MATHS 7025 - Research Methods and Statistics
North Terrace Campus - Semester 2 - 2016
General Course Information
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 Incompatible STATS 7053 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 Coordinator: Professor Matthew Roughan
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning OutcomesStudents should
- Be aware of their responsibilities as research students, including scientific ethics, and data and code management requirements.
- Improve their ability to communicate research results, including building an argument orally and in writing.
- Understand the basic concepts of probability, random variables, statistical inference, hypothesis testing and regression.
- Understand the role of probability in modelling random phenomena that occur in engineering applications.
- Have the ability to analyse experimental and observational data and draw appropriate conclusions.
- Have the ability to apply appropriate statistical analysis to research problems in engineering.
- 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)
1-7 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
1-7 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
1,2 Career and leadership readiness
- technology savvy
- professional and, where relevant, fully accredited
- forward thinking and well informed
- tested and validated by work based experiences
1-7 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
Required ResourcesNone. Notes will be provided.
- Handbook of Writing for the Mathematical Sciences, N.J. Higham, SIAM, 1995
- Statistics text, tba.
Online LearningThe 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 ModesThis course relies on 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 24 lectures.
It is expected that students will preread the 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 24 60 Practicals 6 24 Tutorials 6 24 Assignments 6 48 Total 156
Learning Activities Summary
- Introduction, outline, purpose.
- Responsibilities and expectations of research students. How is a research project different from other parts of your education? The importance of teamwork. Working effectively withyour supervisor.
- Research processes. Meshing statistics (e.g. experimental design) with your research. Don’t do the statistics last! Reproducibility and transferability of research.
- Ethics and responsible research. What is ethics in science? What are the requirements for students?
- Communication skills in the context of research projects. Requirements. Processes to get you writing.
- Anatomy of a thesis. Compelling introductions. The literature review. Informative scientific writing.
- Data management. Data cleaning. Data storage.
- Backups and revision control. Requirements and methods for data retention. Revision control and Git.
- Overview of statistics, histogram, sample mean, sample variance and standard deviation.
- Five number summary, scatter plots, sample covariance, sample correlation.
- Basic probability theory 1: axioms of probability, probability rules, conditional probability.
- Basic probability theory 2: law of total probability, Bayes' theorem, independent events.
- Discrete random variables 1: Bernoulli, binomial, geometric distributions.
- Discrete random variables 2: Poisson process, Poisson distribution, mean, variance and standard deviation.
- Continuous random variables: uniform, normal, log normal and exponential distributions.
- Bivariate distributions: independent random variables, covariance, correlation.
- Linear combinations of random variables.
- Random samples, statistics, distribution of the sample mean, central limit theorem.
- Statistical estimation, point estimates, standard errors, confidence intervals.
- Tests of statistical hypotheses, significance, P-values.
- One sample, two independent samples and paired t-tests, inference for proportions.
- Sample size calculation, margin of error, statistical power.
- Linear regression, least squares estimation, inference, prediction, model checking.
- Multiple linear regression.
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.
Component Weighting Learning Outcomes Assessed Assignments 20 Summative and Formative Statistics Assignments 30 Summative and Formative Research Methods Examination 50 Summative Statistics only
Assessment Related RequirementsAn aggregate score of at least 50% is required to pass the course.
Assessment DetailAssessment will be based on 6 written assignments and a final exam.
SubmissionAll written assignments are to be submitted to the designated hand-in boxes within the School of Mathematical Sciences with a signed cover sheet attached. Late assignments will not be accepted.
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.
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.
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