# MATHS 162 : Computational Mathematics

## Science

### Course Prescription

An introduction to computational mathematics and programming in MATLAB. The course will introduce some basic concepts in computational mathematics and give applications that include cryptography, difference equations, stochastic modelling, graph theory and Markov chains.

### Course Overview

This course is an introduction to essential tools in computational mathematics, particularly mathematical modelling and scientific computation. Students learn how to formulate mathematical models of a variety of real-world problems, and how to solve them using analytical and numerical methods. The software package MATLAB is taught and used extensively. After successfully completing MATHS 162 and other core mathematics courses, students will be well-prepared for further courses in mathematics, such as MATHS 260 and MATHS 270. MATHS 162 is a requirement for a major in mathematics. Those not wishing to continue studying mathematics will find that the modelling and computational foundations laid in this course will support their work in other areas of science.

### Course Requirements

Corequisite: ENGGEN 150 or ENGSCI 111 or MATHS 108 or 120 Restriction: MATHS 199

### Capabilities Developed in this Course

 Capability 3: Knowledge and Practice Capability 4: Critical Thinking Capability 5: Solution Seeking Capability 6: Communication
Graduate Profile: Bachelor of Science

### Learning Outcomes

By the end of this course, students will be able to:
1. Think algorithmically about computational mathematics. (Capability 3, 4 and 5)
2. Perform and analyze various tasks in the field of mathematical modelling. (Capability 3, 4 and 5)
3. Make mathematical models using an appropriate form of equation. (Capability 3, 4 and 5)
4. Validate and defend the ideas and axioms underpinning the mathematics. (Capability 3, 4, 5 and 6)
5. Recognize when different types of mathematical models (e.g., difference equations, stochastic equations, graphs) are appropriate. (Capability 3, 4, 5 and 6)
6. Write and understand simple MATLAB programs. (Capability 3)

### Assessments

Assessment Type Percentage Classification
Assignments 20% Individual Coursework
Final Exam 50% Individual Examination
Mid-Semester Test 20% Individual Test
Tutorials 10% Group & Individual Coursework
Assessment Type Learning Outcome Addressed
1 2 3 4 5 6
Assignments
Final Exam
Mid-Semester Test
Tutorials

### Tuākana

Tuākana Science is a multi-faceted programme for Māori and Pacific students providing topic specific tutorials, one-on-one sessions, test and exam preparation and more. Explore your options at
https://www.auckland.ac.nz/en/science/study-with-us/pacific-in-our-faculty.html
https://www.auckland.ac.nz/en/science/study-with-us/maori-in-our-faculty.html

Whanaungatanga and manaakitanga are fundamental principles of our Tuākana Mathematics programme which provides support for Māori and Pasifika students who are taking mathematics courses. The Tuākana Maths programme consists of workshops and drop-in times, and provides a space where Māori and Pasifika students are able to work alongside our Tuākana tutors and other Māori and Pasifika students who are studying mathematics.

### Key Topics

Programming
1. If statements, for loops and while loops.
2. Reading and debugging code.
3. Creating and using functions.
Difference equations
1. Building models as difference equations.
2. Fixed points.
3. Stability.
4. Bifurcations.
5. Chaos.
Cryptography
1. Creating ciphers and de-ciphers in Matlab.
2. Modular arithmetic.
3. Cribbing and frequency analysis.
Stochastic methods and stochastic modelling
1. Randomness, probability and simulation
2. Random variables.
3. Estimating probabilities.
4. Monte Carlo integration.
Networks and graphs
1. Walks and circuits.
2. The travelling salesman problem.
3. Colourings.

### Special Requirements

You will either need a home computer to run MATLAB on, or you will need to be regularly on campus to make use of the University of Auckland's computer labs to work on any assignment tasks that use MATLAB.  You can find details about our computer labs here: https://www.library.auckland.ac.nz/services/it-essentials/computer-facilities

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 each week of 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 expected at scheduled activities, including labs, to receive credit for components of the course.
• Lectures will be available as recordings. Labs, however, will not be available as recordings.
• The activities for the course are scheduled as a standard weekly timetabled class.

### 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.

COURSEBOOK: MATHS 162 has its own coursebook, covering all of the material covered in this class. You can download this coursebook for free from the MATHS 162 Canvas page.

MATLAB: MATHS 162 is also a course that will teach you how to code in MATLAB, a numerical computing environment and programming language. You can download MATLAB for home use by following the instructions here: https://www.software.auckland.ac.nz/en/matlab.html

MATLAB GRADER: MATHS 162 also uses Matlab Grader for some questions in Tutorials/Assignments. This online tool allows students to practise their programming. Please make an account at https://grader.mathworks.com/

### 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.

Based on student feedback from past cohorts, the order of chapters in MATHS 162 has been slightly modified to allow for the introduction of programming concepts over multiple weeks. The coursebook will also be modified to reflect this rearrangement.

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 for potential plagiarism or other forms of academic misconduct, 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 .

### 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 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 31/10/2023 10:52 a.m.