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During 2021 we will continue to support students who need to study remotely due to the ongoing impacts of COVID-19 and travel restrictions. Make sure you check the location code when selecting a unit outline or choosing your units of study in Sydney Student. Find out more about what these codes mean. Both remote and on-campus locations have the same learning activities and assessments, however teaching staff may vary. More information about face-to-face teaching and assessment arrangements for each unit will be provided on Canvas.

Unit of study_

MATH1902: Linear Algebra (Advanced)

This unit is designed to provide a thorough preparation for further study in mathematics and statistics. It is a core unit of study providing three of the twelve credit points required by the Faculty of Science as well as a Junior level requirement in the Faculty of Engineering. It parallels the normal unit MATH1002 but goes more deeply into the subject matter and requires more mathematical sophistication.

Details

Academic unit Mathematics and Statistics Academic Operations
Unit code MATH1902
Unit name Linear Algebra (Advanced)
Session, year
? 
Semester 1, 2020
Attendance mode Normal day
Location Camperdown/Darlington, Sydney
Credit points 3

Enrolment rules

Prohibitions
? 
MATH1002 or MATH1014
Prerequisites
? 
None
Corequisites
? 
None
Assumed knowledge
? 

(HSC Mathematics Extension 2) OR (90 or above in HSC Mathematics Extension 1) or equivalent

Available to study abroad and exchange students

Yes

Teaching staff and contact details

Coordinator Daniel Daners, daniel.daners@sydney.edu.au
Administrative staff MATH1902@sydney.edu.au
Type Description Weight Due Length
Final exam Final exam
See Canvas
70% Formal exam period 1.5 hours
Outcomes assessed: LO1 LO2 LO3 LO5 LO6 LO7 LO8 LO9
Assignment Assignment 1
See Canvas - written assignment
5% Week 05 n/a
Outcomes assessed: LO1 LO7 LO6 LO5 LO3 LO2
Assignment Assignment 2
Computer Algebra Assignment
5% Week 09 n/a
Outcomes assessed: LO1 LO4 LO2
Assignment Assignment 3
See Canvas - written assignment
10% Week 11 n/a
Outcomes assessed: LO1 LO8 LO2
Tutorial quiz Online Quizzes
Completed in Canvas
10% Weekly n/a
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9
  • Examination: Further information about the exam will be made available later on Canvas.
  • Online quizzes: There are twelve weekly online quizzes. Each online quiz consists of a set of randomized questions. The best 10 of your 12 quizzes will count, making each worth 1%. You cannot apply for special consideration for the quizzes. The better mark principle will apply for the total 10% - i.e. if your overall exam mark is higher, then your 10% for quizzes will come from your exam. The deadline for completion of each quiz is 11:59 pm Tuesday (starting in week 2). We recommend that you follow the due dates outlined below to gain the most benefit from these quizzes.
    • The better mark principle means that for the total quiz mark, the quizzes count if and only if the total quiz mark is better than or equal to your exam mark. If your total quiz mark is less than your exam mark, the exam mark will be used for that portion of your assessment instead. The assignment marks count for 20% regardless of whether they are better than your exam mark or not.
  • Assignments: There are three assignments: two written assignments and one computer algebra assignment. The written assignments must be submitted electronically, as PDF files only via Canvas, by the deadline. Note that your assignment will not be marked if it is illegible or if it is submitted sideways or upside down. It is your responsibility to check that your assignment has been submitted correctly. The computer algebra assignment must be submitted within the Ed system, edstem.org.

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

At HD level, a student demonstrates a flair for the subject as well as a detailed and comprehensive understanding of the unit material. A ‘High Distinction’ reflects exceptional achievement and is awarded to a student who demonstrates the ability to apply their subject knowledge and understanding to produce original solutions for novel or highly complex problems and/or comprehensive critical discussions of theoretical concepts.

Distinction

75 - 84

At DI level, a student demonstrates an aptitude for the subject and a well-developed understanding of the unit material. A ‘Distinction’ reflects excellent achievement and is awarded to a student who demonstrates an ability to apply their subject knowledge and understanding of the subject to produce good solutions for challenging problems and/or a reasonably well-developed critical analysis of theoretical concepts.

Credit

65 - 74

At CR level, a student demonstrates a good command and knowledge of the unit material. A ‘Credit’ reflects solid achievement and is awarded to a student who has a broad general understanding of the unit material and can solve routine problems and/or identify and superficially discuss theoretical concepts.

Pass

50 - 64

At PS level, a student demonstrates proficiency in the unit material. A ‘Pass’ reflects satisfactory achievement and is awarded to a student who has threshold knowledge.

Fail

0 - 49

When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see sydney.edu.au/students/guide-to-grades.

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.

Special consideration

If you experience short-term circumstances beyond your control, such as illness, injury or misadventure or if you have essential commitments which impact your preparation or performance in an assessment, you may be eligible for special consideration or special arrangements.

Academic integrity

The Current Student website provides information on academic honesty, academic dishonesty, 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 dishonesty or plagiarism seriously.

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

WK Topic Learning activity Learning outcomes
Week 01 Introduction to linear algebra. Vector space. Vector addition and scalar multiplication. Lecture (3 hr) LO3
Week 02 Length and angle: the dot product, orthogonal vectors, projections, cross product. Lecture and tutorial (3 hr) LO6
Week 03 Line in the plane and space, planes in space. Lecture and tutorial (3 hr) LO5
Week 04 Systems of linear equations. Row operations, row echelon form, and Gaussian elimination. Reduced row-echelon form and Gauss-Jordan elimination. Lecture and tutorial (3 hr) LO7
Week 05 Matrices and matrix operations. Inverse of a matrix. Lecture and tutorial (3 hr) LO8
Week 06 Computing inverses of matrices. Elementary matrices. Span and linear independence. Lecture and tutorial (3 hr) LO8
Week 07 Subspaces. Null, row, and column spaces. Basis and dimension. Lecture and tutorial (3 hr) LO1 LO2 LO3
Week 08 Rank, Nullity and the Rank-Nullity Theorem. Coordinate vectors. Linear transformations. Lecture and tutorial (3 hr) LO1 LO2 LO3
Week 09 Markov chains. Introduction to eigenvalues and eigenvectors, and to determinants. Lecture and tutorial (3 hr) LO8
Week 10 Determinants. Change of basis. Similarity. Lecture and tutorial (3 hr) LO8
Week 11 Eigenvalues and eigenvectors. Diagonalisation. Lecture and tutorial (3 hr) LO8 LO9
Week 12 Applications, including more on Markov chains. Lecture and tutorial (3 hr) LO9
Week 13 Revision. Lecture (2 hr) LO1 LO2 LO3 LO5 LO6 LO7 LO8 LO9

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 3 credit point unit, this equates to roughly 60-75 hours of student effort in total.

Prescribed readings

  • Textbook - A Linear Algebra: A Modern Introduction, by David Poole, 4th edition. Available from the Co-op Bookshop: digital access available from the publisher www.cengage.com.

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.

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

  • LO1. apply mathematical logic and rigour to solving problems;
  • LO2. express mathematical ideas coherently in written and oral form;
  • LO3. demonstrate fluency in vector and matrix arithmetic, and their applications to solving systems of equations;
  • LO4. solve routine problems of linear algebra with the help of a computer algebra system.
  • LO5. perform arithmetic of geometric vectors in the plane and in space, and in n-dimensional space;
  • LO6. perform and manipulate dot, cross and triple products and vector projections, with applications to lines and planes in space;
  • LO7. develop fluency with systems of equations and the methods of Gaussian and Gauss-Jordan elimination;
  • LO8. perform matrix arithmetic, calculate matrix inverses, determinants, eigenvalues and eigenvectors;
  • LO9. develop fluency with methods of diagonalisation and applications.

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
GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9
No changes have been made since this unit was last offered.
  • Tutorials: Tutorials start in week 1. There are no tutorials in week 13. You should attend the tutorial given on your personal timetable. Attendance at tutorials will be recorded. Your attendance will not be recorded unless you attend the tutorial in which
    you are enrolled. If you are absent from a tutorial do not apply for Special Consideration or Special Arrangements, since there
    is no assessment associated with the missed tutorial.
  • Tutorial and exercise sheets: The question sheets for a given week will be available on the MATH1902 webpage. Solutions
    to tutorial exercises for week n will usually be posted on the web by the afternoon of the Friday of week n.
  • Ed Discussion forum: https://edstem.org

Disclaimer

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

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