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

本課程將介紹一些社會科學與資訊科學中的數學問題,以及相關的分析與計算工具,例如:線性系統與線性規劃,傅立葉分析與訊號處理,統計方法與資料分析。
This course is aimed to study analytical and computational methods in mathematical problems arising in social science and information science. For example: linear systems and linear programming, Fourier analysis and signal process, statistics and data analysis.

課程學習目標 Course Objectives

  • 學習由各個不同領域的應用問題建立相對應的平衡方程式
  • 學習解平衡方程式的求解方法,包括解析與計算
  • 學習線性錐優化,包括二次錐規劃與半正定規劃的基本知識
  • 課程進度 Course Outline

    週次 Week進度說明 Progress Description
    1Modeling the equilibrium equations of dynamic systems
    2The fundamental framework of mechanics and the rank theorem in linear algebra
    3The stiffness matrix and the minimal potential energy
    4From Mechanics to Electrical network
    5From discrete networks to continuous flows
    6Solution methods for solving the equilibrium equations (cholesky factorization)
    7Solution methods for solving the equilibrium equations (cholesky factorization)
    8Solution methods for solving the equilibrium equations (matrix sparsity)
    9Solution methods for solving the equilibrium equations (matrix sparsity)
    10Solution methods for solving the equilibrium equations (matrix sparsity)
    11Solution methods for solving the equilibrium equations (Fourier transform)
    12Solution methods for solving the equilibrium equations (Fourier transform)
    13Solution methods for solving the equilibrium equations (Fourier transform)
    14Conic Linear Programming
    15Conic Linear Programming
    16Conic Linear Programming
    17Conic Linear Programming
    18Final Presentation
     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?