MODULE DATA

MODULE TITLE Business mathematics for the railway infrastructure MODULE LEVEL 7 MODULE CREDIT POINTS 15 SI MODULE CODE 16-7001-00 MODULE JACS CODE G190 SUBJECT GROUP Mathematics

MODULE DELIVERY PATTERN ( as applicable or give dates for non-standard delivery) NB "Semester 3" ends on 31 July each year LONG (2 semesters) SHORT (1 semester)

NON-STANDARD DELIVERY

Sem 1 & 2 Sem 1 Start Date As required

Sem 2 & 3 Sem 2 End Date As required

Sem 3 (Typically: half day primer plus two separated three day blocks)

MODULE ASSESSMENT PATTERN ( as applicable - also complete Table A, Section 5, below) Single Module Mark with Overall Module Pass Mark of 40% Single Module Mark - Pass/Fail only Up to Three Assessment Tasks with Pass Mark of 40% for each Task and Overall Module Pass Mark of 40%

Up to Three Assessment Tasks - Pass/Fail only Other - if choosing "Other" please give further details of assessment pattern in the blank space below.

Overall Module Pass Mark if other than 40% (subject to approval) %

MODULE INFORMATION ( as applicable - also complete Table A, Section 5 Is a timetabled examination required for the assessment of this module? Is a timetabled examination required for the reassessment of this module? Is the module delivered wholly by Distance Learning (i.e. not timetabled at SHU) Are any staff who are responsible for teaching on this module non-SHU employees?

MODULE STATUS ( as applicable to status of module in the context of current proposal) Unchanged: an existing module, presented as unchanged from previous years Modified: an existing module being modified as a result of this validation, e.g. changes to delivery or assessment pattern, title, credit weighting etc

New: new module to be approved through current validation process If status is 'Modified', please give date when modified version is to be available from

Modified Version Available from ??/??/??

Breakdown of notional study hours by type (Typically requires 10 hours of notional study time for 1 CATS credit)

Tutor-Led (Contact Hours)

Tutor-Directed Study

Self-Directed Study

TOTAL STUDY HOURS for this Module

16 11 123 150

OTHER COURSES FEATURING THIS MODULE (please list below) None

1 AIM OF THIS MODULE • To develop your mathematical skills in areas applicable to the

management of railway infrastructure. • To help you to analyse working situations from a mathematical

standpoint, identify where mathematics can aid planning and decision making, select and apply mathematical techniques accordingly.

• To enhance your ability to make critical judgements based on evaluation of quantitative evidence.

2 BY ENGAGING SUCCESSFULLY WITH THIS MODULE YOU WILL BE ABLE TO

LO1 - Confidently undertake arithmetic processes in situations where the data

are uncertain or ambiguous, and perform appropriate error estimation, LO2 - Develop formulae to assist future projections, and manipulate such

formulae according to algebraic rules, LO3 - Make estimates of capital and project costs and analyse and calculate

cash flow, LO4 - Critically analyse probabilistic situations and construct appropriate tree

diagrams and fault trees using the laws of probability, LO5 - Provide a well-documented rationale for taking decisions based on,

e.g., calculations of reliability, risk, present value and depreciation, LO6 - Critically analyse data relating to e.g. accidents, traffic, demand etc.

using statistical methods, LO7 - Select and use relevant information from a balance sheet drawn up

according to current accountancy practices, LO8 - Select suitable software (e.g. spreadsheets and/or computer algebra

packages) to implement mathematical calculations. Illustrate the results with graphs and tables etc. which are carefully selected to promote deep understanding and presented to have maximum clarity and impact.

3 THESE ARE EXAMPLES OF THE CONTENT OF THE MODULE Basic Maths Revision of fundamental mathematical techniques. Discounted Cash Flow. Depreciation. Probability and Statistics Probability.

Independence, Mutual Exclusivity and Probability Trees including Fault Tree Analysis.

Risk and Reliability. Poisson distribution, queues, accident rates. Normal Distribution, Normal errors, confidence limits. Spreadsheets Tables and formulae. Implementing DCF, depreciation and risk calculations.

Use of graphs. Balance Sheets and latest accountancy practices. Financial Calculations Risk review, risk ranking and cost of risk. Cost of capital. Calculations supporting asset replacement decisions. Valuation of assets. Profit and loss.

4 THESE ARE THE MAIN WAYS YOU WILL BE SUPPORTED IN YOUR LEARNING TO

ACHIEVE THESE OUTCOMES Before teaching on the module starts formally, introductory material will be made available via the web. This will enable you to assess your current mathematical skills, and to practice and improve these where necessary. Further work will be carried out in relation to this introductory material in the initial class sessions, to ensure that all students have a common subset of fundamental mathematical skills on which to build. The class contact time will be split approximately 60:40 between lecture rooms and computer rooms. In the lecture sessions methods will be presented and you will have the opportunity to practice key mathematical techniques. In the computer sessions you will undertake calculations with spreadsheets and a computer algebra package based on the mathematical techniques you have learned. This will involve, for example, setting up spreadsheets for data analysis, risk and financial calculations and forecasting, and using a computer algebra package as an aid to manipulating formulae. Towards the end of the teaching time, the information on which the final assessment will be based will be introduced, with time for some preliminary discussion. All relevant information will be available on the web and you will be able to discuss this with tutors via email, the web or ’phone contact in the period between the end of formal teaching and the due date for the assignment.

5 THESE ARE THE WAYS THAT WILL BE USED TO ENABLE YOU TO DEMONSTRATE YOU HAVE MET THE LEARNING OUTCOMES The major theme of this module is the use of mathematics in problems likely to be encountered in the railway infrastructure environment. To reflect this, the assessment is 100% continuous with the emphasis on application. To Achieve A Pass You must achieve a balanced threshold performance across all the learning outcomes. In a little more detail, what is expected for each learning outcome is as detailed below. A typical pass level would be represented by an ability to undertake most of the techniques described, but with some errors and in some cases a need for further guidance in completing a task.

learning outcome 1 • Make correct calculations and, where these are based on approximate

data, make estimates of possible error in the calculated quantity. learning outcome 2 • Describe methods of calculation in terms of formulae. • Undertake common algebraic processes in order to simplify and

transpose formulae. learning outcome 3 • Interpret available data and implement appropriate formulae to arrive at

estimates of costs, asset value and cash flow. These should be well-documented so that estimates are verifiable and easily checked.

learning outcome 4 • Approximate probabilities of events from available data and use these as

a basis from which to construct probability and fault trees. • Gauge the likelihood of compound events and faults. learning outcome 5 • Put together, in report form, the quantitative elements of an argument on

which a decision is based. The report should show clearly what methods have been used and why, what the results of calculations are, and why these point to a particular decision.

learning outcome 6 • Carry out a range of calculations based on the Normal and Poisson

distributions to assess, for example, improvements in accident rates, proportions of normally distributed demand falling into particular categories etc.

learning outcome 7 • Explain the conventions operating in balance sheets. • Construct a balance sheet according to these conventions. learning outcome 8 • Demonstrate competence in constructing spreadsheets which apply

mathematical formulae. • Produce appropriate graphs and charts which clearly illustrate quantitative

arguments and conclusions.

ASSESSMENT STRATEGY AND METHODS

Task No.

TASK DESCRIPTION SI Code

Task Weighting %

Word Count / Duration

In-module retrieval available

1 Coursework CW 100%

6 THIS IS HOW YOU WILL BE GIVEN FEEDBACK ON YOUR PERFORMANCE

The first feedback you will receive will be as a consequence of your study of the introductory material. At this stage you will be given guidance on where, if necessary, you need to work on your fundamental mathematical skills. Throughout teaching you will receive feedback as you practice and implement the methods taught. This will often take the form of informal one to one discussion, with feedback to groups if particular common difficulties occur. More formal feedback will come as a result of the in-class test and first assignment. Feedback from each task is available in time to inform work on the next task.

7 THESE ARE EXAMPLES OF THE KEY LEARNING RESOURCES YOU WILL USE

Learning materials available over the web and in paper form. Data forming the basis of exercises and assessments. Standard computer laboratories with demonstration material in Excel and

DERIVE. FINAL TASK According to the Assessment Strategy shown in the Module Descriptor, which task will be the LAST TASK to be taken or handed-in? (Give task number as shown in the Assessment Strategy)

Task No. 1

MODULE REFERRAL STRATEGY Task for Task (as shown for initial assessment strategy) Y Single Referral Package for All Referred Students N

REVISIONS Date Reason July 2012 Assessment Framework review