Outline

Overview

This unit provides an introduction to multivariable differential calculus and modelling as well as mathematical statistics. Emphasis is given both to the theoretical and foundational aspects of the subject, as well as developing the valuable skill of applying the mathematical theory to solve practical problems. Topics covered in this unit of study include mathematical modelling, first order differential equations, second order differential equations, systems of linear equations, visualisation in 2 and 3 dimensions, partial derivatives, directional derivatives, the gradient vector, and optimisation for functions of more than one variable. The statistics part provides an introduction to mathematical statistics including descriptive statistics, the normal model and hypothesis testing. Concepts will be illustrated using statistical software. The unit includes a series of seminars showcasing a diverse range of topics not covered in regular units.

Unit details and rules

Academic unit	Mathematics and Statistics Academic Operations
Credit points	6
Prerequisites ?	None
Corequisites ?	None
Prohibitions ?	MATH1905 or MATH1903 or MATH1907 or MATH1923 or MATH1933 or MATH1062 or MATH1962 or MATH1003 or MATH1023 or MATH1005 or MATH1015
Assumed knowledge ?	(HSC Mathematics Extension 2) or (Band E4 in HSC Mathematics Extension 1) or equivalent
Available to study abroad and exchange students	Yes

Teaching staff

Coordinator	Daniel Daners, daniel.daners@sydney.edu.au
Lecturer(s)	Linh Nghiem, linh.nghiem@sydney.edu.au
Lecturer(s)	James Parkinson, james.parkinson@sydney.edu.au

Assessment

The census date for this unit availability is 2 September 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	Weekly Online Quizzes 3-10 Online task (may require written calculations)	7%	Multiple weeks	Short questions
Outcomes assessed:
Participation	Seminars Participation in seminars	3%	Multiple weeks	1x50 minutes/week
Outcomes assessed:
Small test	Weekly Online Quizzes 1-2 #earlyfeedbacktask Online task (may require written calculations)	2%	Week 03 Due date: 18 Aug 2024 at 23:59 Closing date: 18 Aug 2024	short questions
Outcomes assessed:
Short release assignment	Assignment 1 Written mathematical problem solving or proof	4%	Week 04 Due date: 25 Aug 2024 at 23:59 Closing date: 04 Sep 2024	2-5 pages
Outcomes assessed:
Online task	Mid-Semester Quiz Multiple choice quiz	13%	Week 07 Due date: 11 Sep 2024 at 23:59 Closing date: 11 Sep 2024	50 minutes
Outcomes assessed:
Short release assignment	Assignment 2 Written mathematical problem solving or proof	8%	Week 10 Due date: 13 Oct 2024 at 23:59 Closing date: 23 Oct 2024	2-5 pages
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. Your work for each assignment must be submitted electronically via Canvas by the deadline. Note that your submission 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.
Weekly Online Quizzes: There are ten (equally weighted) weekly online quizzes. The first two quizzes 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 weekly online 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 10 minute group presentation to the seminar class.
Final Exam: There is one examination during the examination period at the end of Semester. 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.

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	Introduction to models	Lecture (2 hr)
Week 01	Introduction, descriptive statistics (graphical and numerical summaries)	Lecture (2 hr)
Week 02	First-order differential equations	Lecture (3 hr)
Week 02	Review: probabilities and random variables	Lecture (3 hr)
Week 03	Integrating factors and direction fields	Lecture and tutorial (3 hr)
Week 03	Mathematical expectations	Lecture and tutorial (3 hr)
Week 04	Second-order differential equations, boundary conditions	Lecture and tutorial (3 hr)
Week 04	Law of large numbers and probability inequalities	Lecture and tutorial (3 hr)
Week 05	Systems of linear differential equations, interpretation through diagonalisation, introduc- tion to phase plane analysis	Lecture and tutorial (3 hr)
Week 05	Bivariate random variables	Lecture and tutorial (3 hr)
Week 06	Functions of more than one real variable	Lecture and tutorial (3 hr)
Week 06	Sampling distributions and central limit theorem	Lecture and tutorial (3 hr)
Week 07	Limits of functions of more than one real variable	Lecture and tutorial (3 hr)
Week 07	Point estimation and confidence intervals for normal distribution	Lecture and tutorial (3 hr)
Week 08	Partial derivatives, tangent planes, linear approximation	Lecture and tutorial (3 hr)
Week 08	Point estimation and confidence intervals for proportion	Lecture and tutorial (3 hr)
Week 09	Directional derivatives, gradient vector, and applications	Lecture and tutorial (3 hr)
Week 09	Hypothesis testing concepts, one-sample statistical tests	Lecture and tutorial (3 hr)
Week 10	Chain rule, implicit differentiation	Lecture and tutorial (3 hr)
Week 10	Two-sample and chi-square tests	Lecture and tutorial (3 hr)
Week 11	Optimising functions of two or more variables	Lecture and tutorial (3 hr)
Week 11	Correlation and simple linear regression	Lecture and tutorial (3 hr)
Week 12	Further optimisation and interpretation using diagonalisation	Lecture and tutorial (3 hr)
Week 12	Correlation and simple linear regression	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 and participation will be recorded to determine the participation mark. 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 for statistics: Introductory Statistics (4th. edition), by Sheldon M. Ross (online access via Usyd library)
Recommended textbook for calculus: James Stewart. Calculus. Cengage Learning. 7th Edition, International Edition, 2012, ISBN 978-0-538-49884-5 or 8th Edition, Metric Version, 2015, ISBN 978-1-305-26672-8. Available from the Co-op Bookshop.
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 statistical thinking to solve problems
LO2. express mathematical and statistical ideas and arguments coherently in written form and oral form
LO3. identify and analyse appropriate methods to describe, summarise and visualise a given data set
LO4. identify and apply appropriate methods of inference for a variety of data types
LO5. apply statistical software such as R to analyse example sets of data
LO6. express surfaces and curves in two or three dimensions in implicit or explicit form
LO7. calculate partial derivatives of functions of several variables and use these to find directional derivatives and gradient vectors and to interpret the physical and geometric significance of these quantities
LO8. set up differential equations models and use a variety of techniques to solve these differential equations and interpret their solutions in terms of the original problem
LO9. apply concepts of mathematical statistics and calculus to a variety of contexts and applications
LO10. 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 MATH1962/1972 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

MATH1972: Mathematics 1B (SSP)

Semester 2, 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