MATHS 2203 - Advanced Mathematical Perspectives II

North Terrace Campus - Semester 2 - 2020

The aim of this course is to foster a broad appreciation of the mathematical sciences with an exposure to the areas of major research strength within the School. It will be taught in four three week blocks covering Mechanics, Operations research, Pure Mathematics and Statistics. Students will be required to participate proactively in the course by possible involvement in open ended problems, independent reading and mini projects.

  • General Course Information
    Course Details
    Course Code MATHS 2203
    Course Advanced Mathematical Perspectives II
    Coordinating Unit School of Mathematical Sciences
    Term Semester 2
    Level Undergraduate
    Location/s North Terrace Campus
    Units 3
    Contact Up to 3.5 contact hours per week
    Available for Study Abroad and Exchange Y
    Prerequisites MATHS 1012 and MATHS 1015
    Restrictions Available to BMaSc(Adv) students only
    Course Description The aim of this course is to foster a broad appreciation of the mathematical sciences with an exposure to the areas of major research strength within the School. It will be taught in four three week blocks covering Mechanics, Operations research, Pure Mathematics and Statistics. Students will be required to participate proactively in the course by possible involvement in open ended problems, independent reading and mini projects.
    Course Staff

    Course Coordinator: Associate Professor Nicholas Buchdahl

    Course Timetable

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

  • Learning Outcomes
    Course Learning Outcomes
    1. Develop appreciation for the distinction between "good" and "bad" mathematics.
    2. Develop appreciation of the importance of classification in mathematics.
    3. Understand the connections between probability, statistical data and evidence.
    4. Be able to apply probabilistic reasoning in real contexts involving data and evidence.
    5. Be able to analyse simple Hidden Markov Models.
    6. Be able to develop simple mathematical models.
    7. Be able to utilise mathematical tools in tackling real-world problems.
    8. Develop the ability to write project reports.

    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)
    1,2,3,4,5,6,7
    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
    1,2,3,4,5,6,7
    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
    8
  • Learning Resources
    Required Resources
    None.
    Recommended Resources
    Course materials will be provided by the lecturers.
  • Learning & Teaching Activities
    Learning & Teaching Modes
    The course is taught in four blocks of three weeks.
    Workload

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

    Activity Quantity Workload hours
    Lecture 36 108
    Project/Assignment 4 48
    Total 156
    Learning Activities Summary
    Pure Mathematics

    Week 1:  An overview of perspectives in mathematics, particularly as they apply to mathematics at The University of Adelaide.

    Week 2:  Separation, tessellation and triangulation.

    Week 3:  The classification of closed surfaces.

    Applied Mathematics I: Dynamics, Modelling and Computation

    Week 4:  Fourier transforms and properties.

    Week 5:  Fast Fourier Transforms and signal processing.

    Week 6:  Transforms used to solve partial differential equations.

    Applied Mathematics II: Stochastic Modelling and Operations Research

    Week 7:  Introduction to Hidden Markov Models - review of discrete-time Markov chains, definition of a Hidden Markov Model, understanding of the three classical problems.

    Week 8:  Detailed exploration of the first two classical problems in Hidden Markov Models – likelihood calculation, and filtering and smoothing.

    Week 9:  Detailed explanation of the third classical problem in Hidden Markov Models – maximum likelihood estimation, including computational aspects; introduction of the project.

    Statistics

    Week 10: Introduction to Bayesian inference.

    Week 11: Bayesian hierarchical model and its application to meta-analysis (statistical overview).

    Week 12: Applications of meta analyses and use of the R bayesmeta package.
  • 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 Topic Objective assessed
    Project/Assignment 1 25% Pure Mathematics 1, 2, 8
    Project/Assignment 2 25% Applied Mathematics I 6, 7, 8 
    Project/Assignment 3 25% Applied Mathematics II 5, 6, 7, 8
    Project/Assignment 4 25% Statistics 3, 4, 8
    Assessment Related Requirements
    An aggregrate score of 50% or more is required to pass this course.
    Assessment Detail
    Assessment item Distributed Due
    Project/Assignment 1 Weeks 1-3 End of Week 8
    Project/Assignment 2 Weeks 4-6 TBA
    Project/Assignment 3 Weeks 7-9 TBA
    Project/Assignment 4 Weeks 10-12 TBA
    Submission
    Reports are submitted to the relevant lecturer via MyUni. Late assignments are not accepted.
    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
  • 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’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.