# MATHS 199 : Advancing in Mathematics

## Science

### 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:

• Infinity. This four-week module is centered around the mathematical concept of infinity, and will serve as our `introductory' module in this course.  In these four weeks, we'll study the idea of infinite sums and series, examine how primes and infinity are related, investigate the idea of a ``size'' of infinity, and also study a bit of cryptography!
• Modelling. This four-week module will cover a number of different mathematical modelling techniques and ideas.  Amongst them will be difference equations, differential equations, stochastic modelling, and also how to use iterated function systems to create 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

### 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)

### Assessments

Assessment Type Percentage Classification
Projects/Assignments 30% Individual Coursework
Test 20% Individual Test
Final Exam 50% Individual Examination
1 2 3 4
Projects/Assignments
Test
Final Exam

Students will need to have a minimum mark of 35% in the final exam to pass this course.

### Learning Resources

A course book containing lecture notes for the course is available as a PDF download from Canvas. A paper copy of this coursebook can also be purchased from the University Book Store for the cost of printing (approximately \$20.)

### 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:

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.

### 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.

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.

### 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 http://disability.auckland.ac.nz

### 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: https://www.auckland.ac.nz/en/students/academic-information/exams-and-final-results/during-exams/aegrotat-and-compassionate-consideration.html.

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 (https://www.auckland.ac.nz/en/students/forms-policies-and-guidelines/student-policies-and-guidelines/student-charter.html).

### 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 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 11/01/2020 03:10 p.m.