Theoretical Computer Science - Bridging Course
Graduate Course - Summer Term 2020
Fabian Kuhn
Course description
The aim of the course is to provide basic knowledge of theoretical computer science to computer science M.Sc. students who do not yet have this necessary background (e.g., because of a different major during their undergraduate studies). The course introduces the (mathematical) foundations of theoretical computer science. We will see what can be computed and how efficiently, as well as what cannot. More specifically, the following topics will be included:
- Automata
- Formal languages
- Formal grammars
- Turing machines
- Decidability
- Complexity theory
- Logic
Course Format
The course is based on existing recordings provided by Diego Tipaldi combined with weekly interactive online exercise lessons. This will prepare the participants for the final exam.
Exam
- Type of exam: The exam will be oral.
- Date: 8th September.
- Time: Each Student will be assigned a time slot. We will contact you with the exact time you should appear.
- Duration: 30 Minutes.
- Place: Probably some seminar room in building 106. We will clarify that soon.
- Measures due to Corona: We might offer to do the exam online via a online conference system (we will clarify that later). If the exam takes place physically, we will have a large, well ventilated room and distancing measures. Also you should bring a mask when entering the building and the seminar room (you can remove it during the exam).
Schedule
There are no weekly lectures just weekly online exercise lessons. The exercise lessons will take place online every Tuesday at 12:15 - 14:00 via the conference system Zoom. The link on how to access the zoom meetings is available on the lecture online access information page, which is only visible from within the university network (i.e., use VPN to access the page from home).
Slides and Recordings
The course is based on existing recordings provided by Diego Tipaldi
| Topic | Slides | Recordings |
| Mathematical Preliminaries | MP4 (44:30) | |
| DFA, NFA, Regular Languages | MP4 (1:14:04) | |
| Regular Languages and closure wrt elementary operations | ||
| Regular expressions | MP4 (1:37:55) | |
| Non-regular languages | MP4 (22:12) | |
| Context Free Grammars I | MP4 (1:34:09) | |
| Context Free Grammars II | MP4 (42:00) | |
| Pushdown Automata | MP4 (1:11:18) | |
| Pumping Lemma for Context Free Grammars | MP4 (1:29:51) | |
| Turing Machines I | MP4 (52:31) | |
| Turing Machines II | MP4 (1:23:03) | |
| Decidability and decidable languages. | MP4 (52:54) | |
| Decidability, mathematical backgrounds on cardinality, Cantor's diagonal argument | MP4 (1:15:40) | |
| Decidability and the halting problems. | MP4 (12:50) | |
| Complexity I | MP4 (1:28:51) | |
| Complexity II | MP4 (1:34:27) | |
| Complexity III | MP4 (1:28:08) | |
| Propositional Logic and basic definitions, CNF/DNF, logical entailment. | MP4 (37:11) | |
| Propositional Logic. Deduction/Contraposition/Contradiction Theorems and Derivations. | MP4 (1:00:14) | |
| Propositional Logic. Derivations, Soundness and Completeness of calculi. | MP4 (53:16) | |
| Propositional Logic. Refutation-completeness and Resolution. | MP4 (04:16) | |
| First Order Logic. Derivations. | MP4 (46:47) | |
| First Order Logic. Satisfaction, closed formulae and brief overview on Normal Forms. | MP4 (1:39:04) |