MATHS 1015 - Advanced Mathematical Perspectives I

North Terrace Campus - Semester 1 - 2015

The aim of this course is to develop foundational research skills in the mathematical sciences. It will be taught as three small group workshops per week and assessed through guided discovery projects. Students will be required to participate proactively in the small groups workshops and by involvement in open-ended problems, independent reading and completion of the guided discovery projects.

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Course Details

Course Code	MATHS 1015
Course	Advanced Mathematical Perspectives I
Coordinating Unit	Mathematical Sciences
Term	Semester 1
Level	Undergraduate
Location/s	North Terrace Campus
Units	3
Contact	Up to 3 contact hours per week
Available for Study Abroad and Exchange	Y
Restrictions	Available to BMaSc (Adv) students only
Assessment	Ongoing assessment 100%

Course Staff

Course Coordinator: Associate Professor Ben Binder

Course coordinator: Ben Binder
Email: benjamin.binder@adelaide.edu.au
Office: Ingkarni Wardli, room 659
Phone: 8313 3244
Administrative enquiries: School of Mathematical Sciences office, Level 6, Ingkarni Wardli

Course Timetable

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

Course Learning Outcomes

Students who successfully complete the course should:

1. appreciate the way pure mathematics is built on rigorous arguments

2. appreciate the difference between discrete and continuum modelling approaches

3. appreciate the need for statistics in parameter estimation

4. be able to develop their own rigorous mathematical arguments

5. be able to develop simple mathematical models

6. be able to implement models using Matlab

7. be able to analyse experimental data

8. be able to write project reports and give an oral presentation

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
The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner.	7
An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems.	5,6,7,8
Skills of a high order in interpersonal understanding, teamwork and communication.	8
A proficiency in the appropriate use of contemporary technologies.	6,8
A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life.	all

Learning Resources

Required Resources

None.

Recommended Resources

Materials provided by lecturers.

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 students make appropriate use of these resources. Link to MyUni login page: https://myuni.adelaide.edu.au/webapps/login/

Learning & Teaching Modes

This course is run in a workshop format. Students will work closely with academic members of staff in a small group discovery environment. Two written projects and a presentation constitute the assessment for the course.

Workload

The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

Activity	Quantity	Workload hours
Workshops	36	108
Projects	2	32
Presentation	1	16
Total		156

Learning Activities Summary

Workshop Outline

Week 1
                  1. Introduction to the course, to pure mathematics, and to the first project

                  2. Proofs and mathematical arguments, background material

                  3. LaTeX tutorial

Week 2
                  4. Public holiday

                  5. Proofs and mathematical arguments, background material

                  6. LaTeX tutorial

Week 3      7. Seminar-style discussion of the project

                  8. Seminar-style discussion of the project

                  9. Seminar-style discussion of the project

Week 4
                 10. Theory: Outline for mathematical modelling project: Discrete and continuous models

                 11. Practical: Introduction to Matlab--basic plotting, programs, populating domains

                 12. Practical: Implementation of cellular automata mechanism for tissue growth

Week 5     13. Theory: Development of continuum model and analytical solutions

                 14. Practical: Implementation of cellular automata mechanism for tissue growth

                 15. Practical: LaTeX session

Week 6
                 16. Theory: Continuum paths and space-time diagrams

                 17. Practical: Comparison of averaged cellular automata data with continuum paths

                 18. Practical: Comparison of averaged cellular automata data with continuum paths

Week 7
                 19. Theory: Probabilistic description of discrete model, probability trees

                 20. Practical: Implementation of other cellular automata mechanisms

                 21. Practical: LaTeX session

Week 8
                 22. Theory: Uniform and negative hypergeometric distribution

                 23. Practical: Implementation of other cellular automata mechanisms

                 24. Practical: Implementation of other cellular automata mechanisms

Week 9
                 25. Theory: Polya distribution mean and variance, comparison with continuum paths

                 26. Practical: Comparison of averaged cellular automata data with paths/distributions

                 27. Practical: LaTeX session

Week 10
                 28. Theory: Outline of statistical analysis of experimental data, linear regression

                 29. Practical: Basic curve fitting in Matlab

                 30. Practical: Parameter estimation for discrete and continuous models

Week 11
                 31. Theory: Derive equations for intercept and slope for least squares

                 32. Theory: Matrix form of linear regression. Show equivalence to least squares

                 33. Practical: LaTeX session

Week 10
                 34. Theory: Non-linear regression via linearization and also numerical optimization.

                 35. Practical: Matlab implementation of stats theory

               36. Practical: LaTeX session

Small Group Discovery Experience

This course aims to develop independent student learning in a small group discovery environment.

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

Component	Weighting	Objective Assessed
Project report 1	25%	1,4,8
Project report 2	60%	2,3,5,6,7,8
Presentation	15%	2,3,4,5,6,7,8

Assessment Detail

Assessment item	Distributed	Due Date	Weighting
Project 1	Week 1	Week 6	25%
Project 2	Week 4	Week 12	60%
Presentation	Week 7	Week 11-12	15%

Submission

1. The reports are to be submitted to the relevant lecturer with a signed cover sheet attached.

2. Late reports will not be accepted.

3. Reports 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 .

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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Authorised by:	Deputy Vice-Chancellor and Vice-President (Academic)
Maintained by:	Course Outlines Administrator