# MATHS 363 : Advanced Modelling and Computation

## Science

### Course Prescription

In real-world situations, the interesting and important variables are often not directly observable. To address this problem, mathematical models and quantities that are observable are usually employed to carry out inference on the variables of interest. This course is an introduction to fitting of models to (noisy) observational data and how to compute estimates for the interesting variables. Numerical methods for partial differential equations, which are commonly used as models for the observations, will also be covered.

### Course Overview

This course considers some of the most common topics that applied mathematicians encounter in their work: fitting of models to observational (noisy) data, interpreting all computed solutions as (multivariate) random variables, numerical methods for partial differential equations, and the related modelling problems. The software package MATLAB is used for computation. The 21st Century has seen an explosion in data generation, so data driven modelling is now one of the most important skills in applied mathematics. This course teaches the essential skills in this field, and leads to further study at postgraduate level. The course can contribute to a major in mathematics and a pathway in applied mathematics.

### Course Requirements

Prerequisite: MATHS 260 and 270

### 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

### Learning Outcomes

By the end of this course, students will be able to:
1. Apply the basic theory of multivariate random variables to calculate conditional mean and covariance. (Capability 1, 2, 3, 4 and 5)
2. Apply least squares estimation, e.g. fitting polynomials to data, and compute related error estimates. (Capability 1, 2, 3, 4 and 5)
3. Apply line search methods to nonlinear least squares problems. (Capability 1, 2, 3, 4 and 5)
4. Apply maximum likelihood estimates and conditional mean estimates. (Capability 1, 2, 3, 4 and 5)
5. Apply the variational method to boundary value problems for ordinary differential equations. (Capability 1, 2, 3, 4 and 5)
6. Apply and program the finite element method in one spatial dimension. (Capability 1, 2, 3, 4 and 5)

### Assessments

Assessment Type Percentage Classification
Three assignments 40% Individual Coursework
Final Exam 60% Individual Coursework
1 2 3 4 5 6
Three assignments
Final Exam

### Tuākana

Whanaungatanga and manaakitangi are fundamental principles of our Tuakana Mathematics programme which provides support for Maori and Pasifika students who are taking mathematics courses. The Tuakana Maths 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 Pasifika students who are studying mathematics.

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

### Key Topics

Introduction to parameter estimation: Multivariate statistics, Linear least squares , Nonlinear least squares, Estimation theory.

Numerical methods for partial differential equations and initial-boundary value problems: Variational formulation of partial differential equations, Finite element method in one spatial dimension, Semidiscrete approach for diffusion-type problems

### Special Requirements

There is no compulsory attendance and no must-pass assessments. The use of calculators in the exam is not permitted.

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 3 hours of lectures, no tutorial, 4 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/tutorials to complete components of the course.
Lectures will be available as recordings. Other learning activities including tutorials/labs will not be available as recordings.
The course will not include live online events including tutorials.
Attendance on campus is required for the test and exam.
The activities for the course are scheduled as a standard weekly timetable delivery.

### Learning Resources

All lecture notes and supporting reading material, as well as some Matlab codes, will be available on 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.

### 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 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.

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 your assessment is fair, and not compromised. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator, and if disruption occurs you should refer to the University Website for information about how to proceed.

Level 1: Delivered normally as specified in delivery mode
Level 2: You will not be required to attend in person. All teaching and assessment will have a remote option. The following activities will also have an on campus / in person option: Lectures, labs, tutorials, office hours.
Level 3 / 4: All teaching activities and assessments are delivered remotely .

### 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 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 26/01/2021 09:34 a.m.