MATH230-15S2 (C) Semester Two 2015

Logic, Automata, and Computability

15 points

Details:
Start Date: Monday, 13 July 2015
End Date: Sunday, 15 November 2015
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Friday, 24 July 2015
  • Without academic penalty (including no fee refund): Friday, 9 October 2015

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
  • have developed skills in informal and formal reasoning
  • understand the link between mathematical proof and computational demonstration
  • understand some fundamental ideas concerning proof, proof checking, and proof search
  • be able to apply basic automata theory to design machines for specific tasks
  • be convinced that computers, despite their amazing computing power, have fundamental
    limitations

Prerequisites

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

Maarten McKubre-Jordens

Lecturer

Maarten McKubre-Jordens

Assessment

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


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.

Indicative Fees

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 .

All MATH230 Occurrences

  • MATH230-15S2 (C) Semester Two 2015
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