Holiday
GEN III綜三 203 R1R2R3
本課程從邏輯出發探討數學分析之基礎,從集合論,實數完備性,數列收斂發散,函數連續性,可微分性到函數序列做詳細確實的推演。 目的在於教導學生對應用現象有困擾時能回歸邏輯回到嚴謹的數學推理來解決問題,以堅實理論為基礎迎接AI時代的來臨。
Course keywords: Rigorous proof, Completeness of Real number, Continuous function, Differentiable function, Sequence 一、課程說明(Course Description) 電腦日益發達,隨著AI時代來臨很多複雜金融計算皆有程式可處理,但使用者須具備嚴謹邏輯及數學基礎才能在 混亂的資訊中找到重點,做出合邏輯之判斷與決策。本課程以傳統高等微積分內容為主佐以最新之實例來培養學 生嚴謹之數學素養。 二、指定用書(Text Books) W.R.Wade: An Introduction to Analysis, 4th edition, 2014 三、參考書籍(References) 1. W.Rudin: Principles of Mathematical Analysis, 3rd edition, 1976 2. Robert R. Reitano: Introduction to Quantitative Finance A Math Tool Kit 3. Frank Werner & Yuri N. Sotskov: Mathematics of Economics and Business 四、教學方式(Teaching Method) 課堂: 理論推導,實例講解,應用介紹。 演習課: 習題演算及討論,平時考。 演習課時間:週二晚上19:00-21:00。 2月21日開始上演習課。 五、教學進度(Syllabus) This is a fundamental course of analysis, a rigorous version of calculus. The contents for this semester include 1. Logic and set theory 2. The Real Number System 3. Sequences in R 4. Continuity on R 5. Differentiability on R 6 Integrability on R 7. Infinite Series of Real Numbers 8. Infinite Series of Functions 六、成績考核(Evaluation) 平時考(20%),期中考(40%),期末考(40%)。 七、可連結之網頁位址 https://www.youtube.com/user/hualunli/videos
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Average Percentage 63.92
Std. Deviation 13.12
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