PURE MTH 3022 - Geometry of Surfaces III

North Terrace Campus - Semester 2 - 2019

The geometry of surfaces is a classical subject, dating back to the 19th century and the work of Gauss. It provides an excellent introduction to the ideas of contemporary differential geometry and Riemannian geometry. Topics covered are: The inverse and implicit function theorems; submanifolds of Rn; differential forms; Stokes' theorem for submanifolds of Rn. Curvature of curves and surfaces in R3; geodesics. The Gauss-Bonnet theorem. Surfaces of zero gaussian curvature; minimal surfaces.

  • General Course Information
    Course Details
    Course Code PURE MTH 3022
    Course Geometry of Surfaces III
    Coordinating Unit School of Mathematical Sciences
    Term Semester 2
    Level Undergraduate
    Location/s North Terrace Campus
    Units 3
    Contact Up to 3 hours per week
    Available for Study Abroad and Exchange Y
    Prerequisites MATHS 2100 0r MATHS 2101 or MATHS 2202
    Assumed Knowledge MATHS 2101 or MATHS 2202
    Course Description The geometry of surfaces is a classical subject, dating back to the 19th century and the work of Gauss. It provides an excellent introduction to the ideas of contemporary differential geometry and Riemannian geometry.

    Topics covered are: The inverse and implicit function theorems; submanifolds of Rn; differential forms; Stokes' theorem for submanifolds of Rn. Curvature of curves and surfaces in R3; geodesics. The Gauss-Bonnet theorem. Surfaces of zero gaussian curvature; minimal surfaces.
    Course Staff

    Course Coordinator: Dr Stuart Johnson

    Course Timetable

    The full timetable of all activities for this course can be accessed from Course Planner.

  • 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)
    Deep discipline knowledge
    • informed and infused by cutting edge research, scaffolded throughout their program of studies
    • acquired from personal interaction with research active educators, from year 1
    • accredited or validated against national or international standards (for relevant programs)
    all
    Critical thinking and problem solving
    • steeped in research methods and rigor
    • based on empirical evidence and the scientific approach to knowledge development
    • demonstrated through appropriate and relevant assessment
    all
  • Learning Resources
    Required Resources
    None.
    Recommended Resources
    1. Manfredo de Carmo: Differential Geometry of Curves and Surfaces 514.75 C287
    2. John A. Thorpe: Elementary Topics in Differential Geometry 514.7 T519e
    3. Baxandall, Peter and Liebeck, Hans: Vector Calculus 517.2 B355v
    4. Lipshutz, Martin: Shaum's Outline of Theory and Problems of Differential Geometry 513.73 L767
    5. 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.


    ActivityQuantityWorkload 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 review


    Specific Course Requirements
    None.
  • Assessment

    The University's policy on Assessment for Coursework Programs is based on the following four principles:

    1. Assessment must encourage and reinforce learning.
    2. Assessment must enable robust and fair judgements about student performance.
    3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
    4. 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
    Week 2
    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 electronically in MyUni

    2. The School of Maths Late assignment policy will apply, assignments submitted within 24 hours after the due date will receive 40% of the full grade which would otherwise be awarded. No submissions will be accepted after 24 hours.

    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 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
  • Policies & Guidelines
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