Note: This is an archived Handbook entry from 2015.
|Dates & Locations:|| |
This subject has the following teaching availabilities in 2015:Semester 2, Parkville - Taught on campus.
Timetable can be viewed here. For information about these dates, click here.
|Time Commitment:||Contact Hours: 36 hours comprising one 2-hour lecture and one 1-hour lecture per week. |
Total Time Commitment:
The following, or equivalent:
Study Period Commencement:
Semester 1, Semester 2
|Recommended Background Knowledge:||None|
|Non Allowed Subjects:||None|
|Core Participation Requirements:||
For the purposes of considering request for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Student Support and Engagement Policy, academic requirements for this subject are articulated in the Subject Overview, Learning Outcomes, Assessment and Generic Skills sections of this entry.
It is University policy to take all reasonable steps to minimise the impact of disability upon academic study, and reasonable adjustments will be made to enhance a student's participation in the University's programs. Students who feel their disability may impact on meeting the requirements of this subject are encouraged to discuss this matter with a Faculty Student Adviser and Student Equity and Disability Support: http://services.unimelb.edu.au/disability
CoordinatorProf Christian Haesemeyer
Riemann surfaces arise from complex analysis. They are central in mathematics, appearing in seemingly diverse areas such as differential and algebraic geometry, number theory, integrable systems, statistical mechanics and string theory.
The first part of the subject studies complex analysis. It assumes students have completed a first course in complex analysis so begins with a quick review of analytic functions and Cauchy's theorem, emphasising topological aspects such as the argument principle and Rouche's theorem.
Topics also include: Schwarz's lemma; limits of analytic functions, normal families, Riemann mapping theorem; multiple-valued functions, differential equations and Riemann surfaces. The second part of the subject studies Riemann surfaces and natural objects on them such as holomorphic differentials and quadratic differentials.
Topics may also include: divisors, Riemann-Roch theorem; the moduli space of Riemann surfaces, Teichmueller space; integrable systems.
After completing this subject, students will gain an understanding of:
Assignments during the semester (60%), a 2-hour end-of-semester exam in the examination period (40%).
|Prescribed Texts:|| |
Ahlfors, Lars V. Complex analysis. An introduction to the theory of analytic functions of one complex variable. Third edition. International Series in Pure and Applied Mathematics. McGraw-Hill Book Co., New York, 1978.
|Breadth Options:|| |
This subject is not available as a breadth subject.
|Fees Information:||Subject EFTSL, Level, Discipline & Census Date|
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
Master of Philosophy - Engineering |
Master of Science (Mathematics and Statistics)
Mathematics and Statistics |
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