General information
GENERAL INFORMATION
Who is IP for? Advantages Main goals Main activities
The course is dedicated to students of Master and PhD studies in Mathematics, Computer science and Physics. Students who would like to learn new skills and knowledge from behind regular study courses are welcome to take part in the programme.
We will work in an international group of students and teachers from Poland, Romania, Germany and Hungary. The course will take place in Bydgoszcz – a picturesque city in the bother Poland. We spend a weekend resting at the Polish seaside.
During the course students will collect maximum 8 ECTS credits. The exact amount of credits depends on a number of tests passed by a particular student. Preparatory e-learning activities are included into the number of credits to be obtained. Participants will be provided with a confirmation of participation and transcript of records. Partner universities have a long tradition and experience in recognizing ECTS grades and credits earned by students in foreign locations. Based on that we do not expect any difficulties in recognizing the earned credits and grades. Therefore full recognition is guaranteed at each partner university. ECTS credits and grades achieved during the summer course will be recognized as a equivalent of one standard course at the home university.
The IP’s goal is to offer a new innovative more open approach to teaching based on use of modern computer applications and presentation of first line scientific research. As an example, computer methods will be applied in mathematical models applicable both in physical and mathematical analyses.
The focus of this course in terms of its content and methods applied is on mathematics, physics, computer use and computer science.
Students will learn about
- numerical analysis and computer-assisted proofs for photonic crystals (Maxwell’s equations, photonic band gaps),
- calculus of variations, applications to elasticity and optimization
- functional equations and inequalities
- convexity and generalized convexity.
Students will use in (1) and (3) the numerical toolbox and computer algebra system Matlab for searching solutions of functional equations and inequalities and will write new computer applications.
Some of the newest scientific achievements will be presented directly by their authors. Students will approach a new theory by attending lectures and tutorials, where problems are discussed and computer experiments are carried out. Students will also learn how to write a computer application in computer algebra system in order to solve functional equations and inequalities. Similarly, students will gain experience in using programming languages for the numerical solution of Maxwell's equations and in using programming tools for establishing rigorous enclosures in the area of computer-assisted proofs.
After the course students will be able to understand how the basics concepts from convexity and from the calculus of variations can be used to describe the deformation of elastic materials. They will experience how analysis, functional analysis and mechanics are combined. At the same time they will realize that similar notions of convexity are the key to solving problems in finite dimensional optimization theory. Students will be also able to use computer methods to solve problems related to the above mentioned issues.
Students will be able to understand how to approach and elaborate mathematical models for various practical problems arising from the industrial and economic environment. They will know how the basics concepts from convexity and from the calculus of variations can be used to describe the deformation of elastic materials. They will experience how analysis, functional analysis and mechanics are combined. Simultaneously they will realize that similar notions of convexity are the key to solving problems in finite dimensional optimization theory. Students will be also able to use computer methods to solve problems related to the above mentioned issues.
Students will obtain new convexity concepts from a generic way of thinking, to identify those properties of the convex objects that are necessary in solving optimization problems, to use some main convex programming techniques.
Students will be given some problems to be solved in international groups. Students results will stand for the final project which has to be prepared using ICT tools and presented at the end of the course in front of the whole group. Students should also take final test finishing each module of the course. During the course students will gain maximum 8 ECTS credits which include also pre-recruitment e-learning activities.
Apart from the intensive work we will rest while visiting Polish splendor triple city: Gdańsk, Sopot, Gdynia as well as the nearest neighborhood of the university – the cities of Bydgoszcz and Toruń.
We will taste a Polish culture and share cultural and social experience of partners of other nationalities.