## PURE MTH 7073 - Finite Geometry

### North Terrace Campus - Semester 2 - 2014

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 Finite Geometry Pure Mathematics Semester 2 Postgraduate Coursework North Terrace Campus 3 Up to 3 hours per week MATHS 1012 PURE MTH 2106 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.
##### 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.

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. 1,2,3,4,5
The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner. 1,2,3,4,5
An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. 5
Skills of a high order in interpersonal understanding, teamwork and communication. 6
A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. 1,2,3,4,5,6
A commitment to the highest standards of professional endeavour and the ability to take a leadership role in the community. 6
An awareness of ethical, social and cultural issues within a global context and their importance in the exercise of professional skills and responsibilities. 6
• Learning Resources
None.
##### 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 present their solutions to 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.

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 30 Assignments 5 35 Total 155

##### 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. Geometrical Structures, 7 lectures
Tutorials in Weeks 2, 4, 6, 8, 10, 12 cover the material of the previous two weeks.

• 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 Due Weighting Learning Outcomes exam examination period 70% all assignments weeks 3,5,7,9,11 12% all tutorials weeks 2,4,6,8,10,12 6% all mid semester test week 8 12% all
##### Assessment Related Requirements
An aggregate score of 50% is required to pass the course.
##### Assessment Detail
 Assesment Task Set Due Weighting Tutorial 1 week 1 week 2 see below Assignment 1 week 2 week  3 2.4% Tutorial 2 week 3 week 4 Assignment 2 week 4 week 5 2.4% Tutorial 3 week 5 week 6 Assignment 3 week 6 week 7 2.4% Tutorial 4 week 7 week 8 mid-semester test week 8 week 8 12% Assignment 4 week 8 week 9 2.4% Tutorial 5 week 9 week 10 Assignment 5 week 10 week 11 2.4% Tutorial 6 week 11 week 12

Tutorials contribute 6% to the final grade. Students are expected to attend all tutorials and to present twice in the term. This may have to be adjusted depending on enrolment.
##### Submission
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.

Grades for your performance in this course will be awarded in accordance with the following scheme:

M10 (Coursework Mark Scheme)
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
• 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 studentâ€™s disciplinary procedures.

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

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