MATHS 199 : Advancing in Mathematics


2022 Semester One (1223) (15 POINTS)

Course Prescription

An introduction to University level mathematics, for high-achieving students currently at high school. The numerical computing environment MATLAB is used to study beautiful mathematics from algebra, analysis, applied mathematics and combinatorics. Students will learn to write mathematical proofs and create mathematical models to find solutions to real-world problems.

Course Overview

MAX (Maths 199) is a course designed to survey beautiful and interesting results from the fields of algebra, analysis, combinatorics, and applied mathematics. In this paper, we will study mathematics on both a practical and an abstract level; students leaving this course will know how to write rigorous mathematical proofs, and also be capable of modelling concrete solutions to problems using MATLAB (a mathematical programming language.) 

MAX is also a lot of fun! Mathematically keen students who want to see what rigorous University-level mathematics is like are strongly encouraged to take this course.  

On a week-by-week basis, we intend to cover the following:

  • Cryptography. This four-week module is centered around the art of cryptography (both as a mathematical field and as an introduction to MATLAB), and will serve as our `introductory' module in this course. 
  • Modelling. This four-week module will cover a number of different mathematical modelling techniques and ideas, covering difference equations, differential equations, stochastic modelling, and fractals!
  • Graph theory. This four-week module will cover a number of aspects of graph theory.  Students will be introduced to the basic language of graphs, study the four-color theorem, examine how to model real-life phenomena with graphs, and finally end the course by examining infinite graphs!

Course Requirements

Prerequisite: Departmental approval

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
Capability 6: Social and Environmental Responsibilities
Graduate Profile: Bachelor of Science

Learning Outcomes

By the end of this course, students will be able to:
  1. Explore a sampling of mathematical ideas from algebra, analysis, applied mathematics (in particular, modelling), and graph theory. Students leaving this course should have an idea for what each of the major branches of mathematics is like, and be excited to study further mathematics in their career. (Capability 1, 2 and 3)
  2. Be able to communicate mathematically to their peers about the concepts studied in this course. This communication should span written work (e.g. able to write down a rigorous argument that explains why a solution is correct), code (e.g. able to write commented and coherent code), and oral communication (e.g. able to work in a group with students from different backgrounds/schools to solve problems.) (Capability 2, 3, 4, 5 and 6)
  3. Be able to solve problems in both a pen-and-paper and a computer-aided setting. When working with code, students should be able to write pseudocode to solve problems, translate that pseudocode into an actual language (e.g. MATLAB), and debug that code as needed. When working on paper, students should be able to creatively combine ideas from class and come up with novel approaches to solve problems. (Capability 1, 2, 3 and 4)
  4. Create and justify appropriate mathematical models for various phenomena. (Capability 1, 2 and 3)


Assessment Type Percentage Classification
Projects/Assignments 30% Individual Coursework
Online Mid-Semester Test 20% Individual Test
Final Exam 50% Individual Examination
Assessment Type Learning Outcome Addressed
1 2 3 4
Online Mid-Semester Test
Final Exam

Special Requirements

This course is only available to students currently enrolled in high school.  To see precise requirements, visit the Department of Mathematics' MAX webpage:

Workload Expectations

MATHS 199 is a standard 15 point University course; this means that students are expected to spend 150 hours over the entire semester (i.e. about 10 hours per week) on this paper. Given that we have approximately 40 hours of lecture and laboratory sessions during the semester, this leaves you with about 110 more hours (i.e. about 7-8 per week) that we're expecting you to work on this paper outside of class. While this will vary from student to student, I'd expect most students to spend 2-3 hours per week revising the material from class/labs, and 4-5 hours per week working on the assessments/final project.

Please stay on top of the course material as it is covered. If you get behind, it can be difficult to catch up. Make use of the help available; ask for help as soon as you need it.

Delivery Mode

Campus Experience or Online

This course is offered in two delivery modes: on-campus and online.


If you are a student in Auckland, we hope that you will be able to attend our lectures+labs in person.  These run once-weekly on Wednesdays from 4:30-7:30pm, and are where you'll see the week's material, get started on the weekly labs, and also make friends to work on assignments/projects/etc with!  If you do have to miss a lecture or two, however, don't worry: we post recordings/class materials shortly after each talk finishes.

Attendance is not required on campus for the test (as it is online), but is required for the exam if you are in Auckland.


Students can enroll in MAX from anywhere in New Zealand.  If you enroll in MAX and are not able to attend lectures due to geographical or other barriers, you can still participate fully in our course!   We will livestream all of our lectures, so that you can watch live and ask questions to your peers; we also record lectures for viewing after the fact, and post these (along with lecture notes and other resources) shortly after each weekly lecture.  We will also have dedicated tutor/lecturer time set aside for you specifically to help you get started on the weekly labs.

Attendance is not required on campus for the test (as it's online) nor for the exam if you are outside of Auckland (we will liaise with your high school to set up a sitting of your exam.)

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.

A course book containing lecture notes for the course is available as a PDF download from Canvas.

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.

With the above (University-standard boilerplate) said, collaboration is allowed (and indeed encouraged) on the homework sets!   Mathematics at the research level is a collaborative activity, and there is no reason that it should not also be this way in a classroom. 
The only things that we ask of you are the following:
  • You must write up your work separately, write up solutions in your own words, and only write up solutions you understand fully.   
  • When writing up your own work, you can directly cite and use without proof anything proven in class or in the class notes posted online. Anything else --- i.e. results from textbooks, Wikipedia, etc. --- you need to both cite in your writeup, and reprove the results you're using from those sources carefully in your own words.  Simply copying solutions over directly is plagiarism / cheating / otherwise poor academic form; it is passing off the ideas of others as your own work (which is bad!) 

    With that said: you are certainly welcome (indeed, encouraged) to read and learn what other people have thought about the concepts that we're covering in this class! All I am asking you to do here is to not claim the ideas of others as your own work, and to rephrase and present any such ideas you encounter in a new way so that it is clear that you have actually learned something. 
If you have any questions on the collaboration policy, please email me and I'll be glad to clarify matters.

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 10:57 a.m.