Selected Topics in Mathematics
Forms of Teaching
4 hours of lectures a week. The lecturer is going to follow the lecture materials.Independent assignments
Each student will get a project in one of the three major areas: discrete mathematics, probability or mathematical modelling. The project includes analysis of a problem, studying as well as solving it using the computer.
|Type||Threshold||Percent of Grade||Threshold||Percent of Grade|
|Seminar/Project||0 %||25 %||0 %||25 %|
|Mid Term Exam: Written||0 %||25 %||0 %|
|2. Mid Term Exam: Written||0 %||25 %||0 %|
|Final Exam: Written||0 %||25 %|
|Exam: Written||0 %||75 %|
Week by Week Schedule
- Introduction to the main topics and challenges. Student project presentations. Generation of all subsets of a given set. Different lexicographical orderings.
- Generation of all k-subsets, all functions, injective and surjective functions. Adding constraints and software solutions.
- Permutations. The successor function. Permutations without fixed elements. Integer partitions.
- Bell's numbers. Stirling numbers. Software solutions. Combinatorial designs.
- Introduction to mathematical modelling. Weak formulation of a mathematical model. Introduction to the finite element method.
- Implementation of the finite element method for the 1D problem. Methods of solving linear systems.
- Finite element method for a two-dimensional Poisson problem. GMSH and non-trivial domains.
- Midterm exam
- Weak formulation and finite element solvers for several models from practice.
- Parameter tables for designs. Construction strategies. Difference sets. Introduction to Monte Carlo simulations.
- Introduction to Markov chains. Transition probability matrix. Chapman-Kolmogorov Equations.
- Simulation of Markov chains. Classification of States.
- Limiting distribution. Stationary distribution. Ergodic theorem.
- Project work and presentation.
- Final exam