MATHS 190G : Great Ideas Shaping our World


2020 Semester One (1203) (15 POINTS)

Course Prescription

Mathematics contains many powerful and beautiful ideas that have shaped the way we understand our world. This course explores some of the grand successes of mathematical thinking. No formal mathematics background is required, just curiosity about topics such as infinity, paradoxes, cryptography, knots and fractals.

Course Overview

Mathematics contains many powerful and beautiful ideas that have shaped the way we understand our world. This course explores some of the grand successes of mathematical thinking. No formal mathematics background is required, just curiosity about topics such as infinity, paradoxes, knots and fractals, and cryptography. This course would be of interest to anyone considering a degree in mathematics, or for those who are curious about the ideas in the world of mathematics.

Course Requirements

No pre-requisites or restrictions

Capabilities Developed in this Course

Capability 1: Disciplinary Knowledge and Practice
Capability 2: Critical Thinking
Capability 3: Solution Seeking
Capability 4: Communication and Engagement
Graduate Profile: University

Learning Outcomes

By the end of this course, students will be able to:
  1. Generalise statements about finite sets to infinite sets (Capability 1, 2 and 3)
  2. Calculate the dimension of a fractal and create a fractal of a given dimension. (Capability 1 and 3)
  3. Determine symmetries of geometric objects. (Capability 1 and 3)
  4. Compare and contrast geometric and topological properties of different objects. (Capability 1, 2 and 4)
  5. Know what it means to prove a statement by contradiction, and give some fascinating mathematical proofs by contradiction. (Capability 1 and 3)
  6. Create complicated dynamical structures from simple rules. (Capability 1)
  7. Discover and develop basic properties of numbers, and put them to use in interesting ways. (Capability 1 and 3)
  8. Apply abstract mathematical ideas to solve real world problems. (Capability 2)
  9. Communicate, written and orally, abstract mathematical concepts. (Capability 4)
  10. Work in teams to solve mathematical problems and discuss mathematical ideas. (Capability 4)


Assessment Type Percentage Classification
Assignments 24% Individual Coursework
Tutorials 5% Group Coursework
Team Tasks 6% Group Coursework
Test 15% Individual Test
Final Exam 50% Individual Examination
Assessment Type Learning Outcome Addressed
1 2 3 4 5 6 7 8 9 10
Team Tasks
Final Exam
Students must achieve at least 35% in the final exam in order to pass the course.
Calculators are not allowed in the mid-semester test or the final exam.


Whanaungatanga and Manaakitanga are fundamental principles of our Tuakana Mathematics Programme which provides support for Maori and Pacific students who are taking mathematics courses.  The Tuakana Programme consists of workshops and drop-in times, and provides a space where you are able to work alongside our Tuakana Tutors and other Maori and Pacific students who are studying mathematics. For information please visit the website (

Key Topics

 Fun and Games: Text Chapter 1 (1 lecture)
 Number Contemplations: Text Chapter 2 (5 lectures)
 In finity: Text Chapter 3 (3 lectures)
 Geometric Gems: Text Chapter 4 (4 lectures)
 Chaos and Fractals: Text Chapter 7 (4 lectures)
 Contortions of Space: Text Chapter 5 (2 lectures)
 Graphs: Text Chapter 6 (2 lectures)

Learning Resources

The textbook for this course is The Heart of Mathematics, 4th Edition, by Edward Burger and Michael Starbird.
The course makes extensive use of the text. It is available in the University Bookshop and also available as an ebook, which you can buy direct from Wiley at the following link:

Special Requirements

Students are expected to attend all lectures and tutorials. The team tasks and tutorials carry marks for participation and the mid-semester will be scheduled during a lecture hour in week 5 or 6 of semester.

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 2 hours of lectures, a one hour tutorial, 5 hours of reading and thinking about the content and 2 hours of work on assignments and/or test preparation.

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.

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.

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

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.

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 (


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 14/02/2020 09:03 p.m.