MATH2061: Semester 1, 2025

Overview

This unit starts with an investigation of linearity: linear functions, general principles relating to the solution sets of homogeneous and inhomogeneous linear equations (including differential equations), linear independence and the dimension of a linear space. The study of eigenvalues and eigenvectors, begun in junior level linear algebra, is extended and developed. The unit then moves on to topics from vector calculus, including vector-valued functions (parametrised curves and surfaces; vector fields; div, grad and curl; gradient fields and potential functions), line integrals (arc length; work; path-independent integrals and conservative fields; flux across a curve), iterated integrals (double and triple integrals; polar, cylindrical and spherical coordinates; areas, volumes and mass; Green's Theorem), flux integrals (flow through a surface; flux integrals through a surface defined by a function of two variables, though cylinders, spheres and parametrised surfaces), Gauss' Divergence Theorem and Stokes' Theorem.

Unit details and rules

Academic unit	Mathematics and Statistics Academic Operations
Credit points	6
Prerequisites ?	{(MATH1X61 or MATH1971) or [(MATH1X21 or MATH1931 or MATH1X01 or MATH1906 or MATH1011) and (MATH1014 or MATH1X02)]} and (MATH1X62 or MATH1972 or MATH1013 or MATH1X23 or MATH1X03 or MATH1933 or MATH1907)
Corequisites ?	None
Prohibitions ?	MATH2961 or MATH2067 or MATH2021 or MATH2921 or MATH2022 or MATH2922
Assumed knowledge ?	None
Available to study abroad and exchange students	Yes

Teaching staff

Coordinator	John Mitry, john.mitry@sydney.edu.au
Lecturer(s)	John Mitry, john.mitry@sydney.edu.au

Assessment

The census date for this unit availability is 31 March 2025

Details
Criteria

Type	Description	Weight	Due	Length
Supervised exam ?	Final exam Supervised exam	50%	Formal exam period	2 hours
Outcomes assessed:
Participation	Peer-Learning Session Participation Peer-Learning Session Participation	4%	Multiple weeks	1 hour
Outcomes assessed:
Participation	Tutorial Participation Tutorial Participation	4%	Multiple weeks	60 minutes
Outcomes assessed:
Online task	Fortnightly Quizzes Online quizzes	8%	Multiple weeks	30 minutes
Outcomes assessed:
Online task	Early Feedback Task Online quiz #earlyfeedbacktask	2%	Week 02	30 minutes
Outcomes assessed:
Assignment	Linear Algebra Assignment Assignment	7%	Week 05 Due date: 27 Mar 2025 at 23:59	3-5 pages
Outcomes assessed:
Small test	Mid-Semester Test Supervised test	18%	Week 08 Due date: 15 Apr 2025 at 18:00	45 minutes
Outcomes assessed:
Assignment	Vector Calculus Assignment Assignment	7%	Week 12 Due date: 22 May 2025 at 23:59	3-5 pages
Outcomes assessed:
= group assignment ? = AI allowed ? = early feedback task ?

Early feedback task

This unit includes an early feedback task, designed to give you feedback prior to the census date for this unit. Details are provided in the Canvas site and your result will be recorded in your Marks page. It is important that you actively engage with this task so that the University can support you to be successful in this unit.

Assessment summary

Tutorial Participation: A series of satisfactory/unsatisfactory assessments of participation in tutorial activities.
Peer-Learning Participation: A series of satisfactory/unsatisfactory assessments of participation in peer-learning session activities.
Regular Quizzes: A series of fortnightly quizzes held online on Canvas in weeks 2, 4, 6, 9, 11, and 13. The first quiz forms the early feedback task (EFT).
Assignments: Two take home assignments with at least a week between the release of questions and the due date.
Mid-Semester Test: A supervised test held on campus.
Final Exam: A supervised test held on campus during the exam period.

Detailed information for each assessment will be available on Canvas.

Late submissions will receive penalties according to the University policy. Please submit an application for Special Consideration or Special Arrangements if you miss a session or assessment.

Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name	Mark range	Description
High distinction	85 - 100	Representing complete or close to complete mastery of the material.
Distinction	75 - 84	Representing excellence, but substantially less than complete mastery.
Credit	65 - 74	Representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence.
Pass	50 - 64	Representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course.
Fail	0 - 49	When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see guide to grades.

Use of generative artificial intelligence (AI) and automated writing tools

Except for supervised exams or in-semester tests, you may use generative AI and automated writing tools in assessments unless expressly prohibited by your unit coordinator.

For exams and in-semester tests, the use of AI and automated writing tools is not allowed unless expressly permitted in the assessment instructions.

The icons in the assessment table above indicate whether AI is allowed – whether full AI, or only some AI (the latter is referred to as “AI restricted”). If no icon is shown, AI use is not permitted at all for the task. Refer to Canvas for full instructions on assessment tasks for this unit.

Your final submission must be your own, original work. You must acknowledge any use of automated writing tools or generative AI, and any material generated that you include in your final submission must be properly referenced. You may be required to submit generative AI inputs and outputs that you used during your assessment process, or drafts of your original work. Inappropriate use of generative AI is considered a breach of the Academic Integrity Policy and penalties may apply.

The Current Students website provides information on artificial intelligence in assessments. For help on how to correctly acknowledge the use of AI, please refer to the  AI in Education Canvas site.

Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

Deduction of 5% of the maximum mark for each calendar day after the due date.
After ten calendar days late, a mark of zero will be awarded.

Academic integrity

The Current Student website provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

Learning support

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

Support for students

The Support for Students Policy 2023 reflects the University’s commitment to supporting students in their academic journey and making the University safe for students. It is important that you read and understand this policy so that you are familiar with the range of support services available to you and understand how to engage with them.

The University uses email as its primary source of communication with students who need support under the Support for Students Policy 2023. Make sure you check your University email regularly and respond to any communications received from the University.

Learning resources and detailed information about weekly assessment and learning activities can be accessed via Canvas. It is essential that you visit your unit of study Canvas site to ensure you are up to date with all of your tasks.

If you are having difficulties completing your studies, or are feeling unsure about your progress, we are here to help. You can access the support services offered by the University at any time:

Support and Services (including health and wellbeing services, financial support and learning support)
Course planning and administration
Meet with an Academic Adviser

Weekly schedule

WK	Topic	Learning activity
Week 01	Linear systems, Gaussian elimination, vector spaces and subspaces	Lecture and tutorial (4 hr)
Week 01	Linear systems, Gaussian elimination, vector spaces and subspaces	Seminar (1 hr)
Week 02	Subspaces, linear combinations, span,linear dependence and independence	Lecture and tutorial (4 hr)
Week 02	Subspaces, linear combinations, span,linear dependence and independence	Seminar (1 hr)
Week 03	Linear dependence and independence, span, basis and dimension	Lecture and tutorial (4 hr)
Week 03	Linear dependence and independence, span, basis and dimension	Seminar (1 hr)
Week 04	Basis and dimension, Lagrange interpolation, column space, null space, rank, nullity and linear transformations	Lecture and tutorial (4 hr)
Week 04	Basis and dimension, Lagrange interpolation, column space, null space, rank, nullity and linear transformations	Seminar (1 hr)
Week 05	Eigenvalues and eigenvectors, diagonalisation theorem and Leslie population model	Lecture and tutorial (4 hr)
Week 05	Eigenvalues and eigenvectors, diagonalisation theorem and Leslie population model	Seminar (1 hr)
Week 06	Recurrence relations and systems of linear differential equations	Lecture and tutorial (4 hr)
Week 06	Recurrence relations and systems of linear differential equations	Seminar (1 hr)
Week 07	Vector equations of lines and curves (revision), arc length, two types of line integrals and work done by a force	Lecture and tutorial (4 hr)
Week 07	Vector equations of lines and curves (revision), arc length and two types of line integrals and work done by a force	Seminar (1 hr)
Week 08	Vector fields, grad and curl, normals to surfaces, conservative fields and potential functions	Lecture and tutorial (4 hr)
Week 08	Vector fields, grad and curl, normals to surfaces, conservative fields and potential functions	Seminar (1 hr)
Week 09	Double integrals, area, volume and mass. Div (divergence of a vector field), green’s theorem and flux across a curve	Lecture and tutorial (4 hr)
Week 09	Double integrals, area, volume and mass. Div (divergence of a vector field), green’s theorem and flux across a curve	Seminar (1 hr)
Week 10	Green’s theorem continued., surface area, surface integrals, flux across a surface, polar, cylindrical and spherical coordinates	Lecture and tutorial (4 hr)
Week 10	Green’s theorem continued., surface area, surface integrals, flux across a surface, polar, cylindrical and spherical coordinates	Seminar (1 hr)
Week 11	Triple integrals., volume and mass revisited and Gauss’ divergence theorem	Lecture and tutorial (4 hr)
Week 11	Triple integrals., volume and mass revisited and Gauss’ divergence theorem	Seminar (1 hr)
Week 12	Triple integrals in cylindrical/spherical coordinates, stokes’ theorem and connections between different types of integrals	Lecture and tutorial (4 hr)
Week 12	Triple integrals in cylindrical/spherical coordinates, stokes’ theorem and connections between different types of integrals	Seminar (1 hr)
Week 13	Revision	Lecture and tutorial (4 hr)

Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

Outcomes
Graduate qualities

At the completion of this unit, you should be able to:

LO1. solve a system of linear equations
LO2. apply the subspace test in several different vector spaces
LO3. calculate the span of a given set of vectors in various vector spaces
LO4. test sets of vectors for linear independence and dependence
LO5. find bases of vector spaces and subspaces
LO6. find a polynomial of minimum degree that fits a set of points exactly
LO7. find bases of the fundamental subspaces of a matrix
LO8. test whether an n × n matrix is diagonalisable, and if it is find its diagonal form
LO9. apply diagonalisation to solve recurrence relations and systems of DEs
LO10. extended (from first year) their knowledge of vectors in two and three dimensions, and of functions of several variables
LO11. evaluate certain line integrals, double integrals, surface integrals and triple integrals
LO12. understand the physical and geometrical significance of these integrals
LO13. know how to use the important theorems of Green, Gauss and Stokes.

Graduate qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1	Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.
GQ2	Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.
GQ3	Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.
GQ4	Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.
GQ5	Inventiveness Generating novel ideas and solutions.
GQ6	Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.
GQ7	Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.
GQ8	Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.
GQ9	Influence Engaging others in a process, idea or vision.

Outcome map

Learning outcomes	Graduate qualities
Learning outcomes

Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

Marks have been assigned to tutorials, practice seminars will be run with active learning (peer-learning) and will also have marks associated to encourage regular practice. Regular online quizzes have been written and added to the assessment to also encourage keeping up with course content. The weighting of the final exam has been reduced to compensate the added assessment. The two tests have been reduced to 1 mid-semester test. The canvas page has been reorganised to make navigation easier. Lecture content will focus on learning objectives. Other changes have been made to encourage community and to gain student feedback on changes throughout the semester.

Additional information

Disclaimer

The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

This unit of study outline was last modified on 11 Feb 2025.

To help you understand common terms that we use at the University, we offer an online glossary.

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Early feedback task

Assessment summary

Assessment criteria

Use of generative artificial intelligence (AI) and automated writing tools

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Study commitment

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Disclaimer

On this page

Useful links

Media

Student links

About us

Connect

Current students

MATH2061: Linear Mathematics and Vector Calculus

Semester 1, 2025 [Normal day] - Camperdown/Darlington, Sydney

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Early feedback task

Assessment summary

Assessment criteria

Use of generative artificial intelligence (AI) and automated writing tools

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Study commitment

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Disclaimer

On this page

Useful links

Media

Student links

About us

Connect