MATHS 7025 - Research Methods and Statistics

North Terrace Campus - Semester 2 - 2021

Fundamental concepts of probability theory and statistics. Applications of statistical methods in engineering and the use of statistical software in modern data analysis. Good research practice, procedures, ethics and data management. Skills in building an argument and communicating it orally and in writing.

  • General Course Information
    Course Details
    Course Code MATHS 7025
    Course Research Methods and Statistics
    Coordinating Unit School of Mathematical Sciences
    Term Semester 2
    Level Postgraduate Coursework
    Location/s North Terrace Campus
    Units 3
    Contact 3 hours per week
    Available for Study Abroad and Exchange N
    Incompatible STATS 7053
    Restrictions Not available to MMaSc students.
    Course Description Fundamental concepts of probability theory and statistics. Applications of statistical methods in engineering and the use of statistical software in modern data analysis. Good research practice, procedures, ethics and data management. Skills in building an argument and communicating it orally and in writing.
    Course Staff

    Course Coordinator: Dr Peter Ballard

    Course Timetable

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

  • Learning Outcomes
    Course Learning Outcomes
    Students should
    1. Be aware of their responsibilities as research students, including scientific ethics, and data and code management requirements.
    2. Improve their ability to communicate research results, including building an argument orally and in writing.
    3. Understand the basic concepts of probability, random variables, statistical inference, hypothesis testing and regression.
    4. Understand the role of probability in modelling random phenomena that occur in engineering applications.
    5. Have the ability to analyse experimental and observational data and draw appropriate conclusions.
    6. Have the ability to apply appropriate statistical analysis to research problems in engineering.
    7. Have the ability to manipulate data and use Matlab to perform statistical analysis and probability calculations.
    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
    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
    None.  Notes will be provided.
    Recommended Resources

    Recommended reading:
    1. Handbook of Writing for the Mathematical Sciences, N.J. Higham, SIAM, 1995
    2. Research Methods for Postgraduates (3e), Tony Greenfield and Sue Greener (editors), Wiley, 2016
    3. Probability and Statistics for Engineers and Scientists (8e), Jay Devore, Brooks/Cole, 2010
    4. Statistics in Engineering (2e) - with examples in MATLAB and R, Andrew Metcalfe et al, Chapman & Hall, 2019
    Students should also read the University's policies on academic honesty and plagiarism, and research data and primary materials:
    Online Learning
    The course notes will be available online.

    All assignments, tutorials, handouts and solutions where appropriate will also be available online as the course progresses.

  • Learning & Teaching Activities
    Learning & Teaching Modes
    This course relies on instructional videos and lectures as the primary delivery mechanism for the material. The lecturers will guide the students through the material presented in this course in a total of 12 lectures, with each lecture having one or more instructional videos.

    It is expected that students will watch the intructional videos, and preread any online notes, to enable them to more actively engage the material and interact during lectures.

    Practicals and tutorials supplement the lectures by providing exercises and example problems to enhance the understanding obtained through lectures. A sequence of written assignments provides assessment opportunities for  students to gauge their progress and understanding.


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

    Activity Quantity Hours
    Lectures 12 60
    Practicals 6 24
    Tutorials 6 24
    Assignments 6 48
    Total 156
    Learning Activities Summary


    Week 1: Introduction, outline. Introduction to Matlab.

    Week 2: Writing and communication. Communication skills in the context of research projects. Requirements. Processes to get you writing. Anatomy of a thesis. The literature review. Informative scientific writing. Citing correctly and avoiding plagiarism.

    Week 3: Reponsibilities and ethics: How is a research project different from other parts of your education? The importance of teamwork. Working effectively with your supervisor. Requirements for students. Ethics in science and engineering.

    Week 4: Data. Meshing statistics with your research. Reproducibility and transferability of research. Data management. Data formats. Data retention and backups. Revision control.

    Week 5: Overview of statistics, sample mean, sample variance and standard deviation. Types of data. Histogram, box plots, five number summary, scatter plots. Sampling.

    Week 6: Basic probability theory: axioms of probability, probability rules, conditional probability. Law of total probability, Bayes' theorem, independent events. Permutations and combinations.

    Week 7: Discrete random variables: Probability Mass Function (PMF). Bernoulli, binomial, geometric, poisson distributions.

    Week 8: Continuous random variables: Probability density function (PDF) and cumulative distribution function (CDF). Uniform, normal, log normal and exponential distributions. Independent random variables, covariance, correlation.

    Week 9: Linear combinations of random variables. Distribution of the sample mean, central limit theorem. t-test.

    Week 10: Hypothesis testing: test statistic, confidence intervals, significance, P-values, sample size.

    Week 11: Linear regression: least squares estimation, inference, prediction, model checking.

    Week 12: Multiple linear regression.

  • 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 Learning Outcomes Assessed
    Assignments 18 Formative Research Methods
    Tutorials 2 Formative Research Methods
    Practicals 3 Formative Research Methods and Statistics
    Assignments 18 Formative Statistics
    Online Tests 9 Summative Research Methods
    Examination 50 Summative Statistics only
    Assessment Related Requirements
    An aggregate score of at least 50% is required to pass the course.
    Assessment Detail
    Assessment will be based on 5 written or online assignments, active participation in tutorials and practicals, 4 online tests, and a final exam.
    All written assignments are to be submitted online. Late assignments will not be 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 ( 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.

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