Outline

Overview

The Mathematics Special Studies Program is for students with exceptional mathematical aptitude, and requires outstanding performance in past mathematical studies. Students will cover the material of MATH1921 Calculus of One Variable (Adv), and attend a weekly seminar covering special topics on available elsewhere in the Mathematics and Statistics program.

Unit details and rules

Unit code	MATH1931
Academic unit	Mathematics and Statistics Academic Operations
Credit points	3
Prohibitions ?	MATH1001 or MATH1011 or MATH1901 or ENVX1001 or MATH1906 or MATH1021 or MATH1921
Prerequisites ?	None
Corequisites ?	None
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)	Sharon Stephen, sharon.stephen@sydney.edu.au
	Florica-Corina Cirstea, florica.cirstea@sydney.edu.au
	Daniel Daners, daniel.daners@sydney.edu.au
	Alexander Fish, alexander.fish@sydney.edu.au

Type	Description	Weight	Due	Length
Final exam (Record+)	Final exam written calculations and multiple choice	60%	Formal exam period	1.5 hours
Outcomes assessed:
Assignment	Assignment 1 Written calculations	4%	Week 03 Due date: 18 Mar 2021 at 23:59 Closing date: 28 Mar 2021	10 days
Outcomes assessed:
Assignment	Special assignment 1 written calculations	3%	Week 06 Due date: 15 Apr 2021 at 23:59 Closing date: 25 Apr 2021	10 days
Outcomes assessed:
Online task	Tutorial Quiz 1 Written calculations	9%	Week 07 Due date: 19 Apr 2021 at 23:59 Closing date: 19 Apr 2021	40 Minutes
Outcomes assessed:
Assignment	Assignment 2 Written calculations	4%	Week 09 Due date: 06 May 2021 at 23:59 Closing date: 16 May 2021	10 days
Outcomes assessed:
Assignment	Special assignment 2 written calculations	3%	Week 10 Due date: 13 May 2021 at 23:59 Closing date: 23 May 2021	10 days
Outcomes assessed:
Online task	Tutorial Quiz 2 Written calculations	9%	Week 12 Due date: 24 May 2021 at 23:59 Closing date: 24 May 2021	40 Minutes
Outcomes assessed:
Assignment	Special assignment 3 written calculations	3%	Week 13 Due date: 03 Jun 2021 at 23:59 Closing date: 13 Jun 2021	10 days
Outcomes assessed:
Participation	Weekly seminar participation Seminar participation	5%	Weekly	50 minutes
Outcomes assessed:
= Type B final exam ?

Assessment summary

Assignments and Special Assignments: Students must submit the assignments electronically, as PDF files 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 (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.
Quizzes: Quizzes will be held online in Canvas. The quizzes are 40 minutes.
Better mark principle: 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.
Special assignments: The better mark principle with apply for the Special Assignment component (9%) if all Special Assignments are submitted.
Seminar participation: This is a satisfactory/non-satisfactory mark assessing whether or not you participate in class and group discussions during the seminars. It is 0.5 marks per seminar session up to 10 sessions (there are 12 sessions).

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	At High-distinction level, a student demonstrates a flair for the subject as well as a detailed and comprehensive understanding of the unit material. A ‘High Distinction’ reflects exceptional achievement and is awarded to a student who demonstrates the ability to apply their subject knowledge and understanding to produce original solutions for novel or highly complex problems and/or comprehensive critical discussions of theoretical concepts.
Distinction	75 - 84	At Distinction level, a student demonstrates an aptitude for the subject and a welldeveloped understanding of the unit material. A ‘Distinction’ reflects excellent achievement and is awarded to a student who demonstrates an ability to apply their subject knowledge and understanding of the subject to produce good solutions for challenging problems and/or a reasonably well-developed critical analysis of theoretical concepts.
Credit	65 - 74	At CR level, a student demonstrates a good command and knowledge of the unit material. A ‘Credit’ reflects solid achievement and is awarded to a student who has a broad general understanding of the unit material and can solve routine problems and/or identify and superficially discuss theoretical concepts.
Pass	50 - 64	At PS level, a student demonstrates proficiency in the unit material. A ‘Pass’ reflects satisfactory achievement and is awarded to a student who has threshold knowledge.
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.

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
Multiple weeks	Special Topic 1	Seminar (1 hr)
	Special Topic 2	Seminar (1 hr)
	Special Topic 3	Seminar (1 hr)
Week 01	Complex numbers in Cartesian and polar form. Complex powers and De Moivre's Theorem.	Lecture (2 hr)
Week 02	The complex exponential function, n-th roots. Representing complex functions.	Lecture and tutorial (3 hr)
Week 03	Injective and bijective functions. Inverse functions. Hyperbolic functions.	Lecture and tutorial (3 hr)
Week 04	Limits and the limit laws.	Lecture and tutorial (3 hr)
Week 05	Continuity. Intermediate Value Theorem.	Lecture and tutorial (3 hr)
Week 06	Differentiability. Rolle's Theorem and the Mean Value Theorem.	Lecture and tutorial (3 hr)
Week 07	Cauchy's Mean Value Theorem and L'Hopital's Rule.	Lecture and tutorial (3 hr)
Week 08	Taylor polynomials with remainder. Taylor series of standard functions.	Lecture and tutorial (3 hr)
Week 09	Evaluation of Riemann sums. Definition of the Riemann integral.	Lecture and tutorial (3 hr)
Week 10	Fundamental Theorem of Calculus. Functions defined by integrals.	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 12	Improper integrals. Integrals of unbounded functions. Integrals over unbounded intervals. Comparison tests.	Lecture and tutorial (3 hr)
Week 13	overflow and revision	Lecture and tutorial (3 hr)

Attendance and class requirements

Due to the exceptional circumstances caused by the COVID-19 pandemic, attendance requirements for this unit of study have been amended. Where online tutorials/workshops/virtual laboratories have been scheduled, students should make every effort to attend and participate at the scheduled time. Penalties will not be applied if technical issues, etc. prevent attendance at a specific online class. In that case, students should discuss the problem with the coordinator, and attend another session, if available.

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.

Required readings

Course notes for MATH1921/MATH1931 Calculus of One Variable (Advanced) are available for purchase from Kopystop, 55 Mountain St, Broadway.

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 rigor to solving problems, and express mathematical ideas coherently using precise mathematical language.
LO2. understand new mathematical concepts beyond routine methods and calculations
LO3. demonstrate fluency in the mathematical manipulation of complex numbers and functions, including concepts of surjectivity, injectivity and inverse functions
LO4. understand and be able to use fundamental properties of continuous and differentiable functions including limits, limit laws, intermediate and extreme value theorems as well as mean value theorems and applications
LO5. work with Taylor polynomial approximations and Taylor series representations of functions including dealing with remainder estimates
LO6. demonstrate an understanding of the definition and computation or estimation of definite, indefinite and improper Riemann integrals including proficiency in using integration methods without too much guidance
LO7. understand and be able to use the relationships between integral and differential calculus via the Fundamental Theorem of Calculus
LO8. apply concepts of calculus to a variety of contexts and applications
LO9. gain an appreciation of a diverse range of mathematical problems and applications through participating in class discussions and the completion of assignments

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.

Minor changes made to assessment weightings. A seminar participation mark introduced.

Additional information

Tutorial and Exercise Sheets: The question sheets for a given week will be available through Canvas. Solutions to tutorial exercises for week n will usually be posted on the web by the afternoon of the Friday on week n.
Ed Discussion forum:‭ ‬https://edstem.org
Please check the Canvas site for this unit for any other information.

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

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

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

MATH1931: Calculus Of One Variable (SSP)

Semester 1, 2021 [Normal day] - Camperdown/Darlington, Sydney

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

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