Units

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Sample subject outline - Semester 1 2013

Note: Subject outlines often change before the semester begins. Below is a sample outline.

Rationale

This unit is intended for all mathematics degree students, all double degree students with mathematics, secondary education students with mathematics as a teaching area, and quantitatively-oriented students in other courses, particularly in Science, Information Technology, Engineering and areas of Business. The unit will provide you with fundamental skills and operational knowledge for all further study in statistics, and highly relevant foundations for other areas of mathematics such as mathematical modelling and operations research. The unit will also help you develop fundamental problem-solving skills in statistics and mathematics.

Aims

The aims of this unit are
1. to introduce you to the basic principles, concepts and methods of stochastic and statistical modelling for applications in a wide range of areas and
2. to provide you with an understanding of what it means

• to use stochastic and statistical concepts


• in order to build a model


• with the purpose of solving a practical problem.

Objectives

Successful completion of this unit should enable you to:

1. Understand and apply the basic concepts of introductory stochastic and statistical modelling.

2. Draw on your knowledge of probability, random variables and distributions to identify and solve problems.

3. Understand what it means to build and use stochastic and statistical models for practical problems in a competent, creative and critical way.

4. Work in a group to solve problems and express a coherent argument.

Content

The topics in this unit develop the fundamental concepts, understanding, knowledge and skills in probability and distributions that are the foundations for models and applications across all of probability and statistics and their applications across disciplines. As a consequence, this unit develops problem-solving skills relevant to all quantitative areas involving chance and data.

The unit does not assume any prior knowledge of probability and distributions (though such a knowledge is likely to be of advantage) as this knowledge is developed in the first part of the unit. However, the unit takes for granted the full range of algebraic skills taught up to high school year 10 and builds on a general mathematical understanding and some of the skills (such as integration) that are typically acquired in Senior Mathematics B and C (or equivalent).

The content of the unit includes, but is not limited to, all or almost all of the following topics:

1. Foundations of probabilistic modelling

Probability rules and language; independence and conditional probability; law of total probability and Bayes' rule and application to estimating probabilities; Discrete and continuous random variables and distributions (such as Bernouilli, binomial, geometric, Poisson, uniform and exponential distributions); expected value and variance; evaluation of model assumptions using goodness of fit tests; introduction to discrete bivariate distributions.

2. Introduction to stochastic processes

Simple Markov chains; Poisson processes; queueing processes (including an illustration of conditioning arguments to obtain results such as Little's formula).

The emphasis throughout is on applications in both familiar and new contexts, and on skills for describing and setting up problems, and identifying methods and tools to solve them. This implies that the focus of this course is not on developing calculation skills, but most of all on developing a conceptual understanding of stochastic and statistical thinking that allows for approaching practical problems by building stochastic and statistical models in a competent, creative and critical way.

Approaches to Teaching and Learning

The motivation, structure and development of the concepts and techniques in this unit are based on examples and applications.

During lectures you will be see key concepts, results, examples, and exercises, with the opportunity for participation and interaction.

Whenever possible, you will be introduced to new sections by exploring and understanding your existing knowledge which will then be formalised and developed.

In workshops , a combination of discussion, working through small and larger real world problems and expressing solutions individually and in groups, will promote your creativity in problem-solving, critical assessment skills, and intellectual debate.

The most valuable learning approach is for you to do regularly all the problem solving tasks including the weekly exercises and the assignments. These will enable you to synthesise concepts, techniques and applications, and assist you in developing all the key knowledge that later parts of the unit, other units at a later stage of your studies and the final exam of this unit will be based on.

Full solutions to all problem solving tasks will be made available on Blackboard progressively. All materials required for the semester, will be available on Blackboard

Assessment

All assessment in this unit is skills-based and operational assessment. The focus is on problem-solving skills using operational knowledge and understanding of key concepts, techniques and procedures.

The assessment package is carefully designed to help you manage and optimise your learning throughout the semester, allowing for different individual situations and capabilities. The assessment package is designed to help you develop your understanding and skills throughout the semester, aiming for achievement of the synergies and synthesis of the unit by the end of semester.Full solutions will be provided in a timely manner for all formative and summative assessment in problem-solving throughout the semester. Feedback on individual work will also be provided during workshop classes. Ongoing guidance will be provided with individual development of skills, knowledge and confidence in tackling problems, in working individually and in groups and in communication.

Assessment name: Problem Solving Task
Description: These consist of exercises and problems both in and out of class strategically timed to optimise your learning. They cover the core operational knowledge and skills of the unit and provide you with an excellent way of learning through applying techniques to real problems within context. The individual components of the exercises and problems will be marked with feedback to help with understanding and given to you within two weeks of submission of each. Further assessment details will be posted on Blackboard.
Relates to objectives: 1, 2, 3, 4
Weight: 40%
Internal or external: Internal
Group or individual: Group with Individual Component
Due date: Approx Weekly

Assessment name: Examination (Theory)
Description: This is a written exam assessing the skills, problem-solving and operational knowledge you have developed over the whole semester.
Relates to objectives: 1, 2 and 3.
Weight: 60%
Internal or external: Internal
Group or individual: Individual
Due date: Exam Period

Academic Honesty

QUT is committed to maintaining high academic standards to protect the value of its qualifications. To assist you in assuring the academic integrity of your assessment you are encouraged to make use of the support materials and services available to help you consider and check your assessment items. Important information about the university's approach to academic integrity of assessment is on your unit Blackboard site.

A breach of academic integrity is regarded as Student Misconduct and can lead to the imposition of penalties.

Resource materials

All necessary materials are placed on Blackboard.

References:

You will not specifically be referred to buy any of these, but may find them useful:

1. Bertsekas, D.P. and J.N. Tsitsiklis: Introduction to Probability. 2nd edition. Athena Scientific 2008.

2. Grinstead, C.M. and J.L. Snell: Introduction to Probability. 2nd revised edition, American Mathematical Society, 1997. A free copy can be downloaded under GNU FDL:


1. Ross, Sheldon M.: A first course in probability. 8th edition, Pearson, 2008.

4. Schaeffer, R.L. and L.J. Young: Introduction to Probability and its Applications. 3rd edition, Brooks/Cole (or earlier editions authored by Schaeffer only).

Risk assessment statement

There are no out of the ordinary risks associated with this unit. Emergency exits, evacuation procedures and assembly areas will be pointed out in the first few lectures. More information on Health and Safety can be obtained from the university's website
http://www.hrd.qut.edu.au/healthsafety/healthsafe/index.jsp.

Disclaimer - Offer of some units is subject to viability, and information in these Unit Outlines is subject to change prior to commencement of semester.

Last modified: 19-Feb-2013