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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 computationhave insight into the way humans reasonhave developed skills in informal and formal reasoningunderstand the link between mathematical proof and computational demonstrationunderstand some fundamental ideas concerning proof, proof checking, and proof searchbe able to apply basic automata theory to design machines for specific tasksbe convinced that computers, despite their amazing computing power, have fundamentallimitations
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).
PHIL210
Maarten McKubre-Jordens
In order to pass this course you must both pass the course as a whole (≥50%) and obtain a mark of at least 40% is required in the final examination.
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Domestic fee $699.00
International fee $3,450.00
* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.
For further information see Mathematics and Statistics .