MATHS 254 : Fundamental Concepts of Mathematics


2022 Semester Two (1225) (15 POINTS)

Course Prescription

Fundamentals of mathematics important to many branches of the subject and its applications. Topics include equivalence relations, elementary number theory, counting techniques, elementary probability, geometry, symmetry and metric spaces. This is an essential course for all students advancing beyond Stage II in pure mathematics, and highly suitable for other students in the mathematical sciences.

Course Overview

This course is designed  to provide students with some of the fundamentals of mathematics not covered in the core courses MATHS 120, 130 and 250. This is an essential course for all students advancing to Stage 3 or graduate level in pure mathematics.

The focus is on understanding how to develop mathematics with rigour, while appreciating its beauty and potential for applications throughout the mathematical sciences.  The course aims to promote deep understanding of concepts and approaches, rather than to simply present mathematical techniques.

This is an essential course for all students advancing beyond Stage 2 in pure mathematics, and highly suitable for other students in the mathematical sciences.

Course Requirements

Corequisite: MATHS 250 Restriction: MATHS 255

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. Display a high level of knowledge of mathematical concepts (Capability 1, 2, 3, 4 and 5)
  2. Demonstrate understanding of potential applications and connections with other disciplines (Capability 1 and 4)
  3. Demonstrate understanding of a range of methods used in pure mathematics (Capability 1, 2, 3 and 4)
  4. Demonstrate understanding of the nature of precision and proof in mathematics, and the ability to present valid arguments in verbal and written form (Capability 1, 2, 3 and 4)
  5. Engage in critical interactions (Capability 1, 2 and 4)


Assessment Type Percentage Classification
Tutorials 10% Individual Coursework
Assignments 20% Individual Coursework
Mid-semester Test 25% Individual Test
Final Exam 45% Individual Examination
Assessment Type Learning Outcome Addressed
1 2 3 4 5
Mid-semester Test
Final Exam

Key Topics

(a) Relations and orderings (4 lectures)

(b) Modular arithmetic (4 lectures)

(c) Metric spaces (10 lectures)

(d) Geometry and symmetry (11 lectures)

(e) Counting and probability (7 lectures)

Special Requirements

This course has no 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 [36] hours of lectures, a [11] hour tutorial, [36] hours of reading and thinking about the content and [67] hours of work on assignments and/or test preparation.

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.
Attendance on campus is [required] for the [test/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.

There will be no fixed textbook or course book.  Detailed course notes will be provided, and these will include motivation, definitions, examples, properties and applications of the key concepts developed in the course, as well as some exercises, and references for background reading and further directions in which the topics lead.

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.

Other Information

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.

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 09/11/2021 11:09 a.m.