Course Catalog 2014-2015
Basic

Basic Pori International Postgraduate Open University

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Opinto-opas 2014-2015

Mathematics, 50 cr

Type of the study block

Advanced Studies

Contact

Seppo Pohjolainen, Martti Lehto

Learning Outcomes

- The extended advanced study module in Mathematics is intended to give the student an exceptionally solid knowledge of the foundations of mathematics for research, post-graduate studies and other further training, and especially applications in industry and elsewhere. The studies therefore should be focused on at least two of the main three areas: Analysis, Discrete Mathematics, and Mathematical and Semantic Modelling.

Studies in the Analysis focus area mainly deal with functional analysis and its applications, and measure and integration theory. This area lends itself nicely to mathematics itself and the more theoretical engineering sciences. The main topics then are measure and integration, functional analysis and its applications, and geometric algebra.

Discrete Mathematics is mainly mathematics needed in modelling algorithmics, data communication, and symbolical calculation. Applications of the old areas of number theory, logic and algebra will be included, too. The focus area aims at a comprehensive overview. By proper choice of courses any one of these areas may be emphasized.

Mathematical and Semantic Modelling, together with various computational methods (e.g. simulation, optimization and visualization) has a central role in the investigation of many fields of science, and also in high-tech product development. The goal of modelling is to build a sufficiently detailed mathematical model, the solution of which then usually requires heavy numerical computation. Studies in this focus area provide the student with a broad mathematical know-how for modelling incoming multi-discipline phenomena, and developing advanced solution methods.

Prerequisites

Study block Credit points Mandatory/Advisable Additional information
Matematiikka 25 cr Mandatory Or a corresponding prerequisite module of sufficient mathematical content.

Content

Optional Compulsory Courses

Each of the three focus areas has its own compulsory course and a recommended set of choices for the complementary courses which are listed in a separate table. For the extended study module the compulsory courses of at least two of the focus areas should be chosen.

Course Credit points Alternativity Class
MAT-60206 Mathematical Analysis 5 cr 1   IV  
MAT-61006 Introduction to Functional Analysis 7 cr 1   IV  
MAT-62756 Graph Theory 7 cr 1   IV  
MAT-63506 Scientific Computing 5 cr 1   IV  

1. Select 2 courses. Graph Theory is compulsory for the Discrete Mathematics focus area; Mathematical Analysis and Introduction to Functional Analysis for the Analysis focus area; and Scientific Computation is compulsory for the Mathematical and Semantic Modelling focus area.

Complementary Courses

The complementary courses should be chosen mainly according to the recommendation of the department. Choice of some courses may have an extra proviso. All these are given in a separate document as an attachment in the POP study-guide description of the module. Including other courses and courses of other universities is possible with prior permission.

Should be completed to the minimum study module extent of 50 ETCS

Course Credit points Class
MAT-60206 Mathematical Analysis 5 cr IV  
MAT-60250 Matemaattisen mallinnuksen peruskurssi 5 cr IV  
MAT-60356 Multivariate Methods in Statistics 5 cr IV  
MAT-60406 Stochastic Processes 5 cr IV  
MAT-60456 Optimization Methods 5 cr IV  
MAT-60506 Vector Fields 5 cr IV  
MAT-60556 Mathematical Logic 5 cr IV  
MAT-61006 Introduction to Functional Analysis 7 cr IV  
MAT-61256 Geometric Analysis 7 cr IV  
MAT-61506 Dynamical Systems and Chaos 7 cr IV  
MAT-61756 Measure and Integration 7 cr IV  
MAT-62006 Inverse Problems 7 cr IV  
MAT-62256 Advanced Functional Analysis 7 cr V  
MAT-62506 Linear Systems 5-7 cr IV  
MAT-62756 Graph Theory 7 cr IV  
MAT-63006 Information Theory 7 cr IV  
MAT-63256 Mathematical Cryptology 7 cr IV  
MAT-63506 Scientific Computing 5 cr IV  
MAT-64000 Jatkuvat mallit 4 cr IV  
MAT-64250 Satunnaisuus mallintamisessa 4 cr IV  
MAT-64500 Datan analyysimenetelmät mallinnuksessa 4 cr IV  
MAT-64750 Mallinnus ja optimointi 4 cr IV  
MAT-65000 Tilastolliset mallit 4 cr IV  
MAT-65250 Osittaisdifferentiaaliyhtälöt mallinnuksessa 4 cr IV  
MAT-67250 Matematiikan erikoistyö 5-10 cr IV  
MAT-67256 Special Assignment in Mathematics 5-10 cr IV  
MAT-67500 Matematiikan projektityö 2-10 cr IV  
MAT-67506 Mathematics Project Work 2-10 cr IV  
MAT-67756 Post-Graduate Seminar in Mathematics 2-10 cr V  
MAT-68006 Topics in Mathematics 2-10 cr IV  
MAT-68256 Mathematics Literature 0-10 cr V  
MAT-71506 Program Verification 5 cr IV  
MAT-72006 Advanced Algorithms and Data Structures 7 cr IV  
MAT-72306 Randomized Algorithms 4 cr IV  
MAT-72606 Approximation Algorithms 4 cr IV  
MAT-73006 Theoretical Computer Science 7 cr IV  
MAT-74006 Concurrency Theory 7 cr IV  
MAT-75006 Artificial Intelligence 7 cr IV  
MAT-82106 Semantic Modeling 4 cr IV  
MAT-82200 Kvalitatiiviset tutkimusmenetelmät 5 cr IV  
MAT-82306 Scientific Visualization 4 cr IV  

Additional information

Useimmista opintokokonaisuuksista valittavissa on myös suomenkielinen materiaali sekä suomenkielinen harjoitusryhmä. Melkein kaikki kurssit voi myös tenttiä suomenkielellä.

Documents

Mathematics.pdf

Last modified04.02.2015