Mat-2 applied mathematics




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Mat-2 APPLIED MATHEMATICS

Prof Raimo P. Hämäläinen, tel. 451 3054, room U 211
Prof Harri Ehtamo, tel. 451 3058, room U 238
Prof Esa Saarinen, tel. 451 3061, room U 209
Prof Ahti Salo, tel. 451 3055, room U 240


Courses credited in ECTS

Mat-2.1197 Philosophy and Systems Thinking (3 cr) P V

Spring

Lecturer: Prof Esa Saarinen

Contents: The course introduces students to conceptual think­ing in a highly personal and thought provoking style. Drawing from history of philosophy, case studies and from key ideas of sys­tems thinking, the aim is to make students more acutely aware of their own philosophy of life. Spring term courses are indepen­dent units and can be completed separately.

Requirements: Essay, based on the lectures and literature.

Literature: E. Saarinen: Filosofia!, 2004, WSOY. P.M. Senge: The Fifth Discipline, Currency Doubleday.

Additional: This course replaces the course
Mat-2.197 Philosophy and Systems Thinking

Language: Finnish

Mat-2.2103 Design of Experiments and Statistical Models (5 cr)

Spring

Lecturer: Simo Heliövaara, special lecturer

Contents: Fundamental principles of design of experiments and of analysis of experimental data. Linear statistical models: the analysis of variance, randomized blocks, factorial experiments. Response surface methods.

Literature: D.C. Montgomery: Design and Analysis of Experi­ments, John Wiley & Sons

Prerequisites: Applied probability

Additional: This course replaces the course Mat-2.103 Design of Experiments and Statistical Models

Language: Finnish

Mat-2.2104 Introduction to Statistical Inference (5 cr)

Spring

Lecturer: Kai Virtanen, teaching researcher

Contents: Introduction to computer oriented statistical analysis and statistical inference. Parametric and nonparametric tests. Regression analysis: linear, logistic, Poisson regression. Analysis of variance: one-way ANOVA, multiple comparisons, two-way ANOVA.

Literature: P. Laininen: Tilastollisen analyysin perusteet, Otati­eto, 2000, or J.S. Milton and J.C. Arnold: Introduction to Proba­bility and Statistics, McGraw-Hill, 3rd edition, 1995.

Prerequisites: Applied probability

Additional: This course replaces the course Mat-2.104 Introduc­tion to Statistical Inference

Language: Finnish

Mat-2.2105 Introduction to Optimization (3 cr)

Spring

Lecturer: Prof Harri Ehtamo

Contents: An introductory course to linear and non-linear pro­gramming. The following topics are included: Building of opti­mization models, resource allocation models, least-squares problems, goal programming, integer programming and travel­ing salesman problem together with genetic algorithms. In exer­cises Excel and Matlab are used to solve the problems.

Literature: Lecture notes.

Prerequisites: 1st year math.

Additional: This course replaces the course Mat-2.105 Introduc­tion to Optimization

Language: Finnish

Mat-2.2107 Computational Assignments in Applied Mathe­matics (3 cr) V

Autumn & spring

Lecturers: Simo Heliövaara, specialist teacher and teaching assistants

Contents: Studying of mathematical problem solving in tutori­als. The course is suitable for all the departments as an introduc­tion to modeling. Software used in the course include Matlab, Simulink, Mathematica, NCSS, Excel and Web-Hipre.

Requirements: The course is completed either by attending tuto­rials or by completing personal assignments. Tutorials are held both in spring and autumn term. Personal assignments can be collected from the course assistant. The course is recommended for second year students.

Prerequisites: 1st year math and applied probability

Additional: This course replaces the course Mat-2.107 Compu­tational Assignments in Applied Mathematics

Language: Finnish

Mat-2.3111 Stochastic Processes (5 cr) P

Autumn

Lecturer: Jirka Poropudas, researcher

Contents: Branching processes, discrete and continuous-time Markov chains (e.g. Poisson processes, birth and death pro­cesses), basic notions of queuing theory, renewal processes, Brownian motion.

Literature: R. Durrett: Essentials of Stochastic Processes, Springer, 1999

Prerequisites: Applied probability

Additional: This course replaces the course
Mat-2.111 Stochastic Processes.

Language: Finnish

Mat-2.3112 Statistical Multivariate Methods (3-6 cr) P

Spring

Lecturer: Ilkka Mellin, university teacher

Contents: Multiple regression, principal component analysis, factor analysis, cluster analysis, discriminant analysis, MANOVA, canonical correlation. Computer oriented approach.

Literature: S. Sharma: Applied Multivariate Techniques, John Wiley, 1996.

Prerequisites: Applied probability

Additional: Course can be taken in the independent studies, see Mat-2.4193. This course replaces the course
Mat-2.112 Statistical Multivariate Methods.

Language: Finnish

Mat-2.3114 Investment Science (5 cr) P

Spring

Lecturers: Pekka Mild, researcher

Contents: Instruments of investment science and finance, risk analysis, term structure of interest rates, pricing of derivatives, optimization of investment portfolio return.

Requirements: Assignments and exam.

Literature: D.G. Luenberger: Investment Science, Oxford Uni­versity Press, 1998.

Prerequisites: 1st and 2nd years math; applied probability

Additional: This course replace the course
Mat-2.114 Investment Science.

Language: Finnish

Mat-2.3117 Risk Analysis (5 cr) P

Autumn

Lecturers: Prof Ahti Salo

Contents: The aim of the course is to introduce methods and models applied in the risk analysis of various systems, including the models and approaches of economic risk management. Fur­ther, the course provides a deeper view over concepts for han­dling risk and uncertainty, Finally, practical examples on risk analyses are presented.

Literature: Will be announced later.

Additional: This course replaces the course
Mat-2.117 Risk Analysis.

Language: Finnish

Mat-2.3118 Reliability Engineering(4 cr) P

Not lectured this academic year.

Lecturer: Urho Pulkkinen, Docent

Contents: The basic principles and concepts of systems reliabil­ity analysis, and methods applied to analyzing the reliability and availability of complex systems.

Prerequisites: Applied probability and Mat-2.2104

Additional: This course replaces the course
Mat-2.118 Reliability Engineering.

Language: Finnish

Mat-2.3128 Prediction and Time Series Analysis (5 cr) P

Autumn

Lecturer: Ilkka Mellin, university teacher

Contents: Regression and other models and their use in the pre­diction of time series, especially linear time series analysis, ARIMA models and dynamic regression models; model selec­tion, parameter estimation, diagnostic checks.

Requirements: Exam and assignments

Literature: R.S. Pindyck, D.L. Rubinfeld: Econometric models and economic forecasts, 4th edition, 1998; lecture notes; other literature will be announced later

Prerequisites: 1st and 2nd year math and applied probability.

Additional: This course replaces the course
Mat-2.128 Prediction and Time Series Analysis.

Language: Finnish

Mat-2.3130 Mathematical Modelling (3 cr) P

Autumn

Lecturer: Kai Virtanen, teaching researcher

Contents: An introduction to systems thinking and utilization of mathematical models in different application areas. Construc­tion of models, differential and difference equation models, modeling based on optimization, simulation of dynamic systems.

Literature: F.R. Giordano, M.D. Weir, W.P. Fox: A First Course in Mathematical Modeling, Brooks/Cole, 1997

Prerequisites: 1st and 2nd year math and applied probability.

Additional: Course will be held as an Internet course. Basic course of modeling is held in autumn and various advanced courses both in autumn and spring. The advanced courses are arranged within course Mat-2.4195.

Additional: This course replaces the course
Mat-2.130 Mathematical Modelling.

Language: Finnish

Mat-2.3132 Systems Analysis Laboratory I (5 cr)

Spring

Lecturer: Kai Virtanen, teaching researcher

Contents: Two fairly large assignments on the implementation and analysis of mathematical models. The assignments deal with system dynamics and time-series analysis.

Requirements: Written reports

Prerequisites: 1st and 2nd year math, Mat-2.3128.

Additional: This course replaces the course
Mat-2.132 Systems Analysis Laboratory, assignments 2 and 3.

Language: Finnish

Mat-2.3134 Decision Making and Problem Solving (5 cr) P

Autumn

Lecturer: Juuso Liesiö, researcher

Contents: Models for decision making and problem solving: decision criteria, subjective values, uncertainty, dynamics of decision making, group decision making, optimization with mul­tiple objectives.

Requirements: Assignments and exam.

Prerequisites: Mat-2.2105 and applied probability.

Additional: This course replaces the course
Mat-2.134 Decision Making and Problem Solving.

Language: Finnish

Mat-2.3139 Nonlinear Programming (5 cr) P

Autumn

Lecturer: Kimmo Berg, researcher

Contents: Theory and numerical methods to solve problems in nonlinear programming. Applications from natural sciences, engineering and economics.

Requirements: Exam or mid-term exams.

Literature: M.S. Bazaraa, H.D. Sherali, C.M. Shetty: Nonlinear Programming, Theory and Algorithms, Wiley and Sons 1993.

Prerequisites: 1st and 2nd year math.

Additional: Course can be taken as an Internet course, see Mat-2.4195. This course replaces the course
Mat-2.139 Nonlinear Programming.

Language: Finnish

Mat-2.3140 Linear Programming (5 cr) P

Autumn

Lecturer: Juuso Nissinen, special lecturer

Contents: The simplex method, dual of the linear program, inte­rior point algorithms, integer programming. Applications to transportation problems, network problems and production planning.

Requirements: Homework, assignments and take home exam/ exam.

Literature: D. Bertsimas, J.N. Tsitsiklis: Introduction to Linear Optimization, Athena Scientific 1997

Prerequisites: Mat-2.2105

Additional: This course replaces the course
Mat-2.140 Linear Programming.

Language: Finnish

Mat-2.3148 Dynamic Optimization (5 cr) P

Spring

Lecturer: Mitri Kitti, special lecturer

Contents: Optimization methods for dynamic systems: dynamic programming, calculus of variations, maximum principle, numerical solution methods. Application examples on engineer­ing, economics and biology.

Literature: D.E. Kirk: Optimal Control Theory; M.I. Kamien, N.L. Schwarz: Dynamic Optimization - the Calculus of Varia­tions and Optimal Control in Economics and Management;
J.T. Betts: Practical Methods for Optimal Control Using Non-linear Programming; lecture notes

Prerequisites: 1st and 2nd years math.

Additional: This course replaces the course
Mat-2.148 Dynamic Optimization.

Language: Finnish

Mat-2.3152 Game Theory (5 cr) P V

Autumn

Lecturer: Prof Harri Ehtamo

Contents: Annually varying topics on game theory. On autumn 2007 the topic is noncooperative game theory.

Requirements: Exam and assignments.

Literature: R. Gibbons: A Primer in Game Theory, Prentice Hall, 1992.

Prerequisites: Mat-2.2105 and applied probability

Additional: This course replaces the course
Mat-2.152 Game Theory.

Language: Finnish

Mat-2.3170 Simulation (5 cr) P

Spring

Lecturer: Ville Mattila, researcher

Contents: Simulation of systems including discrete events and queues: stochastic queuing models, constructing a model, simu­lation techniques, graphical simulation software.

Requirements: Assignments and a case study.

Prerequisites: 1st and 2nd year math and applied probability

Additional: This course replaces the course
Mat-2.170 Simulation.

Language: Finnish or English

Mat-2.4108 Independent Research Projects in Applied Math­ematics (5-8 cr) V

Supervisors: Prof Raimo P. Hämäläinen, Prof Harri Ehtamo, Prof Esa Saarinen, Prof Ahti Salo as well as other lecturers and researchers of the laboratory

Contents: An individual research project; topics from industry or from research projects of the laboratory. Students can also pro­pose their own topics. The topics need to be discussed and approved by one of the teachers. One of the main aims is to get experience in writing a research report.

Requirements: Written report

Prerequisites: 1st and 2nd year math, courses of the laboratory related to the chosen topic.

Additional: This course replaces the course
Mat-2.108 Independent Research Projects in Applied Mathe­matics.

Language: Finnish

Mat-2.4113 Queuing Theory (3-6 cr) P

Not lectured this academic year.

Lecturer: N.N.

Contents: Queuing problems as stochastic processes, the prob­lems including finite or infinite set of users and servers, queuing disciplines, queues as Markov processes. Applications include various serving systems, telecommunication systems etc.

Prerequisites: 1st and 2nd year math, Mat-2.3111

Additional: For a similar course see S-38.3143. This course replaces the course Mat-2.113 Queuing Theory.

Language: Finnish

Mat-2.4115 Seminar on Stochastic Methods (5 cr) P V

Will be given during this academic year in connection with the Seminar on Optimization.

Lecturer: Prof Raimo P. Hämäläinen

Contents: Varies annually.

Additional: This course replaces the course Mat-2.115 Seminar on Stochastic Methods.

Language: Finnish

Mat-2.4125 Special Topics in Stochastics (3-6 cr) P V

Not lectured this academic year.

Lecturer: N.N.

Contents: Annually varying topics on stochastics. Lectures and their topic will be announced later.

Requirements: Varies annually.

Additional: This course replaces the course Mat-2.125 Special Topics in Stochastics.

Language: Finnish

Mat-2.4126 Statistical Quality Control (3-6 cr) P

Not lectured for the time being.

Lecturer: N.N.

Contents: The course covers the mathematical foundations of methods of quality control and improvement, acceptance sam­pling and Taguchi methods.

Requirements: Exam.

Literature: A. Mitra: Fundamentals of Quality Control and Improvement, Macmillan, 1998.

Prerequisites: Applied probability

Additional: This course replaces the course Mat-2.126 Statistical Quality Control.

Language: Finnish

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