Outline

Overview

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)	Daniel Daners, daniel.daners@sydney.edu.au
	Anne Thomas, anne.thomas@sydney.edu.au
	Holger Dullin, holger.dullin@sydney.edu.au
	Milena Radnovic, milena.radnovic@sydney.edu.au

Assessment

The census date for this unit availability is 2 April 2024

Details
Criteria

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:
Presentation	Presentation Class presentation	3%	Multiple weeks	5 minutes
Outcomes assessed:
Small test	Webwork online quizzes #earlyfeedbacktask	2%	Multiple weeks	40 minutes/week
Outcomes assessed:
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:
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:
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:
Participation	Seminar participation Class discussion	3%	Weekly	1x50 minutes/week
Outcomes assessed:
Small test	Webwork online quizzes Online task (may require written calculations)	7%	Weekly	40 minutes/week
Outcomes assessed:
= 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 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.

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. If you do use these tools, you must acknowledge this in your work, either in a footnote or an acknowledgement section. The assessment instructions or unit outline will give guidance of the types of tools that are permitted and how the tools should be used.

Your final submitted work must be your own, original work. You must acknowledge any use of generative AI tools that have been used in the assessment, and any material that forms part of your submission must be appropriately referenced. For guidance on how to acknowledge the use of AI, please refer to the AI in Education Canvas site.

The unapproved use of these tools or unacknowledged use will be considered a breach of the Academic Integrity Policy and penalties may apply.

Studiosity is permitted unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission as detailed on the Learning Hub’s Canvas page.

Outside assessment tasks, generative AI tools may be used to support your learning. The AI in Education Canvas site contains a number of productive ways that students are using AI to improve their learning.

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

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

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. 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
Learning outcomes

Responding to student feedback

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

This is the first time this unit has been offered.

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. 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.

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Early feedback task

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Attendance and class requirements

Study commitment

Required readings

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

MATH1971: Mathematics 1A (SSP)

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

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Early feedback task

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Attendance and class requirements

Study commitment

Required readings

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