Unit outline_

MATH1013: Mathematical Modelling

Overview

MATH1013 is designed for science students who do not intend to undertake higher year mathematics and statistics. In this unit of study students learn how to construct, interpret and solve simple differential equations and recurrence relations. Specific techniques include separation of variables, partial fractions and first and second order linear equations with constant coefficients. Students are also shown how to iteratively improve approximate numerical solutions to equations.

Unit details and rules

Academic unit Mathematics and Statistics Academic Operations 3 None None MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933 HSC Mathematics or a credit or higher in MATH1111. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February). Please note: this unit does not normally lead to a major in Mathematics or Statistics or Financial Mathematics and Statistics Yes

Teaching staff

Coordinator Sean Gomes, sean.gomes@sydney.edu.au Pantea Pooladvand

Assessment

Type Description Weight Due Length
Final exam (Record+) Final exam
60% Formal exam period 1.5 hours
Outcomes assessed:
Assignment Assignment 1
written calculations
5% Week 03
Due date: 18 Aug 2022 at 23:59

Closing date: 28 Aug 2022
10 days
Outcomes assessed:
12.5% Week 06
Due date: 08 Sep 2022 at 23:59

Closing date: 08 Sep 2022
40 Minutes
Outcomes assessed:
Assignment Assignment 2
written calculations
10% Week 08
Due date: 22 Sep 2022 at 23:59

Closing date: 02 Oct 2022
10 days
Outcomes assessed:
12.5% Week 11
Due date: 20 Oct 2022 at 23:59

Closing date: 20 Oct 2022
40 Minutes
Outcomes assessed:
= Type B final exam

Assessment summary

• Quizzes: Two quizzes will be held online through Canvas. The quizzes are 40 minutes and have 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 quizzes so do not submit an application for Special Consideration or Special Arrangements if you miss a quiz. The better mark principle means that for each quiz, 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.
• Assignments: There are two assignments. Each assignment 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.
• Final Exam: There is one examination during the examination period at the end of Semester. 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.
• No simple extensions are given in first year units in the School of Mathematics and Statistics.

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.

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.

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.

Weekly schedule

WK Topic Learning activity Learning outcomes
Week 01 1. Assumed knowledge for differential equations; 2. Intro to differential equations (general and particular solutions) Lecture and tutorial (2 hr)
Week 02 1. Equilibrium (steady-state) solutions for differential equations; 2. Stability of equilibria for differential equations (graphical method) Lecture and tutorial (3 hr)
Week 03 1. Separation of variables; 2. Simple linear models Lecture and tutorial (3 hr)
Week 04 1. Partial fractions; 2. The logistic function Lecture and tutorial (3 hr)
Week 05 1. Applications of logistic models; 2. More applications of logistic models Lecture and tutorial (3 hr)
Week 06 1. Assumed knowledge for arithmetic and geometric sequences; 2. Intro to recurrence relations (general and particular solutions) Lecture and tutorial (3 hr)
Week 07 1. Equilibrium (fixed-point) solutions; 2. Stability of fixed points Lecture and tutorial (3 hr)
Week 08 1. Numerical solution of equations; 2. Fixed-point iteration (Gregory–Dary method) Lecture and tutorial (3 hr)
Week 09 1. Behaviour of logistic map; 2. Applications of logistic map Lecture and tutorial (3 hr)
Week 10 1. Second-order equations; 2. The characteristic quadratic (positive discriminants only) Lecture and tutorial (3 hr)
Week 11 1. Pairs of first-order differential equations; 2. Pairs of first-order recurrence equations Lecture and tutorial (3 hr)
Week 12 1. The characteristic equation (negative discriminants); 2. Oscillating (trigonometric) solutions Lecture and tutorial (3 hr)
Week 13 Revision Lecture and tutorial (3 hr)

Attendance and class requirements

• Attendance: Students are expected to attend a minimum of 80% of timetabled activities for a unit of study, unless granted exemption by the Associate Dean. For some units of study the minimum attendance requirement, as specified in the relevant table of units or the unit of study outline, may be greater than 80%.
• Tutorial attendance:  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.  While there is no penalty if 80% attendance is not met we strongly recommend you attend tutorials regularly to keep up with the material and to engage with the tutorial questions. Since there is no assessment associated with the tutorials do not submit an application for Special Consideration or Special Arrangements for missed tutorials.

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.

• L. Poladian. Mathematical Modelling. School of Mathematics and Statistics, University of Sydney, Sydney, NSW, Australia, 2011. Available from Kopystop. (also available as a PDF through Canvas)

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.

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

• LO1. write down general and particular solutions to simple differential equations and recurrence relations describing models of growth and decay
• LO2. determine the order of a differential equation or recurrence relation
• LO3. find equilibrium solutions and analyse their stability using both graphical methods and slope conditions
• LO4. recognise and solve separable first-order differential equations
• LO5. use partial fractions and separation of variables to solve certain nonlinear differential equations, including the logistic equation
• LO6. use a variety of graphical and numerical techniques to locate and count solutions to equations
• LO7. solve equations numerically by fixed-point iteration, including checking if an iteration method is stable
• LO8. explore sequences numerically, and classify their long-term behaviour
• LO9. determine the general solution to linear second-order equations or simultaneous pairs of first order equations with constant coefficients.

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

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.

Minor changes were made to the weightings for the assignments and final exam..