PURE MTH 7073 - Finite Geometry

North Terrace Campus - Semester 2 - 2018

Projective geometry is one of the important modern geometries introduced in the 19th century. Projective geometry is more general than our usual Euclidean geometry, and it has useful applications in Information Security, Statistics, Computer Graphics and Computer Vision. The majority of this course will be on projective planes. Topics covered are: projective planes, homogeneous coordinates, field planes, collineations of projective planes, conics in field planes, k-arcs in projective planes, projective geometry of general dimension, quadrics and ovoids in 3-dimensional projective space.

  • General Course Information
    Course Details
    Course Code PURE MTH 7073
    Course Finite Geometry
    Coordinating Unit Mathematical Sciences
    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 1012
    Assumed Knowledge PURE MTH 2106
    Biennial Course Offered in even years
    Assessment Examinations 70%, Ongoing assessment 30%
    Course Staff

    Course Coordinator: Dr Susan Barwick

    Course Timetable

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

  • Learning Outcomes
    Course Learning Outcomes
    1. Demonstrate a deep understanding of the axiomatic approach to projective spaces.
    2. Be able to perform calculations in Desarguesian planes and projective 3-spaces.
    3. Classify the structure of collineations of projective planes.
    4. Demonstrate an understanding of the theory of conics in field planes.
    5. Apply the theory to solve problems of varying levels of difficulty.
    6. Demonstrate skills in communicating mathematics orally and in writing.
    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)
    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
    Teamwork and communication skills
    • developed from, with, and via the SGDE
    • honed through assessment and practice throughout the program of studies
    • encouraged and valued in all aspects of learning
    Career and leadership readiness
    • technology savvy
    • professional and, where relevant, fully accredited
    • forward thinking and well informed
    • tested and validated by work based experiences
    Intercultural and ethical competency
    • adept at operating in other cultures
    • comfortable with different nationalities and social contexts
    • able to determine and contribute to desirable social outcomes
    • demonstrated by study abroad or with an understanding of indigenous knowledges
    Self-awareness and emotional intelligence
    • a capacity for self-reflection and a willingness to engage in self-appraisal
    • open to objective and constructive feedback from supervisors and peers
    • able to negotiate difficult social situations, defuse conflict and engage positively in purposeful debate
  • Learning Resources
    Required Resources
    Recommended Resources
    The material in the course is closely related to the text book:
    L.R.A. Casse, Projective Geometry, An Introduction.
    Online Learning
    This course uses MyUni exclusively for providing electronic resources, such as lecture notes, assignment papers, etc.
  • Learning & Teaching Activities
    Learning & Teaching Modes
    The lecturer guides the students through the course material in 30
    lectures. Students are expected to engage with the material in the
    lectures. Interaction with the lecturer and discussion of any
    difficulties that arise during the lecture is encouraged. Students are
    expected to attend all lectures. In fortnightly tutorials students work
    on assigned exercises and discuss them with the lecturer and each other.
    Fortnightly homework assignments help students strengthen their
    understanding of the theory and their skills in applying it, and allow
    them to gauge their progress. A flipped learning component provides an
    active learning environment when students prepare material before the
    lectures and during the lecture students work in small groups on
    assigned exercises. Further, online multiple choice quizzes are used to
    reinforce the concepts taught in lectures.

    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 5 25
    Online Quizzes 6
    Assignments 5 35
    Total 156
    Learning Activities Summary
    Lecture Outline
    1. Projective Planes, 3 lectures (extended Euclidean plane, finite projective planes)
    2. Projective space, 2 lectures (extended Euclidean 3-space, r-dimensional projective space)
    3. Field Planes, 3 lectures (fields, homogeneous coordinates, subplanes)
    4. Collineations, 7 lectures (eomographies, automorphic collineations, fundamental theorem of field planes, central collineations, elations, homologies)
    5. PG(r,F), 1 lecture
    6. Conics in PG(2,F), 6 lectures (J's equation, polarity, conics when charF=2, conics in the real projective plane)
    7. Combinatorial structures (latin squares, incidence matrices, difference sets), 8 lectures
    Tutorials in Weeks 2, 4, 6, 8, 10, 12 cover the material of the previous two weeks.

    Small Group Discovery Experience
    The final topic on Combinatorial Structures will be conducted in a flipped classroom mode, and students will work in small groups of 2-3 students during the lecture time slots.
  • 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 
    Learning Outcomes
    exam 70% all
    assignments 15% all
    tutorials and quizzes        15% all
    Assessment Related Requirements
    An aggregate score of 50% is required to pass the course.
    Assessment Detail
    Assignments are due in weeks 3, 5, 7, 9, 11, each is worth 3%, contributing a total of 15%.

    Tutorials and online quizzes will be regularly held to enable active learning. These contribute a total of 15%.
    Homework assignments must be submitted on time with a signed assessment cover sheet. Late assignments will not be accepted. Assignments will be returned within two weeks. Students may be excused from an assignment for medical or compassionate reasons.  Documentation is required and the lecturer must be notified as soon as possible.
    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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