Program Overview

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Overview

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.

Unit Details and Rules

• Academic unit: Mathematics and Statistics Academic Operations
• Credit points: 3
• Prerequisites: None
• Corequisites: None
• Prohibitions: MATH1002 or MATH1014
• 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

• Coordinator: Daniel Daners

Assessment

• Type:
  • Final exam: 70%
  • Assignment 1: 5%
  • Assignment 2: 5%
  • Assignment 3: 10%
  • Tutorial quiz: 10%
• Details:
  • Final exam: See Canvas, 1.5 hours, Formal exam period
  • Assignment 1: See Canvas, written assignment, Week 05
  • Assignment 2: Computer Algebra Assignment, Week 09
  • Assignment 3: See Canvas, written assignment, Week 11
  • Tutorial quiz: Online Quizzes, Completed in Canvas, Weekly
• Outcomes assessed:
  • LO1, LO2, LO3, LO5, LO6, LO7, LO8, LO9

Assessment Summary

• 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).
• 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).

• Result name:
  • High distinction: 85 - 100
  • Distinction: 75 - 84
  • Credit: 65 - 74
  • Pass: 50 - 64
  • Fail: 0 - 49

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.

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.

Weekly Schedule

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.

Required 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

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.

• 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
• GQ2: Critical thinking and problem solving
• GQ3: Oral and written communication
• GQ4: Information and digital literacy
• GQ5: Inventiveness
• GQ6: Cultural competence
• GQ7: Interdisciplinary effectiveness
• GQ8: Integrated professional, ethical, and personal identity
• GQ9: Influence

Outcome Map

Learning outcomes | Graduate qualities ---|--- GQ1 | GQ2 | GQ3 | GQ4 | GQ5 | GQ6 | GQ7 | GQ8 | GQ9

Responding to Student Feedback

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

No changes have been made since this unit was last offered.

Additional Information

• 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.

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 14 Jan 2021.