# 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 COMPSCI 225 or MATHS 254

### Capabilities Developed in this Course

 Capability 3: Knowledge and Practice Capability 4: Critical Thinking Capability 5: Solution Seeking

### 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 3, 4 and 5)
2. Describe concrete examples of computationally undecidable or inherently infeasible problems from different fields (Capability 3, 4 and 5)
3. Understand formal definitions of machine models, classical and quantum (Capability 3 and 4)
4. Prove the undecidability or complexity of a variety of problems (Capability 3, 4 and 5)
5. Understand the issue of whether there are limits of computability (Capability 3 and 4)
6. Understand the basic principles of quantum computing (Capability 3)
7. Articulate and demonstrate constructions of different automata and Turing machines (Capability 3, 4 and 5)

### Assessments

Assessment Type Percentage Classification
Assignments 30% Individual Coursework
Practical 10% Individual Coursework
Tests 60% Individual Coursework
1 2 3 4 5 6 7
Assignments
Practical
Tests

### Tuākana

Tuākana Science is a multi-faceted programme for Māori and Pacific students providing topic specific tutorials, one-on-one sessions, test and exam preparation and more. Explore your options at
https://www.auckland.ac.nz/en/science/study-with-us/pacific-in-our-faculty.html
https://www.auckland.ac.nz/en/science/study-with-us/maori-in-our-faculty.html

### Special Requirements

All assignments should be typed. Tutorials are compulsory. Some assessment will require in-person attendance during lectures.

For this course, you can expect 3 hours of lectures, a 1 hour tutorial, 4 hours of reading and thinking about the content, and 2 hours of work on assignments/test/exam preparation per week.

### Delivery Mode

#### Campus Experience

Attendance is expected at scheduled activities including tutorials to receive credit for components of the course.
Lectures will be available as recordings.

The course will not include live online events.

Attendance on campus is required for tests.
The activities for the course are scheduled as a standard weekly timetable.

### Learning 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.

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

### 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.

An example is that the exam was replaced by tests, which makes student preparation easier.

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 for potential plagiarism or other forms of academic misconduct, using computerised detection mechanisms.

### Class Representatives

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.

### 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

### 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 .

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

### Learning Continuity

In the event of an unexpected disruption, we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and course assessment continues to meet the principles of the University’s assessment policy. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator/director, and if disruption occurs you should refer to the university website for information about how to proceed.

The delivery mode may change depending on COVID restrictions. Any changes will be communicated through Canvas.

### 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 .

### 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 students may be asked to submit 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. In exceptional circumstances changes to elements of this course may be necessary at short notice. Students enrolled in this course will be informed of any such changes and the reasons for them, as soon as possible, through Canvas.

Published on 31/10/2023 10:51 a.m.