Scientific Computing Program
Scientific Computing (SC) is a broad, rapidly growing multidisciplinary area that encompasses applications in science/engineering, applied mathematics, numerical analysis, and computer science. Going from application area to computational results requires domain expertise, mathematical modeling, numerical analysis, algorithm development, software implementation, visualization and validation of results. SC makes use of the techniques of applied mathematics and computer science for the development of problem-solving methodologies, which will be the building blocks for solutions to scientific engineering problems of ever-increasing complexity. It differs from mathematics or computer science in that analysis and methodologies are directed specifically at the solution of problem classes from science and engineering, and will generally require a substantial collaboration from those disciplines. On the other hand it is certainly more than using software packages to generate and visualize the results, since it also concerns the development of algorithms for solving scientific and technical problems. Today, many problems in science and engineering can only be treated by means of efficient use of computers. Computation is now regarded as an equal and indispensable partner, along with theory and experiment, in the advancement of scientific knowledge and engineering practice. Numerical simulation enables the study of complex systems and natural phenomena that would be too expensive or dangerous, or even impossible, to study by direct experimentation.
The use of SC is ubiquitous in applications, like solid and structural mechanics, fluid mechanics, optimization in processing and production technology, technological design, aerodynamics, meteorology, electromagnetism, chemistry, physics, biology, medicine, economics and finance. The development of SC is driven by the rapid increase in computer performance. Mathematical analysis has been the basis for the derivation of new algorithms, which often contributed more to overall computational capacity than the increase in computer power. SC has also been a stimulating source for new problems in mathematics. Due to these advances, computational scientists and engineers can now solve large-scale problems that were once thought intractable. The importance of SC as a factor in economic growth and competition has been recognized by leading industry nations and a variety of research programs in Scientific Computing have been initiated and funded (see the reports “Grand Challenges”, USA, 1992; “Real World Computing Program", Japan, 1992; “Rubbia Report”, European Community, 1993). Parallel to the emergence of SC as an interdisciplinary research area, many graduate programs were developed in recent years at the leading universities of the world. The SC graduate programs are designed according to the multidisciplinary nature of SC and include the areas of Applied Mathematics, Numerical Analysis and Mathematical Modeling. In addition to a background in mathematics and computer science, a SC graduate must have a thorough education in an application area. The SC graduate's mathematical knowledge should be sufficient to model technological and scientific problems. Knowledge of computer science, and in particular numerical algorithms, software design and visualization, enable the SC graduate to make efficient use of computers. A SC graduate is expected to communicate within a team of engineers, computer scientists and mathematicians to solve difficult practical problems. It is essential that interdisciplinary collaboration should be an integral part of the curriculum. Accordingly the curriculum includes research projects and industrial applications upon which the Master thesis of the candidate will be based.
OBJECTIVES OF THE PROGRAM
- To train graduates coming from different disciplines at the Master’s level with the aim of developing their skills in solving real life problems and being able to apply them science, engineering and industry,
- To cultivate collaboration among research groups in mathematics, science and engineering departments at METU,
- To provide a platform for active participation of research groups from METU in the international research community by establishing research networks and participating in international projects,
- To organize international workshops and summer schools in order to introduce researchers and upcoming students to the new, developing areas of Scientific Computing.
- To establish contacts among in the Scientific Computing program and the industrial establishment in Turkey for the purpose of demonstrating modern methods applicable to industrial problems, and organize “Mathematics in Industry” workshops with representatives from the industry.
M.Sc. Program-Thesis Option
- 4 core courses
- 3 elective course
- 1 seminar course(non-credit)
- M.Sc. Thesis(non-credit)
Total : 21 credits
Core Courses for Scientific Computing Program
- IAM 561 Scientific Computing I (3-0)3
- IAM 562 Scientific Computing II (3-0)3
- IAM 566 Numerical Optimization (3-0)3
- IAM 567 Mathematical Modeling (3-0)3
- IAM 590 Graduate Seminar (0-2)NC
- IAM 500 M.S. Thesis (Non-credit)
Descriptions of Core Courses for Scientific Computing Program
1. IAM 561 Scientific Computing I (3-0)3
The objective of this course is to provide students mathematical foundations of numerical methods to analyze their stability, accuracy and computational complexity and demonstrate their performance by examples.
Computer Arithmetic, Systems of Linear Equations, Linear Least Squares, Eigenvalue Problems, Partial Differential Equations, Iterative Methods. Coursework and computer lab with MATLAB.
2. IAM 562 Scientific Computing II (3-0)3
Coursework and computer lab with MATLAB.
3. IAM 566 Numerical Optimization (3-0)3
Coursework and computer lab with MATLAB.
4. IAM 567 Mathematical Modeling (3-0)3
This course gives an introduction to real motivations, their translation into mathematical language and, then, the choice and performance of computational means. Students will learn about the nature of mathematical modelling, starting with a physical or biological model, representing it mathematically, simplifying and solving the resulting model and interpreting the results. They will be suggested to work in teams, to communicate appropriately and to present their results. Models and cases studies from mechanics in form of ordinary and partial differential equations. Geometric and discrete models. Stochastic models in finance. Coursework and computer lab with MATLAB
5. IAM 590 Graduate Seminar (0-2)NC
This course is designed to provide students with a chance to prepare and present a professional seminar on subjects of their own choice.
6. IAM 500 M.S. Thesis (Non-credit)