Mathematical Foundations of Computer Science
- Professor Cristian S. Calude,
room 303S-571, Science Building, course coordinator.
- Professor Bakhadyr Khoussainov,
room 303-581, Science Building.
To be announced. Office hours:
By appointment. Any problem
related to marking should be addressed to the tutor.
To be announced.
Course Facebook group.
- Taught: First semester 2015, three hours of lectures and a tutorial a week (see 2016 Academic Dates).
Timetable: Lectures: Monday 13-14, Tuesday 13-14, Thursday 14-15. Tutorial: Thursday 11-12, starting the second
week. Check updates at UoA Timetables 2016.
- Short Description:
The aim of this paper is to present mathematical models for computers and
computation, and derive results about what can and cannot be computed. It
deals with idealised computers (automata) which operate on idealised input
and output (formal languages). For example, we prove that it is impossible
to write a computer program that takes as input any computer program and
tells us whether or not that program will end up in an endless loop (the
Quantum computing will also be briefly described and the Church-Turing Thesis will be critically discussed. In addition we will discuss some problems in algorithmic complexity.
We assume you are comfortable with formal mathematical proofs and can write them
- Automata and regular languages
- Context-free languages
- Computability and decidability
- Algorithmic complexity
- Church-Turing Thesis
- Expected learning outcomes: On completion, students will be able to
- explain the theoretical limits on computational solutions of undecidable and inherently complex problems
- describe concrete examples of computationally undecidable or inherently infeasible problems from different fields
- understand formal definitions of machine models, classical and quantum
- prove the undecidability or complexity of a variety of problems
- understand the issue of whether there are limits of computability
Introduction to the Theory of
PWS Publishing Company, Boston, 2013, third edition.
- Software: Register machine simulation
- Tutorials: Materials will be available on the Tutorial page.
- Assessment: Two assignments worth 20% in total, Test: 30%, Exam: 50%.
- Assignments (the assignment dropbox will be outside the room 303S-571): Assignment 1:
due Wednesday, 23 March, before 4.00pm,
due Thursday 2 June, before 4.00pm,
To be announced.
- Policy on
- Other relevant sites: