課程名稱 |
基本集合論 Elementary Set Theory |
開課學期 |
108-1 |
授課對象 |
文學院 哲學系 |
授課教師 |
鄧敦民 |
課號 |
Phl2805 |
課程識別碼 |
104 13800 |
班次 |
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學分 |
3.0 |
全/半年 |
半年 |
必/選修 |
選修 |
上課時間 |
星期三8,9,10(15:30~18:20) |
上課地點 |
普306 |
備註 |
本課程中文授課,使用英文教科書。(C)哲學專題群組,群組課程請參閱本系網頁修業課程規定。 總人數上限:50人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1081SetTheory |
課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
課程大綱
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課程概述 |
本課程的目的在介紹Zermelo-Fraenkel 公理化集合論的系統以及它的公理,使學生對於數理邏輯或數學哲學文獻所需要的邏輯與集合論背景知識有基本程度的掌握。一般公認集合論為數學提供了一個基礎,在本課程中與此相關的哲學議題也會稍微提及。本課程將詳細研讀Enderton的教科書《The elements of Set Theory》。
This course aims to introduce students to the Zermelo-Fraenkel Set Theory with its basic axioms and motivating conceptions. It will provide students with a sufficient background for pursuing further studies in mathematical logic and the philosophy of mathematics. It is widely acknowledged that set theory provides a basis for pure mathematics, and related to this the philosophical question about the foundation of mathematics will be discussed. The course will go through Enderton’s textbook Elements of Set Theory.
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課程目標 |
本課程目標在使學生能夠
(1) 掌握ZFC系統的主要公理
(2) 對於基數與序數有基本的掌握
(3) 理解集合論與數學基礎之間的關聯
Students will be expected to
(1) Learn the ZFC axioms
(2) Acquire some basic ideas of ordinal and cardinal numbers
(3) Understand how set theory provides the basis for mathematics
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課程要求 |
每週修課學生需完成指派的習題 |
預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
Herbert B. Enderton. Elements of Set Theory. New York: Academic Press, 1977. |
參考書目 |
1. Jech Thomas. Set Theory. The Third Millennium Edition, Revised and Expanded.
Berlin: Springer, 2003.
2. Michael Potter. Set Theory and its Philosophy. Oxford: Oxford University
Press, 2004.
3. Raymond M. Smullyan and Melvin Fitting. Set Theory and the Continuum Problem.
New York: Dover, 2010. |
評量方式 (僅供參考) |
No. |
項目 |
百分比 |
說明 |
1. |
期中考試 |
50% |
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2. |
期末考試 |
50% |
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週次 |
日期 |
單元主題 |
第1週 |
9/11 |
Introduction: sets, classes, axiomatic method |
第2週 |
9/18 |
Axioms and Operations: arbitrary unions and intersections, algebra of sets; Relations and Functions: ordered pairs, relations |
第3週 |
9/25 |
Relations and Functions (1): functions |
第4週 |
10/02 |
Relations and Functions (2): infinite Cartesian products, equivalence relations, ordering relations |
第5週 |
10/09 |
Natural Numbers: inductive sets, Peano's postulates, arithmetic, ordering on omega |
第6週 |
10/16 |
Natural numbers: ordering on omega; Construction of the Real Numbers |
第7週 |
10/23 |
Cardinal numbers and the Axiom of Choice (1): equinumerosity, finite sets |
第8週 |
10/30 |
Cardinal numbers and the Axiom of Choice (2): cardinal arithmetic, ordering cardinal numbers |
第9週 |
11/06 |
Midterm Exam |
第10週 |
11/13 |
Cardinal numbers and the Axiom of Choice (3): axiom of choice |
第11週 |
11/20 |
Cardinal numbers and the Axiom of Choice (4): countable sets, arithmetic of infinite cardinals, continuum hypothesis |
第12週 |
11/27 |
Orderings and Ordinals (1): partial orderings, well orderings |
第13週 |
12/04 |
Joint conference with CUHK |
第14週 |
12/11 |
Orderings and Ordinals (2): replacement axioms, epsilon-images, isomorphisms |
第15週 |
12/18 |
Orderings and Ordinals (3): ordinal numbers |
第16週 |
12/25 |
Orderings and Ordinals (4): debts paid, rank |
第17週 |
1/01 |
National Holiday (no class) |
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