MATH230-16S2 (C) Semester Two 2016

Logic, Automata, and Computability

15 points, 0.1250 EFTS
11 Jul 2016 - 13 Nov 2016

Description

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.

Learning Outcomes

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

Pre-requisites

15 points from MATH102-199, and a further 15 points from 100 level COSC, EMTH, MATH, PHIL or STAT courses, excluding COSC110 and MATH101.

Restrictions

MATH208, MATH308, PHIL208 (prior to 2014), PHIL210, PHIL308 (prior to 2014).

Equivalent Courses

Course Coordinator / Lecturer

Hannes Diener

Lecturer

Maarten McKubre-Jordens

Assessment

Assessment Due Date Percentage 
Tutorial participation 10%
Assignments (x2) 40%
Final Examination 50%

Indicative Fees

Domestic fee $720.00

International fee $3,450.00

* 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.

All MATH230 Occurrences

  • MATH230-16S2 (C) Semester Two 2016