PURE MTH 7054 - Complex Analysis
North Terrace Campus - Semester 1 - 2015
-
General Course Information
Course Details
Course Code PURE MTH 7054 Course Complex Analysis Coordinating Unit Pure Mathematics Term Semester 1 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Contact Up to 3 hours per week Available for Study Abroad and Exchange Y Prerequisites MATHS 2100 or MATHS 2101 or MATHS 2202 Assumed Knowledge MATHS 2101 or MATHS 2202 Assessment ongoing assessment 30%, exam 70% Course Staff
Course Coordinator: Dr Melissa Tacy
Course Timetable
The full timetable of all activities for this course can be accessed from Course Planner.
-
Learning Outcomes
Course Learning Outcomes
- Demonstrate an understanding of the fundamental concepts of complex analysis.
- Demonstrate an understanding of the application of the theory both to other mathematical areas and to physics and engineering.
- Prove the basic results relating to holomorphic functions.
- Apply the theory learnt in the course to solve a variety of problems at an appropriate level of difficulty.
- Demonstrate skills in communicating mathematics orally and in writing.
University Graduate Attributes
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
University Graduate Attribute Course Learning Outcome(s) Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. 1,2,3,4,5 The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner. 2,3,4 An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. 4 Skills of a high order in interpersonal understanding, teamwork and communication. 5 A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. 1,2,3,4,5 An awareness of ethical, social and cultural issues within a global context and their importance in the exercise of professional skills and responsibilities. 4,5 -
Learning Resources
Required Resources
None.Recommended Resources
The course will loosely follow E. M. Stein and R. Shakarchi, Complex Analysis (available to us as an e-book).
Other resources you may wish to use are:
J. Bak and D. J. Newman, Complex Analysis (available as an e-book).
T. W. Gamelin, Complex Analysis.
R. E. Greene and S. G. Krantz, Function theory of one complex variable.Online Learning
Assignments, tutorial exercises, handouts, and course announcements will be posted on MyUni. -
Learning & Teaching Activities
Learning & Teaching Modes
The lecturer guides the students through the course material in 30 lectures. Students are expected to engage with the material in the lectures. Interaction with the lecturer and discussion of any difficulties that arise during the lecture is encouraged and attendance at the lecturer's consultation hour is particularly encouraged. Students are expected to attend all lectures, but lectures will be recorded to help with occasional absences and for revision purposes. In fortnightly tutorials students will work through exercises designed to practise their skills. Fortnightly homework assignments help students strengthen their understanding of the theory and their skills in applying it, and allow them to gauge their progress.Workload
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload Hours Lectures 30 100 Tutorials 4 16 Assignments 5 40 Total 156 Learning Activities Summary
Lecture Schedule Week 1 The complex numbers and the complex plane. Continuity and complex differentiation. Week 2 Holomorphic functions and power series. Integration along curves. Week 3 Goursat's theorem. Cauchy's theorem. Week 4 Cauchy's integral formula and consequences, Liouville's theorem. Week 5 Zeros and poles of holomorphic functions, residues. Week 6 The residue formula and applications, Morera's theorem. Week 7 Classfication of singularities and Laurent series. Week 8 Rouche's theorem, the maximum principle and applications. Week 9 Transformations of the complex plane. Week 10 The Riemann sphere. Generalisations to simply connected regions. Week 11 The complex logarithm, Riemann mapping theorem. Week 12 Connections to harmonic functions and PDE.
Tutorials in Weeks 3, 5, 9, and 11 cover the material of the previous two weeks. -
Assessment
The University's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
- Assessment must maintain academic standards.
Assessment Summary
Assessment Task Task Type Due Weighting Learning Outcomes Exam Summative Examination Period 70% All Test Summative Week 7 10% All Assignments Formative and summative Weeks 4, 6, 8, 10, and 12 20% All Assessment Related Requirements
An aggregate score of 50% is required to pass the course.Assessment Detail
Assessment Set Due Weighting Assignment 1 Week 3 Week 4 4% Assignment 2 Week 5 Week 6 4% Assignment 3 Week 7 Week 8 4% Assignment 4 Week 9 Week 10 4% Assignment 5 Week 11 Week 12 4% Submission
Homework assignments must be submitted on time with a signed assessment cover sheet. Late assignments will not be accepted. Assignments will be returned within two weeks. Students may be excused from an assignment for medical or compassionate reasons. Documentation is required and the lecturer must be notified as soon as possible.Course Grading
Grades for your performance in this course will be awarded in accordance with the following scheme:
M10 (Coursework Mark Scheme) Grade Mark Description FNS Fail No Submission F 1-49 Fail P 50-64 Pass C 65-74 Credit D 75-84 Distinction HD 85-100 High Distinction CN Continuing NFE No Formal Examination RP Result Pending Further details of the grades/results can be obtained from Examinations.
Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.
Final results for this course will be made available through Access Adelaide.
-
Student Feedback
The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.
SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.
-
Student Support
- Academic Integrity for Students
- Academic Support with Maths
- Academic Support with writing and study skills
- Careers Services
- International Student Support
- Library Services for Students
- LinkedIn Learning
- Student Life Counselling Support - Personal counselling for issues affecting study
- Students with a Disability - Alternative academic arrangements
- YouX Student Care - Advocacy, confidential counselling, welfare support and advice
-
Policies & Guidelines
This section contains links to relevant assessment-related policies and guidelines - all university policies.
- Academic Credit Arrangements Policy
- Academic Integrity Policy
- Academic Progress by Coursework Students Policy
- Assessment for Coursework Programs Policy
- Copyright Compliance Policy
- Coursework Academic Programs Policy
- Elder Conservatorium of Music Noise Management Plan
- Intellectual Property Policy
- IT Acceptable Use and Security Policy
- Modified Arrangements for Coursework Assessment Policy
- Reasonable Adjustments to Learning, Teaching & Assessment for Students with a Disability Policy
- Student Experience of Learning and Teaching Policy
- Student Grievance Resolution Process
-
Fraud Awareness
Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's student’s disciplinary procedures.
The University of Adelaide is committed to regular reviews of the courses and programs it offers to students. The University of Adelaide therefore reserves the right to discontinue or vary programs and courses without notice. Please read the important information contained in the disclaimer.
