Difficulty: Advanced. Categories: Mathematics.
This course provides a rigorous introduction to numerical computation methods and optimization theory, focusing on the mathematical foundations and algorithmic techniques used to solve complex computational problems. It bridges theory and practice by equipping students with the tools necessary to design efficient and reliable numerical algorithms. Key topics include numerical linear algebra, iterative methods, nonlinear equation solving, numerical integration and differentiation, and error analysis. On the optimization side, the course covers unconstrained and constrained optimization, convex optimization, gradient-based methods, duality theory, and large-scale optimization techniques. Students will gain hands-on experience implementing numerical algorithms and optimization methods, with applications in machine learning, engineering, economics, and scientific computing. Emphasis is placed on computational efficiency, stability, and convergence analysis.
Learning objectives
Students should be comfortable with calculus, linear algebra, and basic numerical methods.
Yes, programming (typically in Python or MATLAB) is essential for implementing algorithms and experiments.
The course is mathematically rigorous, with strong emphasis on proofs, convergence analysis, and algorithm design.
