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Course Catalog 2011-2012
MAT-55216 Topics in applied mathematics, 3-5 cr |
Additional information
The course topics vary yearly. The aim of the course is to provide advanced-level teaching in a specialised topic of applied mathematics. The teaching may be given as lectures or as a seminar, and often involves guest teachers. Implementations in 2011-2012 include "Quantum Structures" in September 2011.
Suitable for postgraduate studies
Person responsible
Esko Turunen, Robert Piche
Lessons
| Study type | P1 | P2 | P3 | P4 | Summer | Implementations | Lecture times and places |
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Learning outcomes
The student will gain knowledge in a specialised research area of applied mathematics and an understanding of current research questions. The student will be able to understand and solve problems in new situations by applying acquired knowledge, facts, techniques and rules given in the teaching material.
Content
| Content | Core content | Complementary knowledge | Specialist knowledge |
| 1. | Core content is specified separately for each implementation. | Small research project management, report writing |
Prerequisite relations (Requires logging in to POP)
Correspondence of content
| Course | Corresponds course | Description |
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More precise information per implementation
| Implementation | Description | Methods of instruction | Implementation |
| Introduction to Quantum Structures (1 cr) Lectures Sept. 7, 8, 15 2011 1-4pm in TD 308, Sept 14 in TD 418 Various kinds of quantum structures will be introduced starting from Boolean algebras (they represent "classical" non-quantum model), namely orthomodular lattices, orthomodular posets, orthoalgebras and effect algebras (they are the most general structures considered in this lecture). Examples of these structures will be presented and relationships between them will be studied. States (measures) on quantum structures (including Jauch-Piron and subadditive states) and properties of the state space will be defined. Two main representations of quantum structures will be presented: graph orthogonality representations (so-called Greechie diagrams) and set representations (by a family of sets with set-theoretic operations). Basic properties of effect algebras will be derived (e.g. cancellation laws) and nonisotropic, sharp, principal and central elements will be studied. |