- Class Number 6231
- Term Code 3160
- Class Info
- Unit Value 6 units
- Mode of Delivery In Person
- Dr James Tener
- Dr James Tener
- Class Dates
- Class Start Date 26/07/2021
- Class End Date 29/10/2021
- Census Date 14/09/2021
- Last Date to Enrol 02/08/2021
This course is intended both for mathematics students continuing to honours work and for other students using mathematics at a high level in theoretical physics, engineering and information technology, and mathematical economics.
Topics to be covered include:
Complex differentiability, conformal mapping; complex integration, Cauchy integral theorems, Taylor series representation, isolated singularities, residue theorem and applications to real integration. Topics chosen from: argument principle, Riemann surfaces, theorems of Picard, Weierstrass and Mittag-Leffler.
Note: This is an HPC. It emphasises mathematical rigour and proof and develops the material from an abstract viewpoint.
Upon successful completion, students will have the knowledge and skills to:
On satisfying the requirements of this course, students will have the knowledge and skills to:
1. Explain the fundamental concepts of complex analysis and their role in modern mathematics and applied contexts
2. Demonstrate accurate and efficient use of complex analysis techniques
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from complex analysis
4. Apply problem-solving using complex analysis techniques applied to diverse situations in physics, engineering and other mathematical contexts.
The complex analysis techniques which students will learn in this course represent essential tools in the modern study of diverse fields of mathematics, physics, and engineering. Topics will be selected to maximise students’ preparation for undertaking research in these fields, and problems related to the instructors research will be discussed (time permitting).
Examination Material or equipment
Information will be available on Wattle
Recommended student system requirements
ANU courses commonly use a number of online resources and activities including:
- video material, similar to YouTube, for lectures and other instruction
- two-way video conferencing for interactive learning
- email and other messaging tools for communication
- interactive web apps for formative and collaborative activities
- print and photo/scan for handwritten work
- home-based assessment.
To fully participate in ANU learning, students need:
- A computer or laptop. Mobile devices may work well but in some situations a computer/laptop may be more appropriate.
- Speakers and a microphone (e.g. headset)
- Reliable, stable internet connection. Broadband recommended. If using a mobile network or wi-fi then check performance is adequate.
- Suitable location with minimal interruptions and adequate privacy for classes and assessments.
- Printing, and photo/scanning equipment
For more information please see https://www.anu.edu.au/students/systems/recommended-student-system-requirements
Students will be given feedback in the following forms in this course:
- written comments, e.g. on submitted assignments
- verbal comments, e.g. in office hours
ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.
Please note, that where there are multiple assessment tasks of the same type, e.g weekly quizzes, a date range is used in the Assessment Summary. The first date is the approximate due date of the first task, the return date is the approximate return date for the final task. Further information is provided in the assessment section of the class summary, and details are provided on the course wattle site
|Week/Session||Summary of Activities||Assessment|
|1||Complex numbers and differentiability|
|3||Mobius transformations and integration||Assignment 1 due|
|4||Primitives and homotopy|
|6||Power series||Assignment 2 due|
|7||Laurent series and isolated singularities|
|8||Residues and contour integration|
|9||Schwarz's lemma and compact families||Assignment 3 due|
|11||Analytic continuation and the Riemann mapping theorem|
|12||The Riemann mapping theorem (continued)||Assignment 4 due|
|Assessment task||Value||Due Date||Return of assessment||Learning Outcomes|
|Written assignments (60%)||60 %||13/08/2021||06/11/2020||1,2,3,4|
|Final exam (40%)||40 %||04/11/2021||02/12/2021||1,2,3,4|
* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details
ANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:
The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the Academic Integrity . In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.
Moderation of Assessment
Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.
There is a final examination.
Assessment Task 1
Learning Outcomes: 1,2,3,4
Written assignments (60%)
Students will complete four written assignments which will re-enforce and extend the material covered in class. The relevant dates are:
* Assignment 1: Due 2021-08-13 (end of week 3), returned approximately 2021-08-27
* Assignment 2: Due 2021-09-03 (end of week 6), returned approximately 2021-09-17
* Assignment 3: Due 2021-10-08 (end of week 9), returned approximately 2021-10-22
* Assignment 4: Due 2021-10-29 (end of week 12), returned approximately 2021-11-12
Late assignments will be penalised at a rate of 5% of available marks per working day or part thereof. Late assignments will not be accepted after the assignment has been reviewed in class, which will generally be the next class period after the due date.
Assessment Task 2
Learning Outcomes: 1,2,3,4
Final exam (40%)
The final exam is a hurdle assessment. Students not obtaining a mark of 40% on the final exam, but who would otherwise earn a passing grade in the course (at least 50% overall), will be offered a supplementary examination. If they score 40% or higher on the supplementary examination, they will be given a mark of 50PS, and otherwise they will be given a mark of NCN.
In the event of remote administration of exams, oral validation exams may be used to validate final exam performance. Students will be selected for validation exams if there are irregularities in the taking or submission of the exam, if the convener believes there is a significant discrepancy between the exam and other coursework, or if selected by a random process. If there is a significant discrepancy between final exam performance and validation exam performance, students may have their mark adjusted or be asked to take a re-examination.
Academic integrity is a core part of the ANU culture as a community of scholars. At its heart, academic integrity is about behaving ethically, committing to honest and responsible scholarly practice and upholding these values with respect and fairness.
The ANU commits to assisting all members of our community to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to be familiar with the academic integrity principle and Academic Misconduct Rule, uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with.
The Academic Misconduct Rule is in place to promote academic integrity and manage academic misconduct. Very minor breaches of the academic integrity principle may result in a reduction of marks of up to 10% of the total marks available for the assessment. The ANU offers a number of online and in person services to assist students with their assignments, examinations, and other learning activities. Visit the Academic Skills website for more information about academic integrity, your responsibilities and for assistance with your assignments, writing skills and study.
You will be required to electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records.
For some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.
Late submission of assignments is permitted. Late submission of assignments without an extension are penalised at the rate of 5% of the possible marks available per working day or part thereof. Late submission of assessment tasks is not accepted after 10 working days after the due date, on or after the date specified in the course outline for the return of the assessment item, or after the assignment has been reviewed in class (which will generally occur in the first class period following the due date).
Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.
Student work will be returned electronically with feedback.
Extensions and Penalties
Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.
Distribution of grades policy
Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.
Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.
Support for students
The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).
- ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
- ANU Diversity and inclusion for students with a disability or ongoing or chronic illness
- ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
- ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
- ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
- ANUSA supports and represents undergraduate and ANU College students
- PARSA supports and represents postgraduate and research students
Conformal field theory, subfactors, operator algebas, vertex operator algebras, fusion categories
Dr James Tener