm

6. Max-flow min-cut algorithms and applications

7. The minimum cost flow problem. Relationship to linear programming

8. Vertex cover and independent set on bipartite graphs. Applications in covering and packing

9. Eulerian graphs

10. Matching problems, bipartite and general

11. Minimum spanning tree algorithms and applications

12. Connectivity problems

13. Planar graphs

14. Approximation algorithms

Course text 1. Ahuja, Magnanti, Orlin, Network Flows, Prentice Hall, 1993

CSM240: INTRODUCTION TO THE DIFFERENTIAL GEOMETRY

Lecturer NikitaE. Barabanov, Prof., D.Sc..

Basic concepts of analytical and proJective geometry, elements of convex analysis, analysis of curves, surfaces, elements of interior geometry, smooth manifolds, Riemann metrics, Cristoffel symbols, geodesic lines and applications.

1. Elements of analytical geometry

2. Elements ofprojective geometry

3. Concepts of convex analysis: subdifferential, conjugate, support Minkovski functions

4. Curves, its* curvature, torsion, Frechet formula

5. Surfaces, tangent plane, first and second quadratic forms, principal curvatures, total curvature

6. Gaussian curvatures

7. Geodesic curves, deficiency of geodesic triangle, Euler characteristics

8. Vector fields, fundamental groups of transformations

9. Riemann manifolds, Riemann metrics

10. Cristoffel symbols, Ricci identity, geodesic lines.

1. Manfredo P. Do Carmo. Differential Geometry of Curves and Surfaces. Prentice-Hall Inc. Englewood CrifFs, New Jercy, 1976.

2. Heinrich W. Guggenheimer. Differential Geometry. Dover Publications Inc. New Jork, 1977.

3. S.P.Novikov, A.T.Fomenco. Basic Elements of Differential Geometry and Topology. Kruwer Ac. Publisher, Mathematics and It's Applications, v.60, 1987.