最新糖心Vlog

PURE MTH 4122 - Geometry of Surfaces - Honours

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 4122
    Course Geometry of Surfaces - Honours
    Coordinating Unit 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 or MATHS 2101 or MATHS 2202
    Assumed Knowledge MATHS 2101 or MATHS 2202
    Restrictions Honours students only
    Biennial Course Course offered in odd years
    Assessment Ongoing assessment, exam
    Course Staff

    Course Coordinator: Dr Stuart Johnson

    Course Timetable

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

  • Learning Outcomes
    Course Learning Outcomes
    1. Understand basic topology and differentiation in R^n.

    2. Understand and be able to calculate with the geometry of curves.

    3. Understand and be able to apply the inverse and implicit function theorems.

    4. Understand and be able to work with the equivalent definitions of surfaces.

    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.
    最新糖心Vlog Graduate Attributes

    This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

    最新糖心Vlog 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
    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
    Lipschutz, Martin: Schaum'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.


    ActivityQuantityWorkload Hours
    Lectures 30 90
    Tutorials 6 18
    Assignments 4 40
    Tests 2 8
    Total 156
    Learning Activities Summary

    Lecture Outline

    1. Review of topology and differentiable functions on R^n 

    2. Geometry of curves

    3. Definition of surfaces and the inverse function theorem.

    4. The geometry of surfaces

    5. Integration on surfaces.

    6. Gauss-Bonnet theorem


  • Assessment

    The 最新糖心Vlog'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 16% all
    Mid Semester Tests 10% all
    Tutorial Preparation (Quizzes) 4% all
    Exam 70% all
    Assessment Related Requirements
    An aggregate score of at least 50% is required to pass this course.  
    Assessment Detail

    Assessment Item Due Weighting
    Assignment 1 Week 3 4%
    Assignment 2 Week 6 4%
    Assignment 3 Week 9 4%
    Assignment 4 Week 12 4%
    Test 1 Week 5 5%
    Test 2 Week 9 5%
    Quizzes Even Weeks 4% total
    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:

    M11 (Honours Mark Scheme)
    GradeGrade reflects following criteria for allocation of gradeReported on Official Transcript
    Fail A mark between 1-49 F
    Third Class A mark between 50-59 3
    Second Class Div B A mark between 60-69 2B
    Second Class Div A A mark between 70-79 2A
    First Class A mark between 80-100 1
    Result Pending An interim result RP
    Continuing Continuing CN

    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 .

  • Student Feedback

    The 最新糖心Vlog 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 最新糖心Vlog 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
  • 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.

The 最新糖心Vlog of Adelaide is committed to regular reviews of the courses and programs it offers to students. The 最新糖心Vlog of Adelaide therefore reserves the right to discontinue or vary programs and courses without notice. Please read the important information contained in the disclaimer.