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An introduction to various formal logics, the theory of automata, and the theoretical limitations of the computer.
This course takes a tour through some of the rigorous mathematical foundations of modern computer science and logic. Do not let the word "rigorous" scare you off - any student who possesses basic number skills, a healthy desire to grapple with abstract concepts, and perserverance may do well. Topics covered: The first half of the course will take a close look at the concept of logical deduction. Lectures will be drawn from the following topics: natural deduction, soundness and completeness of formal systems, interpretations, Gentzen's sequent calculus, equivalence of logical systems, and links between proof and computation. Lectures for the second half of the course outline formal models of computation and establish the link of these models with formal logic. We will cover topics from the following list: formal languages, finite-state automata, push-down automata, computability, Turing machines, Markov algorithms, effective enumerations, the Church-Markov-Turing thesis, the Halting Problem.
By the end of the course, students should: have developed an appreciation for the mathematical foundations of computation have insight into the way humans reason understand some fundamental ideas concerning proof be convinced that computers, despite their amazing computing power, have fundamental limitations
This course will provide students with an opportunity to develop the Graduate Attributes specified below:
Critically competent in a core academic discipline of their award
Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.
15 points from MATH102-199, and a further 15 points from 100 level COSC, EMTH, MATH, PHIL or STAT courses, excluding COSC110 and MATH101.
MATH208, MATH308, PHIL208 (prior to 2014), PHIL210, PHIL308 (prior to 2014).
Students must attend one activity from each section.
The lecture notes are largely self-contained. For a wider reading, the following are good resources.For the course as a whole:• Loveland, Hodel, and Sterrett’s Three Views of Logic (Princeton)For the logic half:• Prawitz’s Natural Deduction (Dover),• Lemmon’s Beginning Logic• Jeffrey’s Formal Logic: its scope and limits (Hackett)For the automata half:• Linz’s Introduction to Formal Languages and Automata (Jones & Bartlett)• Hopcroft, Motwani, and Ullman’s Introduction to Automata Theory, Languages, and Computation (Addison-Wesley)
General information for students
Domestic fee $749.00
International fee $3,788.00
* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.
For further information see
Mathematics and Statistics.