Fall 2020 - CMPT 409 D100
Special Topics in Theoretical Computing Science (3)
Class Number: 6641
Delivery Method: In Person
Current topics in theoretical computing science depending on faculty and student interest.
Cross-listed with CMPT 701 This course is on theoretical foundations of Computer Science. It provides insights into the nature and limitations of computation and logical reasoning. The first part deals with fundamental theoretical results in logic. It includes first-order logic (syntax and semantics), the completeness theorem for first-order logic, undecidability of first-order logic, Peano Arithmetic, compactness, and Lowenheim-Skolem theorems. The second part focuses on the strength and limitations of computations. It starts with Register machines as a model of computation and proceeds to the theory of primitive recursive, and then recursive, functions and relations. We study the existence of algorithms for solving decision problems. In particular, we learn about the halting problem, for which we prove that no algorithm can solve it. We show that non-computability of many problems follows from a single result, Rice's theorem. We consider Universal functions and Decidability theorem. The course culminates with several result illustrating incompleteness phenomena in mathematics and theory of computation including Tarski's theorem and Godel's Incompleteness Theorems. There is no required textbook. A list of recommended references will be provided. As the main reference, we will use the lecture notes of Stephen A. Cook which will be posted on the course website.
- Syntax and semantics of propositional and predicate calculus
- Completeness of Gentzen proof systems
- Formal theories, nonstandard models
- Recursive and primitive recursive functions, Computability
- Church-Turing thesis
- Computationally unsolvable problems
- Recursively enumerable sets
- Godel Incompleteness Theorems
- To be announced in the first week of classes.
MATERIALS + SUPPLIES:
- A Mathematical Introduction to Logic, 2nd Edition., Herbert B. Enderton, Elsevier Science, 2001, 9780122384523
- Introduction to the Theory of Computation, Michael Sipser, Cengage, 2012, 9781133187790
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TEACHING AT SFU IN FALL 2020
Teaching at SFU in fall 2020 will be conducted primarily through remote methods. There will be in-person course components in a few exceptional cases where this is fundamental to the educational goals of the course. Such course components will be clearly identified at registration, as will course components that will be “live” (synchronous) vs. at your own pace (asynchronous). Enrollment acknowledges that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes. To ensure you can access all course materials, we recommend you have access to a computer with a microphone and camera, and the internet. In some cases your instructor may use Zoom or other means requiring a camera and microphone to invigilate exams. If proctoring software will be used, this will be confirmed in the first week of class.Students with hidden or visible disabilities who believe they may need class or exam accommodations, including in the current context of remote learning, are encouraged to register with the SFU Centre for Accessible Learning (email@example.com or 778-782-3112).