**MATH 499 Graduation Project**

Short description

MATH 499 Graduation Project is a 6-ECTS elective, which is counted towards the mathematics core elective credit requirement. The goal of the course is to engage the student in original thinking and independent work towards the creation of a *capstone thesis* under the supervision of an experienced faculty.

The timeline for the course is the following:

- Fall Semester Week 3: choice of a supervisor among the math faculty.
- Spring Semester Week 1: assessment of the student’s preparation by supervisor.
- Spring Semester Week -4: composition of the thesis committee (choice of second reader).
- Spring Semester Week -2: public defense.
- Spring Semester Week -1: submission of revised thesis.

The grade for the course, decided by majority in the thesis committee (supervisor, second reader and course coordinator) is Pass/Fail.

Remarks:

- Students can withdraw at any time or can be withdrawn by their supervisor in case of inadequate preparation or work.
- It is essential that students contact a supervisor early in the
**fall semester**, even if the course runs formally only in the spring semester.

**Capstone Projects (2018-19)**

- Low rank approximation of matrices for generating pmi (Zhenisbek Assylbekov and Thomas Mach)
- Hirota equation and the wigner transform (Alejandro J. Castro Castilla)
- Well-posedness of nlse and mkdv equations (Alejandro J. Castro Castilla)
- Hirota equation with dissipative and pumping terms (Alejandro J. Castro Castilla)
- A lower bound for double base expansions (Francesco Sica)
- De factorisatione numerorum (Francesco Sica)
- Exactly solvable multi-species stochastic particle models(Eunghyun Lee)
- Analytic solutions of partial differential equations (Daniel Oliveira Da Silva)
- Spectral geometry of partial differential equations and applications (Durvudkhan Suragan)
- Approximations of periodic solutions to problems in micro-electro-mechanical systems (Piotr Skrzypacz)
- Discontinuous galerkin method for nonlinear diffusion-convection problems (Piotr Skrzypacz)
- Solving 1d transmission problems by finite elements (Piotr Skrzypacz)
- The robust finite element discretizations for dead-core problems (Piotr Skrzypacz)
- Differential equations in micro-electrico-mechanical systems (Piotr Skrzypacz)
- Asymptotic behavior of epidemic models (Ardak Kashkynbayev)
- Frobenius singularities of algebraic sets of matrices (Zhibek Kadyrsizova)

- A toy model for nonlinear black-scholes equations (D. da Silva).
- Convergence analysis of retarded fuzzy neural networks (A. Kashkynbayev).
- Functional Analysis (E. Lee).
- Mathematical Concepts for Quantum Mechanics (E. Lee).
- Stochastic Calculus (E. Lee).
- The core of eiscor (T. Mach).
- Matrix polynomials in Chebyshev basis (T. Mach).
- Basic model of storm water and snow melt events (T. Mach).
- Searching for generalizations of Pac-Man conditions (R. Takhanov).

We have 11 capstone project reports from 2016 year and 4 from 2015 in the NU repository which can be found in: http://nur.nu.edu.kz/