MATHS 1015 - Advanced Mathematical Perspectives I

North Terrace Campus - Semester 1 - 2014

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.

  • General Course Information
    Course Details
    Course Code MATHS 1015
    Course Advanced Mathematical Perspectives I
    Coordinating Unit School of Mathematical Sciences
    Term Semester 1
    Level Undergraduate
    Location/s North Terrace Campus
    Units 3
    Contact Up to 3 contact hours per week
    Restrictions Available to Bachelor of Mathematical Sciences (Advanced) students only
    Course Description 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.
    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 Planner.

  • Learning Outcomes
    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 Activities
    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.
  • 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
    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 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.

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