MATHS 735 : Analysis on Manifolds and Differential Geometry
2022 Semester One (1223) (15 POINTS)
Capabilities Developed in this Course
|Capability 1:||Disciplinary Knowledge and Practice|
|Capability 2:||Critical Thinking|
|Capability 3:||Solution Seeking|
|Capability 4:||Communication and Engagement|
|Capability 5:||Independence and Integrity|
- Understand that the subject combines ideas from analysis and geometry and that the geometric aspect imparts some rigidity to the structure (Capability 1 and 2)
- Understand how local analysis and geometry impacts on global structure (Capability 1, 2, 3, 4 and 5)
- Know how to design and execute proofs of theorems in this area (Capability 1, 2, 3, 4 and 5)
- know apply the knowledge to other areas such as complex analysis and theoretical physics (Capability 1, 2 and 4)
- Have a working knowledge of the basic tools of differential geometry, including differential manifolds, forms fields and tensors (Capability 1, 3 and 4)
- Have knowledge of how to combine tools and techniques from many different areas of mathematics in order to prove new results and obtain a heightened level of understanding (Capability 1, 2, 3 and 4)
|Final Exam||60%||Individual Coursework|
|Assessment Type||Learning Outcome Addressed|
Analytic Euclidean geometry
Curves - some general theory and tools
The local theory of plane curves and space curves
Plane curves - global theory
The local theory of immersed surfaces
The intrinsic geometry of surfaces
Riemannian geometry (- especially in two dimensions)
The global geometry of surfaces
This course is a standard  point course and students are expected to spend 10 hours per week involved in each 15 point course that they are enrolled in.
For this course, you can expect  hours of lectures,  hours of reading and thinking about the content and  hours of work on assignments and/or test preparation.
Attendance is expected at scheduled activities.
The course will not include live online events.
Attendance on campus is required for the exam.
The activities for the course are scheduled as a standard weekly timetable.
Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).
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During the course Class Representatives in each class can take feedback to the staff responsible for the course and staff-student consultative committees.
At the end of the course students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback.
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If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page https://www.auckland.ac.nz/en/students/academic-information/exams-and-final-results/during-exams/aegrotat-and-compassionate-consideration.html.
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In the event of an unexpected disruption, we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and course assessment continues to meet the principles of the University’s assessment policy. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator/director, and if disruption occurs you should refer to the university website for information about how to proceed.
The delivery mode may change depending on COVID restrictions. Any changes will be communicated through Canvas.
Student Charter and Responsibilities
The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter https://www.auckland.ac.nz/en/students/forms-policies-and-guidelines/student-policies-and-guidelines/student-charter.html.
Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.
In this course students may be asked to submit coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. In exceptional circumstances changes to elements of this course may be necessary at short notice. Students enrolled in this course will be informed of any such changes and the reasons for them, as soon as possible, through Canvas.