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Unit outline_

MATH1062: Mathematics 1B

Semester 2, 2024 [Normal day] - Camperdown/Darlington, Sydney

Mathematics and Statistics provide powerful quantitative tools to solve problems and make informed decisions in a very diverse range of real-life applications. This unit builds on the calculus that you learnt in Mathematics 1A and introduces you to mathematical statistics. Mathematics 1B gives you a foundational knowledge of the theory of multivariable calculus, differential equations and mathematical statistics that will underpin examples of applications in this unit and in other areas that you will study. At the end of this unit, you will be equipped with the theory and tools that you need to use mathematics and statistics for mathematical and statistical modelling and problem solving. You will also be prepared to continue your studies in mathematics, statistics and financial mathematics and statistics at this university. Please note that this unit is not part of the Data Science major. Students are very strongly recommended to complete MATH1061 Mathematics 1A before starting MATH1062 Mathematics 1B.

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 MATH1972 or MATH1962 or MATH1003 or MATH1023 or MATH1005 or MATH1015
Assumed knowledge
? 

Knowledge of complex numbers and methods of differential and integral calculus including integration by partial fractions and integration by parts as for example in MATH1021 or MATH1921 or MATH1931 or MATH1061 or HSC Mathematics Extension 2

Available to study abroad and exchange students

No

Teaching staff

Coordinator Zhou Zhang, zhou.zhang@sydney.edu.au
Lecturer(s) Tiangang Cui, tiangang.cui@sydney.edu.au
Brad Roberts, brad.roberts@sydney.edu.au
Jack Freestone, jfre0619@uni.sydney.edu.au
Zhou Zhang, zhou.zhang@sydney.edu.au
The census date for this unit availability is 2 September 2024
Type Description Weight Due Length
Supervised exam
? 
Final exam
Multiple choice and written calculations and explanations.
60% Formal exam period 2 hours
Outcomes assessed: LO1 LO2 LO3 LO4 LO6 LO7 LO8
Small test Webwork quizzes and RQuizzes
#earlyfeedbacktask
2% Week 03
Due date: 18 Aug 2024 at 23:59

Closing date: 18 Aug 2024
40 minutes/week
Outcomes assessed: LO1
Short release assignment Assignment 1
written calculations, computational data analysis
5% Week 04
Due date: 25 Aug 2024 at 23:59

Closing date: 04 Sep 2024
2-4 pages and an R markdown report
Outcomes assessed: LO1 LO2 LO3 LO5 LO8 LO9
Online task Quiz
Multiple choice or short answer question
15% Week 07
Due date: 11 Sep 2024 at 23:59

Closing date: 11 Sep 2024
50 minutes
Outcomes assessed: LO1 LO8 LO5 LO3
Short release assignment Assignment 2
written mathematical problem solving, computational data analysis
10% Week 10
Due date: 13 Oct 2024 at 23:59

Closing date: 23 Oct 2024
6-8 pages and an R markdown report
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO9
Small test Webwork quizzes and RQuizzes
Weekly online quizzes
6% Weekly 40 minutes/week
Outcomes assessed: LO1 LO8 LO7 LO6 LO4 LO3
Participation Tutorials and labs
Participation in tutorials and labs
2% Weekly 2x50 minutes/week
Outcomes assessed: LO1 LO9 LO2

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.
  • Webwork Quizzes and RQuizzes: There are ten (equally weighted) weekly online Webwork quizzes and RQuizzes and the marks for the best eight in each quiz series count. The first two Webwork quizzes and RQuizzes 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 8% - i.e. if your overall exam mark is higher, then your 8% 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.
  • Tutorial/Lab Participation: This is a satisfactory/non-satisfactory mark assessing whether or not you participate in class activities during the tutorials and labs. It is 0.125 marks per tutorial class up to 8 calculus tutorials and up to 8 statistics labs (there are 12 calculus tutorials and 12 statistics labs).
  • 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.

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.

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
Week 01 Introduction to mathematical modelling and differential equations Lecture (1 hr) LO1 LO2 LO8 LO9
Graphical summaries Lecture (2 hr) LO1 LO2 LO3 LO5
Week 02 Separable equations and examples Lecture and tutorial (3 hr) LO1 LO2 LO8 LO9
Numerical summaries Lecture and tutorial (2 hr) LO1 LO2 LO3 LO5
Week 03 Applications of separable equations Lecture and tutorial (2 hr) LO1 LO2 LO8 LO9
Numerical summaries and normal model Lecture and tutorial (3 hr) LO1 LO2 LO3 LO5
Week 04 Linear differential equations Lecture and tutorial (3 hr) LO1 LO2 LO8 LO9
Linear models Lecture and tutorial (2 hr) LO1 LO2 LO4
Week 05 Second order linear differential equations Lecture and tutorial (2 hr) LO1 LO2 LO8 LO9
Linear models, understanding chance and variability Lecture and tutorial (3 hr) LO1 LO2 LO3 LO4 LO5
Week 06 Inhomogeneous and linear systems of differential equations Lecture and tutorial (3 hr) LO1 LO2 LO8 LO9
Understanding chance and variability Lecture and tutorial (2 hr) LO1 LO2 LO3 LO4 LO5
Week 07 Curves and surfaces in 3D Lecture and tutorial (2 hr) LO1 LO2 LO6
Understanding chance and variability Lecture and tutorial (3 hr) LO1 LO2 LO3 LO4 LO5
Week 08 Partial derivatives, tangent planes, differentials Lecture and tutorial (3 hr) LO1 LO2 LO6 LO7 LO9
The Central Limit theorem, confidence intervals Lecture and tutorial (2 hr) LO1 LO2 LO4
Week 09 Directional derivatives and chain rule Lecture and tutorial (2 hr) LO1 LO2 LO6 LO7 LO9
Test for a proportion Lecture and tutorial (3 hr) LO1 LO2 LO4 LO5
Week 10 Implicit differentiation and gradient vectors Lecture and tutorial (3 hr) LO1 LO2 LO6 LO7 LO9
Test for a mean and tests for relationships Lecture and tutorial (2 hr) LO1 LO2 LO4 LO5
Week 11 Higher-order derivatives Lecture and tutorial (2 hr) LO1 LO2 LO6 LO7 LO9
Test for a difference of two proportions Lecture and tutorial (3 hr) LO1 LO2 LO4 LO5
Week 12 Optimisation of functions of two variables Lecture and tutorial (3 hr) LO1 LO2 LO7 LO9
Chi-squared tests and p-values Lecture and tutorial (2 hr) LO1 LO2 LO4 LO5
Week 13 Revision Lecture and tutorial (5 hr) LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9

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/lab attendance: Tutorials and labs (one each per week) start in Week 2. You should attend the tutorial and lab given on your personal timetable. Attendance at tutorials and labs and participation will be recorded to determine the participation mark. Your attendance will not be recorded unless you attend the tutorial or lab in which you are enrolled. We strongly recommend you attend tutorials and labs regularly to keep up with the material and to engage with the tutorial questions. 

 

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

  • Course Notes for MATH1023 Multivariable Calculus and Modelling (available on Canvas).

  • There are no required readings for statistics. However, we will loosely follow Statistics, Freedman, Pisani, and Purves (2007). Examples of how to get access to the text book:

  • E-text ($65): www.wileydirect.com.au/buy/statistics-4th-international-student-edition
  • Library
  • 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 statistical thinking to solve problems
  • LO2. express mathematical and statistical ideas and arguments coherently in written form
  • LO3. identify 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 three dimensions as equations in Cartesian coordinates and interpret functions of two variables as surfaces in three-dimensional Cartesian space
  • 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. create 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

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.

No changes have been made since this unit was last 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.

  • Labs: Labs are small classes in which you are expected to work through questions from the tutorial sheet.

  • Tutorial and exercise sheets: The question sheets for a given week will be available on the MATH1062 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.