Mathematical Foundations of Computer Science
 Prerequisites: Basic Mathematics for COMPSCI350
 Lecturers:
 Professor Cristian S. Calude,
room 303427, Science Building, course coordinator.
 Professor Fred Kroon,
room 443 Arts 1.

Tutor:
Yan Kolezhitskiy. Office hours:
By appointment. Any problem
related to marking should be addressed to the tutor.

Class representative:
Daniel Robinson.
 Taught: First semester 2017, three hours of lectures and two tutorials a week
(see 2017 Academic Dates).

Timetable: Lectures: Monday, Tuesday, Wednesday 8.00am9.00am, PLT2/3003G02. Tutorials: Wednesday 10.0011.00am and Thursday 9.0010.00am, starting the second
week. Check updates at UoA Timetables 2017.
 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 halting problem). Quantum computing will also be briefly described and the ChurchTuring 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 properly.
 Content:
 Automata and regular languages
 Computability and decidability
 Algorithmic complexity
 ChurchTuring Thesis
 Quantum computing
 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
 understand the basic principles of quantum computing
 Textbook:
M. Sipser.
Introduction to the Theory of
Computation,
PWS Publishing Company, Boston, 2013, third edition.
 Software: Register machine simulation
 Assessment: Tutorial work: 5%. Three assignments: 15%, Test: 30%, Exam: 50%.
 Assignments (sumitted via Canvas):
Assignment 1:
due Friday 7 April 2017, before 8.00pm, submitted via Canvas,
worth 5%;
assignment 2:
due Friday 19 May 2017, before 8.00pm, submitted via Canvas,
worth 5%; assignment 2:
due Friday 9 June 2017, before 8.00pm, submitted via Canvas,
worth 5%.

Test:
Wednesday 12/04/2017, in class, time: 8:00am9:00am Rooms: PLT2/3003G02 and 302G20.
Test preparation.
 Canvas: COMPSCI350.
 Handouts: Part 1,
Part 3.
 Regulations:
 Other relevant sites: