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Logic and Foundations

MATH3065

This unit is in two halves. The first half provides a working knowledge of the propositional and predicate calculi, discussing techniques of proof, consistency, models and completeness. The second half discusses notions of computability by means of Turing machines (simple abstract computers). (No knowledge of computer programming is assumed.) It is shown that there are some mathematical tasks (such as the halting problem) that cannot be carried out by any Turing machine. This leads to the famous negative answer by Church and Turing to Hilbert's question whether first-order logic is decidable (the Entscheidungsproblem). Set theory, notions of cardinality and variations of Russell's paradox and Cantor diagonalisation permeate the course, culminating in Gˆdel's Incompleteness Theorem.

Unit of study details

Unit of study level: Senior

Credit points: 6

Commencing semesters: 1

Further unit of study information

Unit of study handbook: MATH3065

Costs and scholarships information: Costs and Scholarships

Final dates to withdraw from units of study: Census Dates

Available for study abroad and exchange: Yes

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