This course introduces important algorithms and techniques of scientific computing, focussing on the areas of linear algebra and matrix computations. The course will present both theoretical and practical aspects of the algorithms. The course is highly relevant to students from disciplines such as science, engineering or economics where skills in numerical computations are important.

This is an HPC, taught at a level requiring greater conceptual understanding than MATH3511.

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Use sophisticated scientific computing and visualization environments to solve application problems involving matrix computation algorithms.
2. Analyze numerical algorithms, and understand the relationships between the computational effort and the accuracy of these algorithms.
3. Interpret the results produced by computer implementations of numerical algorithms.
4. Explain the effects of errors in computation and how such errors affect solutions.
5. Demonstrate the necessary analytical background for further studies leading to research in applied mathematics or related disciplines.

Examination Material or equipment

Information about examination material will be made available through the Examinations timetable

Recommended Resources

There is no standard text for the course, extensive notes will be made available on Canvas. The notes are based on Numerical Linear Algebra by Lloyd N. Trefethen and David Bau III (SIAM , 1997).

There are a variety of online platforms you will use to participate in your study program at ANU, across all of your courses. These could include videos for lectures and other instruction, two-way video conferencing for interactive learning, email and other messaging tools for communication, interactive web apps for formative and collaborative activities, print and/or photo/scan for handwritten work and drawings, and home-based assessment.

ANU outlines recommended student system requirements to ensure you are able to participate fully in your learning. Other information is also available about the various Learning Platforms you may use.

Staff Feedback

Students will be given feedback in the following forms in this course:

• Written comments on the assignments.
• Problem discussion in workshop exercises.
• Individual feedback may be given during consultation hours.

Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

Other Information

Use of Artificial Intelligence (AI): unless explicitly allowed in the assessment instructions, assessment tasks for this course should be completed without the assistance of generative AI (for example, without using ChatGPT).

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Weeks 1-2: Singular Value Decomposition, Projectors, QR Factorisation.	Feedback is given through written assignments, programming exercises and workshop questions.
2	Week 3:  Floating Point Arithmetic.	Feedback is given through written assignments, programming exercises and workshop questions.
3	Weeks 4-6: Linear Least Squares/Stability, Back Substitution, Householder Transformations.	Feedback is given through written assignments, programming exercises and workshop questions.
4	Weeks 7-8: Gaussian Elimination, Stability of Gaussian Elimination.	Feedback is given through written assignments, programming exercises and workshop questions.
5	Weeks 9-10:  Eigenvalue Problems, Power Methods.	Feedback is given through written assignments, programming exercises and workshop questions.
6	Weeks 11-12:  Stationary Methods, Preconditioning.	Feedback is given through written assignments, programming exercises and workshop questions.

Tutorial Registration

Workshop registration will be via MyTimetable. ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage.

Assessment Summary

Assessment task	Value	Learning Outcomes
Assignments	60 %	1,2,3,4,5
Final Exam	40 %	2,4,5

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

ANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Policy and General Information
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure

Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the ANU Online website Students may choose not to submit assessment items through Turnitin. In this instance you will be required to submit, alongside the assessment item itself, hard copies of all references included in the assessment item.

Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

Examination(s)

Students should consult the course's Canvas site and the ANU final examination timetable to confirm the date, time and venue of the exam.

Assessment Task 1

Assignments

Five assignments will be handed out fortnightly starting from Week 1. The assignments will usually consist of a written component and a small programming component. For example, students may be asked to implement or run an algorithm to confirm that the numerical results agree with the theoretical analysis, or to see how round-off errors can produce unexpected results. The programming exercises will be done in MATLAB.

The assignments are expected to be graded and returned within a fortnight.

Further details can be found on the course's Canvas site.

Assessment Task 2

Final Exam

A course hurdle is that students score at least 40% in the final exam.

The final exam will take place during the official final examination period at a date, time and location determined by the examination office. Please check the ANU final Examination Timetable http://www.anu.edu.au/students/program-administration/assessments-exams/examination-timetable to confirm the date, time and location of the exam.

Academic Integrity

Academic integrity is a core part of our culture as a community of scholars. At its heart, academic integrity is about behaving ethically. This means that all members of the community commit to honest and responsible scholarly practice and to upholding these values with respect and fairness. The Australian National University commits to embedding the values of academic integrity in our teaching and learning. We ensure that all members of our community understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with. The University has policies and procedures in place to promote academic integrity and manage academic misconduct. Visit the following Academic honesty & plagiarism website for more information about academic integrity and what the ANU considers academic misconduct. The ANU offers a number of services to assist students with their assignments, examinations, and other learning activities. The Academic Skills and Learning Centre offers a number of workshops and seminars that you may find useful for your studies.

Online Submission

You will be required to electronically agree to a declaration as part of the submission of your assignments, that will record your understanding of ANU academic integrity principles. All assignment submissions will be electronic via Canvas and/or the Gradescope platform. Please keep a copy of all your assignment submissions for your records. MATH3512 does not use Turnitin.

Hardcopy Submission

All assignment submissions will be electronic.

Late Submission

Late submission of assessment tasks without an extension are penalised at the rate of 5% of the possible marks available per working day or part thereof. Late submission of assessment tasks is not accepted after 5 working days after the due date, or on or after the date specified in the course outline for the return of the assessment item. No extensions will be granted for the submission of assessment items after the return of the assessment item or any discussion of the solutions of the assessment tasks. Late submission is not accepted for examinations.

Referencing Requirements

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

Returning Assignments

Graded assignments will be returned electronically through Canvas or Gradescope.

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure The Course Convener may grant extensions for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Resubmission of Assignments

Assignments may not be resubmitted.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information. In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service — including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy. If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes. Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

• ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
• ANU Diversity and inclusion for students with a disability or ongoing or chronic illness
• ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
• ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents undergraduate and ANU College students
• PARSA supports and represents postgraduate and research students