# COMPSCI 350 : Mathematical Foundations of Computer Science

## Science

### Course Prescription

The aim of this course is to present mathematical models for programming languages and computation, and derive some theorems regarding what can and cannot be computed. Abstract programming languages (finite automata, context-free grammars, Turing and register machines) are studied. Basic concepts for programming languages, limits on computational power and algorithmic complexity are presented. Church-Turing thesis and quantum computing are briefly and critically discussed.

### Course Overview

The aim of this course is to present mathematical models for computers and computation, classical and quantum, and to prove results about what can and cannot be computed. It deals with idealised computers which operate on idealised input and output. For example, one proves that it is impossible to write a computer program that takes as input any computer program and tells whether or not that program will finish running or continue forever (the halting problem).

Various methods to evaluate algorithmic complexity and prove undecidability, as well as efficient strategies, classical and quantum, for problem solving will be presented. The Church‐Turing Thesis and  quantum computing  are briefly and critically discussed.

This course requires that students have a good knowledge of mathematical proofs and can write them properly.

### Course Requirements

Prerequisite: COMPSCI 220 or PHIL 222, and 15 points from COMPSCI 225, MATHS 254, 255

### Capabilities Developed in this Course

 Capability 1: Disciplinary Knowledge and Practice Capability 2: Critical Thinking Capability 3: Solution Seeking Capability 5: Independence and Integrity

### Learning Outcomes

By the end of this course, students will be able to:
1. Explain the theoretical limits on computational solutions of undecidable and inherently complex problems (Capability 1, 3 and 5)
2. Describe concrete examples of computationally undecidable or inherently infeasible problems from different fields (Capability 1, 2 and 3)
3. Understand formal definitions of machine models, classical and quantum (Capability 1)
4. Prove the undecidability or complexity of a variety of problems (Capability 1, 2 and 3)
5. Understand the issue of whether there are limits of computability (Capability 1, 2 and 3)
6. Understand the basic principles of quantum computing (Capability 1 and 3)
7. Articulate and demonstrate constructions of different automata and Turing machines (Capability 1 and 3)

### Assessments

Assessment Type Percentage Classification
Assignments 15% Individual Coursework
Practical 5% Individual Coursework
Test 30% Individual Coursework
Final Exam 50% Individual Coursework
1 2 3 4 5 6 7
Assignments
Practical
Test
Final Exam

### Learning Resources

Textbook: M. Sipser. Introduction to the Theory of Computation, PWS Publishing Company, Boston, 2013, third edition.

### Special Requirements

All assignments should be typed. Tutorials are compulsory.

For this course, you can expect 3 hours of lectures, an hour tutorial, 4 hours of reading and thinking about the content and 2 hours of work on assignments/test/exam preparation per week.

### Digital Resources

Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).

Please remember that the recording of any class on a personal device requires the permission of the instructor.

The content and delivery of content in this course are protected by copyright. Material belonging to others may have been used in this course and copied by and solely for the educational purposes of the University under license.

You may copy the course content for the purposes of private study or research, but you may not upload onto any third party site, make a further copy or sell, alter or further reproduce or distribute any part of the course content to another person.

The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. This requirement also applies to sources on the internet. A student's assessed work may be reviewed against online source material using computerised detection mechanisms.

### Inclusive Learning

All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.

Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website at http://disability.auckland.ac.nz

### Special Circumstances

If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.

If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page: https://www.auckland.ac.nz/en/students/academic-information/exams-and-final-results/during-exams/aegrotat-and-compassionate-consideration.html.

This should be done as soon as possible and no later than seven days after the affected test or exam date.

### Student Feedback

During the course Class Representatives in each class can take feedback to the staff responsible for the course and staff-student consultative committees.

At the end of the course students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback.

Your feedback helps to improve the course and its delivery for all students.

### Student Charter and Responsibilities

The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter (https://www.auckland.ac.nz/en/students/forms-policies-and-guidelines/student-policies-and-guidelines/student-charter.html).

### Disclaimer

Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.

In this course you may be asked to submit your coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. The final decision on the completion mode for a test or examination, and remote invigilation arrangements where applicable, will be advised to students at least 10 days prior to the scheduled date of the assessment, or in the case of an examination when the examination timetable is published.

Published on 11/12/2019 09:50 p.m.