Program Overview

Overview

MATH1002 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 foundation requirement in the Faculty of Engineering. This unit of study introduces vectors and vector algebra, linear algebra including solutions of linear systems, matrices, determinants, eigenvalues and eigenvectors.

Unit Details and Rules

• Academic unit: Mathematics and Statistics Academic Operations
• Credit points: 3
• Prerequisites: None
• Corequisites: None
• Prohibitions: MATH1012 or MATH1014 or MATH1902
• Assumed knowledge: HSC Mathematics or MATH1111. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February)
• Available to study abroad and exchange students: Yes

Teaching Staff

• Coordinator: Bregje Pauwels
• Lecturer(s): Bregje Pauwels
• Tutor(s): Ruibin Zhang

Assessment

• Type: Supervised exam, Assignment, Online task, Small test, Participation
• Details:
  • Supervised exam: Final exam written calculations and multiple choice, 60%, Formal exam period, 1.5 hours
  • Assignment: Assignment 1 written calculations, 5%, Week 04, 2-4 pages
  • Online task: Quiz Written calculations and multiple choice, 15%, Week 07, 40 minutes
  • Assignment: Assignment 2 written calculations, 10%, Week 11, 6-8 pages
  • Small test: Weekly Quizzes online task, 8%, Weekly, 10 weekly online quizzes
  • Participation: Tutorials Participation in tutorials, 2%, Weekly, 50 minutes/week

Assessment Summary

Below are brief assessment details. Further information can be found in the Canvas site for this unit.

• Weekly online quizzes: There are ten weekly online quizzes and the marks for the best eight count.
• Quiz: One quiz will be held online through Canvas.
• Assignments: There are two written assignments which must be submitted electronically.
• Tutorial Participation: This is a satisfactory
  on-satisfactory mark assessing whether or not you participate in class activities during the tutorials.

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 University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

• Use of generative artificial intelligence (AI) and automated writing tools: You may only use generative AI and automated writing tools in assessment tasks if you are permitted to by your unit coordinator.

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.
• Special consideration: If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time.

Weekly Schedule

WK | Topic | Learning activity | Learning outcomes ---|---|---|--- Week 01 | Introductions, vectors in the plane, vector algebra, vectors in R3 and Rn | Lecture and tutorial (3 hr) | LO1 LO2 Week 02 | Length and angle: the dot product, orthogonal vectors, projections | Lecture and tutorial (3 hr) | LO2 LO5 Week 03 | Cross products | Lecture and tutorial (3 hr) | LO5 Week 04 | Lines and planes | Lecture and tutorial (3 hr) | LO2 LO3 Week 05 | Systems of linear equations and Gaussian elimination | Lecture and tutorial (3 hr) | LO6 LO7 Week 06 | Gauss-Jordan elimination, intro to matrices, matrix algebra | Lecture and tutorial (3 hr) | LO6 LO7 LO8 Week 07 | Matrix algebra, inverse of a matrix | Lecture and tutorial (3 hr) | LO8 Week 08 | Solving systems of linear equations, elementary matrices | Lecture and tutorial (3 hr) | LO6 LO8 Week 09 | Applications to population models and Markov chains | Lecture and tutorial (3 hr) | LO8 LO11 Week 10 | Determinants | Lecture and tutorial (3 hr) | LO8 Week 11 | Eigenvalues and eigenvectors | Lecture and tutorial (3 hr) | LO9 Week 12 | Diagonalisation and more on applications | Lecture and tutorial (3 hr) | LO10 LO11 Week 13 | Revision | Lecture (2 hr) | LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9 LO10 LO11

Learning Outcomes

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

• LO1: apply mathematical logic and rigour to solving problems
• LO2: represent vectors both algebraically and geometrically in two and three dimensions, and perform arithmetic with them
• LO3: use vectors to solve classical geometric problems
• LO4: determine spanning families and check linear independence
• LO5: perform and manipulate dot and cross products
• LO6: set up systems of linear equations
• LO7: solve systems of linear equations using Gaussian elimination
• LO8: perform matrix arithmetic and calculate matrix inverses and determinants
• LO9: find eigenvalues and eigenvectors
• LO10: diagonalise a matrix
• LO11: express mathematical ideas and arguments coherently in written form

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.

• 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

Additional Information

• Lectures: Lectures are face-to-face and streamed live with online access from Canvas.
• Tutorials: Tutorials are small classes in which you are expected to work through questions from the tutorial sheet in small groups on the white board.
• Tutorial and exercise sheets: The question sheets for a given week will be available on the MATH1002 Canvas page.
• Ed Discussion forum:
• Science student portal
• Mathematics and Statistics student portal

Disclaimer

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