MATHS 315 : Mathematical Logic


2022 Semester Two (1225) (15 POINTS)

Course Prescription

Logic addresses the foundations of mathematical reasoning. It models the process of mathematical proof by providing a setting and the rules of deduction. Builds a basic understanding of first order predicate logic, introduces model theory and demonstrates how models of a first order system relate to mathematical structures. The course is recommended for anyone studying high level computer science or mathematical logic.

Course Overview

The course content is split into two halves. In the first half, we develop sentential logic (also known as statement logic or propositional logic). We develop this from both semantic and syntactic perspectives, that is, from a study of implication, and from a formal study of proofs. We will also consider the relationship between these notions. In the second half, we develop a richer logical system called predicate (or first order) logic, which allows us to formalise many ideas from mathematics; in particular, this is the system in which set theory is typically developed, and in which axioms for many mathematical systems are expressed. In this course, predicate logic is studied from both the syntactic and semantic perspectives, paralleling the ideas developed for sentential logic in the first half of the course.

The course is designed to provide an understanding of many of the mathematical concepts and methods involved in mathematical logic and computer science.

This course could be of interest to students majoring in mathematics and/or computer science. The skills gained in this course may be of particular use to any students interested in formal systems, or in further study of the foundations of mathematics.

Course Requirements

Prerequisite: B+ or higher in COMPSCI 225 or MATHS 254 or 255 or PHIL 222

Capabilities Developed in this Course

Capability 1: Disciplinary Knowledge and Practice
Capability 2: Critical Thinking
Capability 3: Solution Seeking
Capability 4: Communication and Engagement
Capability 5: Independence and Integrity
Graduate Profile: Bachelor of Science

Learning Outcomes

By the end of this course, students will be able to:
  1. Be able to formalise arguments in sentential logic and predicate logic (Capability 1, 2, 3 and 5)
  2. Be able to use semantic methods in sentential and predicate logic (Capability 1, 2, 3 and 5)
  3. Be able to prove that formal systems have certain properties (Capability 1, 2, 3 and 5)
  4. Be able to find and work with derivations in formal systems (Capability 1, 2, 3 and 5)
  5. Demonstrate and apply soundness and adequacy of certain formal systems (Capability 1, 2, 3 and 5)
  6. Identify and describe applications of predicate logic (Capability 1, 2 and 5)
  7. Identify and describe which notions can and cannot be expressed in first-order arithmetic (Capability 1, 2 and 5)
  8. Use appropriate language, terminology and symbolic means to communicate proofs both informally and within formal systems (Capability 1 and 4)


Assessment Type Percentage Classification
Assignments 25% Individual Coursework
Test 20% Individual Coursework
Tutorials 5% Individual Coursework
Final Exam 50% Individual Coursework
Assessment Type Learning Outcome Addressed
1 2 3 4 5 6 7 8
Final Exam

Key Topics

Predicate and first order logic, both studied from syntactic and semantic points of view.
Additional topics applying knowledge from first order logic (if time permits)

Special Requirements


Workload Expectations

This course is a standard 15 point course and students are expected to spend 10 hours per week involved in each 15 point course that they are enrolled in.

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

Delivery Mode

Campus Experience

Attendance is required at tutorials to receive credit for components of the course.
Lectures will be available as recordings. Other learning activities including tutorials will not be available as recordings.
The course will not include live online events.
Attendance on campus is required for the test and exam.
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.

MATHS 315 course book

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.

Academic Integrity

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.

Class Representatives

Class representatives are students tasked with representing student issues to departments, faculties, and the wider university. If you have a complaint about this course, please contact your class rep who will know how to raise it in the right channels. See your departmental noticeboard for contact details for your class reps.


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


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 02/11/2021 09:26 p.m.