Master of Science in Applied Mathematics program is a two-year program (120 ECTS credits) designed to train students as professional applied mathematicians who will possess in-depth knowledge of advanced theory and practical knowledge in numerical simulation, statistical analysis, data mining, and computational mechanics.
Graduates are expected to acquire advanced mathematical, statistical, and computational skills as relevant to their subjects of their Master projects. Furthermore, they will develop skills in interdisciplinary numerical simulations, statistical computing, and computer aided design environment and will acquire a command of scientific communication skills. The program is designed to take advantage of the faculty expertise and the computational resources of the School of Science and Technology, Nazarbayev University Research and Innovation System. Graduates of the program will have advanced research skills that will enable them to make contributions in technologically diverse and dynamic economic environments, both in Kazakhstan and abroad.
Framework of the SST Applied Mathematics Master’s Program:
The list of MSc-level Mathematics courses are:
A. Core Courses:
1. MATH 512 Optimization Methods and Techniques
The course covers an introduction to convex sets and convex functions, unconstrained (first and second order conditions) and constrained optimization, existence of solutions (Weierstrass’ theorem), equality constraints: Lagrange’s optimality theorem, second order conditions, Karush-Kuhn-Tucker theorem, convex and non-convex optimization, linear optimization, integer optimization, multiple objective optimization. Some computational methods: line search, steepest descent, Newton, quasi Newton, trust region, feasible points, penalty methods, and augmented Lagrangian methods, applications. Applications to economics, finance, logistics, supply chain, transportation
2. MATH 517 Mathematical Modeling and Simulation
This course uses scientific principles of physics, biology, and engineering in combination with mathematical methods to formulate and design mathematical models and study real life problems. The analysis includes the existence and stability of the steady state and periodic solutions of systems of nonlinear ordinary differential and difference equations and the onset of chaos as parameters vary. Fundamental concepts of linear partial differential equations with important physical applications are also introduced. Numerical analysis methods are used to develop algorithms and compute solutions to the problems.
3. MATH 519 Scientific Computing
This course will make students familiar with algorithm design motivated by problems in physics, engineering, epidemiology, chemistry, and biology. It will use scientific principles in combination with mathematical methods to implement MATLAB algorithms that are grounded in sound principles of scientific computing and in the understanding of machine arithmetic and memory management. The course is designed to teach students programming skills for carrying out computational tasks. Numerical computing will be used for numerical solution of linear and nonlinear equations, differential equations, optimization problems and Monte Carlo simulations as well as for analyzing data. Students will also learn elements of shell programming under Unix/Linux, as well as use of modern software packages AUTO/BVPSuit and preparing scientific reports in Latex.
4. MATH 540 Statistical Analysis
The course covers theoretical foundations and applications of machine learning models. Topics include supervised methods for regression and classification (linear models, trees, neural networks, ensemble methods, instance-based methods), Bayesian parametric learning, density estimation and clustering, sequential models. Programming projects covering a variety of real-world applications are assigned.
5. CSCI 501 Software Principles and Practice
This is an accelerated course in the evolution and design of imperative programming languages, and modern software development techniques. In the first part of the course, we will use the C language to review the fundamentals of programming, and progress on to the concepts of data types, encapsulation, and reusability. Algorithms and performance will also be topics of discussion. While investigating the advantages and drawbacks of C, we will motivate some of the key features of object-oriented languages, such as inheritance and polymorphism, as well as generics. We will then look at the Java language as an instance of the OO paradigm, and discuss good OO design principles. In second part of the course, we will pull several of these threads together, where students will be asked to develop an interpreter for a basic imperative language using the Java language.
6. MATH 541 Data analysis and statistical learning
The course begins with the linear models for regression/classification and proceeds with the model assessment/selection issues such as diagnostics and remedial measures, the comparison of models. We proceed to covering fixed and random effects model, regularization, kernels, design of neural networks and, finally, based on VC theory, we discuss how sample size affects the generalization power.
7. MATH 551 Advanced Numerical Methods
This course covers advanced numerical methods that are used in large scale scientific and engineering computations and simulations. The topics include Krylov subspace methods and preconditioning, especially the conjugate gradient method and BiCGstab, iterative methods for eigenvalue computation, and advanced numerical methods for initial value problems.
8. MATH 576 Numerical Methods for PDEs
The course is a blend of conceptual and practical aspects of numerical solutions of partial differential equations. Topics include finite difference, volume, element, and spectral methods, and explicit/implicit methods for time integration, convergence, consistency, stability, Courant-Friedrichs-Lewy criteria, Lax equivalence theorem, error analysis, Fourier-von Neumann stability analysis. Applications include the Poisson equation, heat equation, wave equation, advection-diffusion equation, and Stokes equation.
B. Elective Courses:
1. MATH 542 Statistical Programming
The course deals with data analysis using advanced statistical programming such as R or SAS. Students will learn syntax, how to read fixed and free format data, use built-in and user-written functions, optimization and graphical capabilities. The applied statistical problems considered include linear and nonlinear regression, experimental design, and others.
2. MATH 514 Operations Research
Operations research helps in solving problems in different environments that needs decisions. This course covers topics that include: mathematical programming, stochastic optimization, fuzzy optimization, dynamic programming, deterministic and stochastic optimal control, multi-criteria decision aid, and application to engineering, finance, management.
3. MATH 518 Applied Finite Element Analysis
This course covers both mathematical foundations and applications of finite element methods including elements in solid mechanics, thermodynamics and fluid flows. It also covers implementation of solution procedures, validation of numerical solutions, algorithms, limitations. Computer exercises are based on Matlab professional FE codes.
4. MATH 571 Nonlinear Differential Equations
The course studies nonlinear differential equations and their solutions. The course covers a quick review on first-order (logistic) differential equations, (non) autonomous and (non)linear equations, general and near equilibrium behavior, the phase-plane, Poincare map, critical points, periodic solutions, Poincare-Bendixson theorem, stability (Lyapunov), stability analysis by linearization, perturbation theory, Poincare-Lindstedt method, averaging, bifurcation, one dimensional chaos, fractal sets, and Hamiltonian systems.
5. MATH 676 Advanced Partial Differential Equations with Applications
Laplace and heat equations, wave equations, fundamental solutions, maximum principles, Sobolev spaces, embedding theorems, weak solutions, energy methods, regularity of solutions, existence and uniqueness of solutions, general linear elliptic, parabolic and hyperbolic equations, and applications.
C. Research Courses:
1. SST 591 Research Methods
This course firstly introduces students to research methodologies including surveys, interviews, experimentation, and case studies. Then, different topics such as research design, and data collection and analysis of data are covered.
2. SST 691 Thesis Proposal
In this course, students will find their thesis advisors and write their thesis proposals.
3. SST 692 Thesis Research
Student will conduct independent work under the direction of a supervisor on a research problem in the student’s designated area of research. The student will prepare and defend the thesis.
D. Teaching and Learning Courses:
1. SST 501 Teaching and Learning
This course introduces the students to best-practice pedagogical methods and innovations in teaching, under the mentorship of senior faculty. The students will conduct classroom and laboratory observations of prominent instructors, using a variety of teaching and learning styles. They will present their observations and experience in a final report.
2. SST 504 Innovation and Entrepreneurship
3. SST 502 Teaching Practicum
Students will apply educational, instructional, and assessment methodologies in recitation sections of their respective disciplines under the supervision of an experienced faculty member. They will summarize their observations and experience in a final report.
4. SST 503 Laboratory Practicum
Students will apply educational and instructional methodologies in laboratory and practical sessions of their respective disciplines under the supervision of an experienced faculty member. They will summarize their observations and experience in a final report.
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Applicants applying to the Master of Science in Applied Mathematics program are expected to have:
1) an undergraduate degree (Bachelor’s degree or equivalent) in a relevant discipline, to be determined by the Admissions Committee;
2) a minimum CGPA of 2.75;
3) 2 letters of recommendation;
4) a personal statement of purpose;
5) submission of a valid IELTS or TOEFL test report (must be submitted) unless the conditions for exemption are met (see below).
Required Level of English Proficiency:
The absolute minimum requirement for English language proficiency test reports for admission to the Master of Science in Applied Mathematics program is overall IELTS test score of 6.5 (with sub-score requirements no less than 6.0), or the equivalent TOEFL score as posted on the ETS website.
Applicants to the Master of Science in Applied Mathematics program, at the discretion of the Admissions Committee, can be exempted from submitting the language proficiency test report if:
- one of their earlier academic degrees was earned in a country with English as the language of official communication, academic instruction and daily life;
- an undergraduate degree was earned in a program which was officially taught in English;
- the applicant is a graduate of Nazarbayev University.