PURE MTH 7108 - Geometry of Surfaces
North Terrace Campus - Semester 2 - 2015
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General Course Information
Course Details
Course Code PURE MTH 7108 Course Geometry of Surfaces Coordinating Unit Pure Mathematics Term Semester 2 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 assessment 30%, exam 70% Course Staff
Course Coordinator: Dr Stuart Johnson
Course Timetable
The full timetable of all activities for this course can be accessed from .
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Learning Outcomes
Course Learning Outcomes
1. Understand basic topology and differentiation in R^n.
2. Understand and be able to apply the inverse and implicit function theorems.
3. Understand and be able to work with submanifolds in their various forms.
4. Understand and be able to calculate with the geometry of curves.
5. Understand and be able to calculate with the geometry of surfaces.
6. Understand integration on surfaces and be able to calculate such integrals.
7. Understand the Gauss-Bonnet theorem and be able to apply it.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. all An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. all -
Learning Resources
Required Resources
None.Recommended Resources
- Manfredo de Carmo: Differential Geometry of Curves and Surfaces 514.75 C287
- John A. Thorpe: Elementary Topics in Differential Geometry 514.7 T519e
- Baxandall, Peter and Liebeck, Hans: Vector Calculus 517.2 B355v
- Lipshutz, Martin: Shaum's Outline of Theory and Problems of Differential Geometry 513.73 L767
- Gray, Alfred: Modern Differential Geometry of Curves and Surfaces 514.7 G778m
Online Learning
This course uses MyUni exclusively for providing electronic resources, such as lecture notes, assignment papers, sample solutions, discussion boards, etc. It is recommended that the students make appropriate use of these resources. Link to MyUni login page:https://myuni.adelaide.edu.au/webapps/login/ -
Learning & Teaching Activities
Learning & Teaching Modes
This course relies on lectures as the primary delivery mechanism for the material. Tutorials supplement the lectures by providing exercises and example problems to enhance the understanding obtained through lectures. A sequence of written assignments provides assessment
opportunities for students to gauge their progress and understanding.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 90 Tutorials 6 22 Assignments 5 44 Total 156 Learning Activities Summary
Lecture Outline
1. Introduction and review of topology on R^n (2 lectures)
2. Differentiable functions on R^n (5 lectures)
3. Inverse and implicit function theorems (3 lectures)
4. Submanifolds (4 lectures)
5. Curves (3 lectures)
6. Surfaces (3 lectures)
7. Integration on submanifolds (7 lectures)
8. Gauss-Bonnet theorem (3 lectures)
Tutorial Outline
1. Topology and differentiation in R^n
2. Inverse and implicit function theorems
3. Submanifolds
4. Curves and surfaces
5. Integration on submanifolds
6. Gauss Bonnet theorem and reviewSpecific Course Requirements
None. -
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 Weighting Objective Assessed Assignments 15% all Mid Semester Test 10% all Tutorial Participation 5% all Exam 70% all Assessment Related Requirements
An aggregate score of at least 50% is required to pass the course.Assessment Detail
Assessment Item Due Weighting Assignment 1 Week 3 3% Assignment 2 Week 5 3% Assignment 3 Week 7 3% Assignment 4 Week 9 3% Assignment 5 Week 11 3% Test Week 6 10% Submission
1. All written assignments are to be submitted to the designated hand in boxes within the School of Mathematical Sciences with a signed
cover sheet attached.
2. Late assignments will not be accepted.
3. Assignments will have a two week turn-around time for feedback to students.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 .
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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.
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Student Support
- Academic Integrity for Students
- Academic Support with Maths
- Academic Support with writing and study skills
- Careers Services
- Library Services for Students
- LinkedIn Learning
- Student Life Counselling Support - Personal counselling for issues affecting study
- Students with a Disability - Alternative academic arrangements
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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
- 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
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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鈥檚 disciplinary procedures.
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