Mathematics, 50 cr
Type of the study module
Advanced Studies
Contact
Esko Turunen, 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 |
| 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
Additional information
Useimmista opintokokonaisuuksista valittavissa on myös suomenkielinen materiaali sekä suomenkielinen harjoitusryhmä. Melkein kaikki kurssit voi myös tenttiä suomenkielellä.
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