基本素養 Basic Literacy

核心能力 Competence

掌握連續與逼進的能力
Ability to handle continuity phenomena and approximations.
處理數字及符號運算的能力
Ability to operate with symbols and digits.
透視形像與空間的能力
Ability to visualize space, shape, and images.
利用計算機處理數學的能力
Ability of computer to do mathematics.
應用隨機理論的能力
Ability to apply stochastic mathematics.
處理大量數據的能力
Ability to handle large amount of data.
處理離散型數學的能力
Ability to do mathematics relating to discrete models.
獨立研究與撰寫論文的能力
Ability to do independent researches and to write thesis.
使用計算機的能力
Abilities to use computer as a tool.

課程概述 Course Description

本課程介紹快速計算方法的理論並透過程式語言的實作來了解此類方法快在哪裡的精髓。課程中將介紹快速排序法、快速富立葉轉換、快速波瓦松求解器、幾何及代數多重網格法、快速多重極方法等等。
The theory of fast computational methods are introduced. Students could understand the essence through the implementation in programming languages. Several methods will be illustrated, such as quick sort, fast Fourier transform, fast Poisson solver, geometry and algebraic multigrid method, fast multipole method, etc.

課程學習目標 Course Objectives

  • Computational Complexity
  • Quick Sort
  • Fast Fourier Transform
  • Fast Poisson Solver
  • Multigrid Method
  • 課程進度 Course Outline

    週次 Week進度說明 Progress Description
    1Introduction
    2Coding in C
    3GIT
    4Matlab Vectorization & Linear Algebra
    5Quick Sort
    6Applications of Quick Sort
    7Presentation
    8Introduction to Fourier Transform
    9Fast Fourier Transform
    10Fast Sine and Cosine Transform
    11Application of Fast Fourier Transform
    12Mid-exam: Implementation of Fast Fourier Transform
    13Introduction of Partial Differential Equations
    14Boundary Value Problems
    15Fast Poisson Solver
    16Multigrid Method
    17Algebraic Multigrid Method
    18Final exam: Implementation of Multigrid Method
     以上每週進度教師可依上課情況做適度調整。The schedule may be subject to change.

    有關課程其他調查 Other Surveys of Courses

    1.本課程是否規劃業界教師參與教學或演講? 否
    Is there any industry specialist invited in this course? How many times? No
    2.本課程是否規劃含校外實習(並非參訪)? 否
    Are there any internships involved in the course? How many hours? No
    3.本課程是否可歸認為學術倫理課程?
    Is this course recognized as an academic ethics course? In the course how many hours are regarding academic ethics topics?
    4.本課程是否屬進入社區實踐課程?
    Is this course recognized as a Community engagement and Service learning course? Which community will be engaged?