This course is intended both for continuing mathematics students 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: Graduate students attend joint classes with undergraduates but will be assessed separately.

Learning Outcomes

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.

Research-Led Teaching

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.

Staff Feedback

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

Student Feedback

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.

Other Information

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

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Complex numbers and differentiability
2	Conformal maps
3	Mobius transformations and integration	Assignment 1 due
4	Primitives and homotopy
5	Cauchy's theorems
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
10	Harmonic functions
11	Analytic continuation and the Riemann mapping theorem
12	The Riemann mapping theorem (continued)	Assignment 4 due

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Written assignments (60%)	60 %	14/08/2020	06/11/2020	1,2,3,4
Final exam (40%)	40 %	05/11/2020	03/12/2020	1,2,3,4

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

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:

• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Policy and General Information 
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure

Assessment Requirements

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.

Examination(s)

There will be a final exam. The exam may contain additional or modified questions relative to the co-taught course MATH3228.

Assessment Task 1

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 2020-08-14 (end of week 3), returned approximately 2020-08-21

* Assignment 2: Due 2020-09-04 (end of week 6), returned approximately 2020-09-11

* Assignment 3: Due 2020-10-09 (end of week 9), returned approximately 2020-10-16

* Assignment 4: Due 2020-10-30 (end of week 12), returned approximately 2020-11-06

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.

Assignments for MATH6213 may contain additional exercises relative to those for the co-taught course MATH3228.

Assessment Task 2

Final exam (40%)

The final exam will be a cumulative written assessment. 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. 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

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.

Online Submission

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. Unless an exemption has been approved by the Associate Dean (Education) submission must be through Turnitin.

Hardcopy Submission

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

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).

Referencing Requirements

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.

Returning Assignments

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.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service – including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

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