- Programme: RealMaths
- ECTS Credits: 3
- Semester: 2
- Year: 2
- Campus: Claude Bernard University Lyon 1
- Content:
– Neural networks
– Sparsity and high dimension
– Graphs and ecological networks
– Optimal transport for statistical learning
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: Gdansk University of Technology
- Unit Coordinator: Tobias Knopp
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: Hamburg University of Technology
- Language: English
- Aims:
After successful completion of the module, students are able to describe reconstruction methods for different tomographic imaging modalities such as computed tomography and magnetic resonance imaging.
They know the necessary basics from the fields of signal processing and inverse problems and are familiar with both analytical and iterative image reconstruction methods.
The students have a deepened knowledge of the imaging operators of computed tomography and magnetic resonance imaging.
- Content:
Overview about different imaging methods, signal processing, inverse problems, computed tomography, magnetic resonance imaging, compressed sensing, magnetic particle imaging.
- Pre-requisites:
Basic knowledge in linear algebra, numerics, and signal processing
- Reading list:
- Introduction to the Mathematics of Medical Imaging; C. L.Epstein; Siam, Philadelphia, 2008
- Medical Image Processing, Reconstruction and Restoration; J. Jan; Taylor and Francis, Boca Raton, 2006
- Principles of Magnetic Resonance Imaging; Z.-P. Liang and P. C. Lauterbur; IEEE Press, New York, 1999
- Unit Coordinator: Jarosław Rybicki
- ECTS Credits: 1
- Semester: 2
- Year: 2
- Campus: Gdansk University of Technology
- Language: English
- Aims:
The course aims at presentation of modern methods of thinking applied in science and technology
- Content:
1. INTRODUCTION. Ontological, psychological, semiotic, theory-cognitive terminology. Formal logic. Philosophy of logic. Methodology vs. science. Science vs. logic.
2. PHENOMENOLOGICAL METHOD. Objectivity of phenomenologists. Return to "issue in itself", intuitive cognition.
3. SEMIOTIC METHODS. Sign and its three dimensions. Formalism. Essence of formalism - calculation. Application of calculation to non-mathematical subjects. Validation of formalism. Eidetic and operational sense. Models. ArtiScial language. Syntactic rules of sense. Construction of language. Atomic and molecular expressions. Notion of syntactic category. Functors and arguments. Examples of syntactic nonsense. Semantic functions and levels Two semantic functions of sign. Designation and signiScance. Semantic levels. Language and meta-language. Semantic meaning and veriSability. Rule of verifiability. Verification levels: technical possibility, physical possibility, logical possibility, transempirical possibility. Principle of intersubjectivity. Verifiability of general clauses.
4. AXIOMATIC METHOD. Structure of indirect cognition. Law and rule. Two basic forms of inference: deduction and reduction. Reliable and unreliable rules of inference. Concept of axiomatic system. Structure of axiomatic clause system. Requirements for axiomatic system. Constitutional system. Progressive and regressive deduction. Mathematical logic. Methodological significance. Implication and derivability. Definition and creation of concepts. Basic types of definition. Real and nominal definitions. Syntactic and semantic definitions. Analytical and synthetic deSnitions. Types of syntactic definitions: clear definitions, contextual definitions, recursive definitions, definitions by axiomatic system. Semantic deictic definitions. Real definitions. Application of axiomatic method. Axiomatization of logic of Hilbert-Ackermann clauses.
5. REDUCTION METHODS. Historical introductory remarks. Concept and division of reduction. Concept of verification and explanation. Regressive reduction. Reduction sciences. Structure of natural sciences. Observation clauses. Progress in natural sciences. Verification of hypotheses. Experience and thinking. Types of explanatory sentences. Causal explanation and teleological explanation. Co-occurrence laws and functional laws. Deterministic laws and statistical laws. Authentic and non-authentic induction. Division of induction. Primary and secondary induction. Qualitative and quantitative induction. Deterministic and statistical induction. Enumerative and eliminatory induction. Postulates of determinism, closed system, relationship between laws, simplicity.
- Reading list:
J. M. Bocheński, Współczesne metody myślenia, wydawnictwo "Wdrodze", Poznań (1992)
Supplementary Literature
K. Popper, Logika odkrycia naukowego, PWN (1983)
M. Grzegorczyk, Logika matematyczna, PWN (1979)
