課程資訊

Introduction to Mathematical Logic

104-1

CSIE5111

922EU4250

Mathematical logic was developed for two reasons: (i) to free mathematics from internal paradoxes and inconsistencies; (ii) as a plausible tool to achieve artificial reasoning. We will discuss the strengths and the weaknesses of the logics developed for these two purposes. We will cover some fundamental topics, from the propositional calculus, i.e., the Boolean algebra, to Gödel's incompleteness theorem, and the relations between logic and computer science and the notions of computability.

Office Hours

We will not follow one particular textbook. All the materials that we will cover can be found in the following textbooks
_ Mathematical logic by H.-D. Ebbinghaus, J. Flum and W. Thomas.
_ A Mathematical Introduction to Logic by H. Enderton.
_ A Concise Introduction to Mathematical Logic by W. Rautenberg

You can find informal treatment of logic in the following books.
_ Gödel, Escher, Bach: An Eternal Golden Braid by D. Hofstadter.
_ Gödel's Theorem: An Incomplete Guide to its Use and Abuse by T. Franzen.
_ A Tour through Mathematical Logic by R. Wolf.

(僅供參考)

 No. 項目 百分比 說明 1. Midterm exam 20% 2. Final exam 20% 3. Assignments 60% Six assignments weigh 10% each

 課程進度
 週次 日期 單元主題 第1週 9/15 Preliminaries 第2週 9/22 Propositional calculus part. I 第3週 9/29 Propositional calculus part. II 第4週 10/06 Proof system in propositional calculus 第5週 10/13 First-order logic part. I 第6週 10/20 First-order logic part. III 第7週 10/27 Proof system in first-order logic 第8週 11/03 Midterm exam 第9週 11/10 Gödel's completeness theorem 第10週 11/17 Compactness and Löwenheim-Skolem theorem 第11週 11/24 Elementary classes and categorical sets 第12週 12/01 Peano system and number theory 第13週 12/08 Gödel's incompleteness theorem part. I 第14週 12/15 Gödel's incompleteness theorem part. II 第15週 12/22 Logic, set theory and mathematics 第16週 12/29 First-order logic in computer science 第17週 1/05 Final exam