Computational Science and Numerical Methods (CN) (4%) For Computer Science Students
CN1. Numerical analysis [elective]
CN2. Operations research [elective]
Recommended Books:
1. Numerical Analysis by S. A. Butti
2. Operation Research by Taha, Hamdy A
From the earliest days of the discipline, numerical methods and the techniques of scientific computing have constituted a major area of computer science research. As computers increase in their problem-solving power, this area -- like much of the discipline -- has grown in both breadth and importance. At the end of the millennium, scientific computing stands as an intellectual discipline in its own right, closely related to but nonetheless distinct from computer science.
Although courses in numerical methods and scientific computing are extremely valuable components of an undergraduate program in computer science, the CC2001 Task Force believes that none of the topics in this area represent core knowledge. From our surveys of curricula and interaction with the computer science education community, we are convinced no consensus exists that this material is essential for all CS undergraduates. It remains a vital part of the discipline, but need not be a part of every program.
For those who choose to pursue it, this area offers exposure to many valuable ideas and techniques, including precision of numerical representation, error analysis, numerical techniques, parallel architectures and algorithms, modeling and simulation, and scientific visualization. At the same time, students who take courses in this area have an opportunity to apply these techniques in a wide range of application areas, such as the following:
- Molecular dynamics
- Fluid dynamics
- Celestial mechanics
- Economic forecasting
- Optimization problems
- Structural analysis of materials
- Bioinformatics
- Computational biology
- Geologic modeling
- Computerized tomography
Topics:
- Floating-point arithmetic
- Error, stability, convergence
- Taylor's series
- Iterative solutions for finding roots (Newton's Method)
- Curve fitting; function approximation
- Numerical differentiation and integration (Simpson's Rule)
- Explicit and implicit methods
- Differential equations (Euler's Method)
- Linear algebra
- Finite differences
- Compare and contrast the numerical analysis techniques presented in this unit.
- Define error, stability, machine precision concepts and the inexactness of computational approximations.
- Identify the sources of inexactness in computational approximations.
- Design, code, test, and debug programs that implement numerical methods.
- Linear programming
- Integer programming
- The Simplex method
- Probabilistic modeling
- Queuing theory
- Petri nets
- Markov models and chains
- Optimization
- Network analysis and routing algorithms
- Prediction and estimation
- Decision analysis
- Forecasting
- Risk management
- Econometrics, microeconomics
- Sensitivity analysis
- Dynamic programming
- Sample applications
- Software tools
- Apply the fundamental techniques of operations research.
- Describe several established techniques for prediction and estimation.
- Design, code, test, and debug application programs to solve problems in the domain of operations research.
