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Unit outline_

MATH1971: Mathematics 1A (SSP)

Semester 1, 2024 [Normal day] - Camperdown/Darlington, Sydney

Mathematics is both a powerful tool with many diverse applications and a subject that is beautiful in itself. This unit provides solid foundations for higher level university mathematics and its applications by building on what you have already learnt. It contains material on calculus, linear algebra and complex numbers, all of which have profound applications in science, engineering, statistics, and economics. This unit investigates differential and integral calculus of one variable and the diverse applications of this theory. Linear algebra begins with vectors and vector algebra. From there we consider matrices, determinants, eigenvalues and eigenvectors which are powerful tools used to solve systems of linear equations and in many other applications. As an advanced unit MATH1971 introduces you to formal mathematical language, proof and rigour. The unit includes a series of seminars showcasing a diverse range of topics not covered in regular units. At the end of this unit you will be equipped with mathematical knowledge and rigorous thinking skills that you will use in a broad range of applications and/or as a foundation for further mathematical studies at University.

Unit details and rules

Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Prerequisites
? 
None
Corequisites
? 
None
Prohibitions
? 
MATH1901 or MATH1902 or MATH1921 or MATH1906 or MATH1931 or MATH1001 or MATH1021 or MATH1061 or MATH1961 or MATH1002 or MATH1014
Assumed knowledge
? 

(at least Band E4 in HSC Mathematics Extension 2) or equivalent

Available to study abroad and exchange students

Yes

Teaching staff

Coordinator Daniel Daners, daniel.daners@sydney.edu.au
Lecturer(s) Anne Thomas, anne.thomas@sydney.edu.au
Daniel Daners, daniel.daners@sydney.edu.au
Milena Radnovic, milena.radnovic@sydney.edu.au
Holger Dullin, holger.dullin@sydney.edu.au
The census date for this unit availability is 2 April 2024
Type Description Weight Due Length
Supervised exam
? 
Final exam
Multiple choice and written calculations or mathematical arguments
60% Formal exam period 2 hours
Outcomes assessed: LO1 LO2 LO3 LO4 LO5
Presentation group assignment Presentation
Class presentation
3% Multiple weeks 5 minutes
Outcomes assessed: LO2 LO7
Small test Webwork online quizzes
#earlyfeedbacktask
2% Multiple weeks 40 minutes/week
Outcomes assessed: LO1
Short release assignment Assignment 1
Written mathematical problem solving or proof
4% Week 04
Due date: 17 Mar 2024 at 23:59

Closing date: 27 Mar 2024
4-6 pages
Outcomes assessed: LO1 LO2 LO3 LO6 LO7
Online task Quiz
Multiple choice quiz
13% Week 08
Due date: 18 Apr 2024 at 23:59

Closing date: 18 Apr 2024
50 minutes
Outcomes assessed: LO1 LO6 LO4 LO3
Short release assignment Assignment 2
Written mathematical problem solving or proof
8% Week 11
Due date: 12 May 2024 at 23:59

Closing date: 22 May 2024
6-10 pages
Outcomes assessed: LO1 LO2 LO3 LO5 LO6 LO7
Participation Seminar participation
Class discussion
3% Weekly 1x50 minutes/week
Outcomes assessed: LO1 LO8 LO2
Small test Webwork online quizzes
Online task (may require written calculations)
7% Weekly 40 minutes/week
Outcomes assessed: LO1 LO5 LO4 LO3
group assignment = group assignment ?

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

  • Assignments:  There are two short release assignments. Each must be submitted electronically, as one single typeset or scanned PDF file 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 and that it is complete (check that you can view each page). Late submissions will receive a penalty. A mark of zero will be awarded for all submissions more than 10 days past the original due date. Further extensions past this time will not be permitted. The maximum extension you can be awarded through Special Consideration for the assignments is 7 calendar days. If you are affected for more than 7 calendar days you will be granted a mark adjustment. This means that your final exam mark will count instead for the assignment mark. The closing date for submissions (with a late penalty) is the same for all students. It is not changed if you are granted an extension. This allows for timely release of the marks and feedback. Note that the assignments are not eligible for a Simple Extension through the Special Consideration system since they are short release assignments (released to you to complete within 10 working days).
  • Quiz: One quiz will be held online through Canvas. The quiz is 50 minutes and has to be submitted by the closing time of 23:59 on the due date. The quiz can be taken any time during the 24 hour period before the closing time.The better mark principle will be used for the quiz so do not submit an application for Special Consideration or Special Arrangements if you miss a quiz. The better mark principle means that the quiz counts if and only if it is better than or equal to your exam mark. If your quiz mark is less than your exam mark, the exam mark will be used for that portion of your assessment instead. No extensions will be granted for the quiz. If you are granted Special Consideration the outcome is a mark adjustment where the exam mark will count instead, regardless of any mark achieved for the quiz.
  • Webwork Online Quizzes: There are ten weekly online quizzes (equally weighted). The first two are used for the Early Feedback Task. Each online quiz consists of a set of randomized questions. You should not apply for special consideration for the quizzes. The better mark principle will apply for the total 9% - i.e. if your overall exam mark is higher, then your 9% for the Webwork quizzes will come from your exam. The deadline for completion of each quiz is 23:59 Sunday (starting in week 2). The precise schedule for the quizzes is found on Canvas. We recommend that you follow the due dates outlined above to gain the most benefit from these quizzes.
  • Seminar Participation: This is a satisfactory/non-satisfactory mark assessing whether or not you participate in class activities during the seminar. It is 0.3 marks per seminar up to 10 seminars (there are 12 seminars).
  • Presentation: There is a 5 minute group presentation to the seminar class.
  • Final Exam: The final exam for this unit is compulsory and must be attempted. Failure to attempt the final exam will result in an AF grade for the course. Further information about the exam will be made available at a later date on Canvas. If a second replacement exam is required, this exam may be delivered via an alternative assessment method, such as a viva voce (oral exam). The alternative assessment will meet the same learning outcomes as the original exam. The format of the alternative assessment will be determined by the unit coordinator.

Detailed information for each assessment can be found on Canvas

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 sydney.edu.au/students/guide-to-grades.

For more information see 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.

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.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

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

WK Topic Learning activity Learning outcomes
Multiple weeks Special Topics Seminar (12 hr) LO8
Week 01 Complex numbers in Cartesian and polar form. Complex powers and De Moivre’s Theorem. Lecture (2 hr) LO1 LO2 LO3
Introduction to linear algebra. Vector space. Vector addition and scalar multiplication. Lecture (2 hr) LO1 LO2 LO3
Week 02 The complex exponential function, n-th roots. Representing complex functions Lecture and tutorial (3 hr) LO1 LO2 LO3
Length and angle: the dot product, orthogonal vectors, projections, cross product. Lecture and tutorial (3 hr) LO1 LO2 LO3 LO6
Week 03 Injective and bijective functions. Inverse functions. Hyperbolic functions Lecture and tutorial (3 hr) LO1 LO2 LO3 LO6
Line in the plane and space, planes in space. Lecture and tutorial (3 hr) LO1 LO2 LO3
Week 04 Limits and the limit laws. Lecture and tutorial (3 hr) LO1 LO2 LO4 LO6 LO7
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) LO1 LO2 LO3 LO6
Week 05 Continuity. Intermediate Value Theorem. Lecture and tutorial (3 hr) LO1 LO2 LO4 LO6 LO7
Matrices and matrix operations. Inverse of a matrix. Lecture and tutorial (3 hr) LO1 LO2 LO3 LO6
Week 06 Differentiability. Rolle’s Theorem and the Mean Value Theorem. Lecture and tutorial (3 hr) LO1 LO2 LO4 LO6 LO7
Computing inverses of matrices. Elementary matrices. Span and linear independence. Lecture and tutorial (3 hr) LO1 LO2 LO3
Week 07 Cauchy’s Mean Value Theorem and L’Hopital’s Rule. Lecture and tutorial (3 hr) LO1 LO2 LO4 LO6
Subspaces. Null, row, and column spaces. Basis and dimension. Lecture and tutorial (3 hr) LO1 LO2 LO3 LO6 LO7
Week 08 Taylor polynomials with remainder, Taylor series of standard functions. Lecture and tutorial (3 hr) LO1 LO2 LO4 LO5
Rank, Nullity and the Rank-Nullity Theorem. Coordinate vectors. Linear transformations. Lecture and tutorial (3 hr) LO1 LO2 LO3 LO6 LO7
Week 09 Evaluation of Riemann sums. Definition of the Riemann integral. Lecture and tutorial (3 hr) LO1 LO2 LO5
Markov chains. Introduction to eigenvalues and eigenvectors, and to determinants. Lecture and tutorial (3 hr) LO1 LO2 LO3 LO6
Week 10 Fundamental Theorem of Calculus. Functions defined by integrals. Lecture and tutorial (3 hr) LO1 LO2 LO4 LO5
Determinants. Change of basis. Similarity. Lecture and tutorial (3 hr) LO1 LO2 LO3 LO6 LO7
Week 11 Applications of Riemann sums and integrals: for instance volumes, arc lengths, volumes of revolution, surface area of revolution. Lecture and tutorial (3 hr) LO1 LO2 LO5 LO6
Eigenvalues and eigenvectors. Diagonalisation. Lecture and tutorial (3 hr) LO1 LO2 LO3 LO6
Week 12 Improper integrals Integrals of unbounded functions. Integrals over unbounded intervals. Comparison tests. Lecture and tutorial (3 hr) LO1 LO2 LO5 LO6
Applications, including more on Markov chains. Lecture and tutorial (3 hr) LO1 LO2 LO3 LO6
Week 13 Revision / spill-over Lecture and tutorial (3 hr) LO1 LO2 LO4 LO5 LO6
Revision / spill over Lecture and tutorial (3 hr) LO1 LO2 LO3 LO6 LO7

Attendance and class requirements

  • Lecture attendance: You are expected to attend lectures. If you do not attend lectures you should at least follow the lecture recordings available through Canvas.

  • Tutorial attendance: Tutorials (two per week) start in Week 2. You should attend the tutorials 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. We strongly recommend you attend tutorials regularly to keep up with the material and to engage with the tutorial questions. 

  • Seminar attendance: The seminars start in Week 2. Attendance at seminars and participation will be recorded to determine the participation mark.

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.

Required readings

  • Textbook: Linear Algebra: A Modern Introduction, David Poole, 4th edition (or an earlier edition). Digital access available from the publisher www.cengage.com.
  • Course Notes for MATH1921 Calculus of One Variable (Advanced) (available on Canvas).

  • See the Canvas site for more reference material.

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 solve problems
  • LO2. express mathematical ideas and arguments rigorously and coherently in written and oral form
  • LO3. demonstrate competence in the mathematical analysis and manipulation of functions of real and complex variables, vectors, linear independence, matrices, inverses and the theory of eigenvalues and eigenfunctions
  • LO4. apply fundamental properties of continuous and differentiable functions including limits, limit laws, to optimisation, finding limits, approximating functions and other uses of differential calculus
  • LO5. demonstrate an understanding of the definition and computation or estimation of Riemann integrals including proficiency in using standard integration methods to evaluate integrals
  • LO6. apply concepts of calculus and linear algebra to a variety of contexts and applications
  • LO7. construct mathematical proofs based on formal definitions and previously established facts
  • LO8. develop understanding of the special topics by participating in discussions or other class activities

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

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

This is the first time this unit has been offered.
  • 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. The role of the tutor is to provide support and to some extent give feedback on your solutions written on the board.

  • Tutorial and exercise sheets: The question sheets for a given week will be available on the MATH1961/1971 Canvas page. 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.