Applied Mathematics: Numerical Analysis and Algorithmic Optimization Design

Course 12: Applied Mathematics: Numerical Analysis and Algorithmic Optimization Design

I. Course Description

Numerical analysis is a subject to study and analyze the numerical calculation method and theory of solving mathematical computing problems by computer. It involves a wide range of fields, and the optimization problems can usually be expressed in the form of mathematical planning. Linear planning is an important branch of early research, rapid development, wide application and mature methods in operations research. It is a mathematical method to assist people in scientific management, and a mathematical theory and method to study the extreme value problem of linear objective function under linear constraints. Linear planning is widely used in military operations, economic analysis, operation and management, and engineering technology, and provides a scientific basis for the rational use of limited human, material and financial resources.

Linear planning is an excellent entry point into larger areas such as operations research, data science, and artificial intelligence. This course will introduce the key concepts of linear planning, introduce the application of linear planning in the economic and financial fields, and some interesting applications, such as diet problems, transportation problems, shortest path problems, etc.

II. Professor Introduction

Ming Gu – Tenured professor at the University of California, Berkeley

Professor Ming Gu of mathematics at the University of California, Berkeley, is known for his outstanding contributions in the fields of numerical linear algebra and scientific computing. He holds a PhD in computer science from Yale University, which provides a solid foundation in computational mathematics. Professor Gus research focuses on numerical algorithms, especially in matrix computing and eigenvalue issues, which are critical to large-scale data analysis, machine learning, and engineering applications.

One of the highlights of his research is the development of efficient and reliable algorithms that are widely used in data science and engineering, including optimization algorithms for structural matrix, fast linear system solution methods, and efficient processing methods suitable for high-dimensional data. Professor Gus research results have been widely published in top academic journals and won many honors. In 2017, he won the Best Paper Award of the International Conference on High Performance Computing (HiPC) for his research results, and published his paper at the International Conference on Machine Learning. In addition, he actively works with experts in applied mathematics and computational science to further promote innovation and development in the field of numerical computing.

III. Syllabus

1. Solution to equation f (x) = 0
2. Numerical derivatives and the integration
3. Numerical differential equations
4. Solve the linear equation, Ax = b
5. Graphic calculator skills
6. Simulation of the solar system motion
7. MATLAB programming foundation
8. Data visualization method
9. Optimize the algorithm for its application
10. The numerical linear algebra