Module Title / Problem Solving Methods
Credit / 30
Aims
The aim of this module is to enable students to apply their mathematical skills to problems they might encounter in other subjects in science and elsewhere. We introduce students to the processes involved in formulating problems mathematically in order to solve them. We will study problems from the breadth of mathematics highlighting their commonalities and differences and use these notions to gain a better understanding of their solutions. Students will work in groups each week on given problems in order to develop an understanding of the processes involved in successfully finding a solution. Computer programming is a vital part of this module and will be taught in lab sessions.
Learning Outcomes
Knowledge
On completion of this module the successful student will be able to:
1. abstract a given problem to identify its constituent parts: the hypothesis, the unknowns and
the data;
2. identify similarities between a problem and their previous knowledge and experience;
3. identify synergies between diverse areas of the mathematical sciences in order to better
tackle a problem;
4. develop topics that enhance their problem solving ability building on prior knowledge.
Skills
This module will call for the successful student to:
5. develop a coherent and feasible problem statement by analysing suitable information;
6. justify a reasoned strategy to solve an unfamiliar problem;
7. effectively work in a group to find solutions to problems;
8. develop a computer programme that solves or studies a given problem.
Syllabus
• The anatomy of problems
• Strategies to solve problems
• Examining problems – experimentation, collecting data, information
• Problems in computer science and operations research: graphs, networks and algorithms and numerical analysis
• Problems in the physical sciences: vector spaces and differential equations
• Using computer programs to explore problems
• Problems in data analysis and operations research: vector spaces, probability and statistics
Learning, Teaching and Assessment Strategies
The nature of mathematics learning is that it is cumulative, and so in order to complete this module successfully students are expected to be actively and continuously involved in all the learning, teaching and assessment methods employed, to develop their appreciation of, and skills in, the application of mathematics.
The teaching strategy for this module is designed specifically to develop the skills necessary to grow as mathematics students and, post-graduation, as professional mathematicians.
For the first five weeks students will learn about the anatomy of problems and different ways to approach their solutions. Sessions will consist of two-hour workshops where topics will be introduced informally using a problem-based approach and students will be encouraged to develop their own
strategies.
For the remainder of the year weekly workshops will introduce students to problems in a variety of fields of the mathematical sciences and students will work in groups to attempt to solve them. These sessions also adopt a problem-based approach and will encourage students to develop subjects
further.
Computers are an integral part of this module and will be used extensively to inform problem analysis and solution. Students will be introduced to pertinent software and computer programming in weekly one-hour computer labs.
Assessment Scheme
As the teaching strategy is predominately problem-based in this module, formative feedback will be offered weekly to students to encourage their development. There will also be formative assessment in the computer labs that is assessed via myLearning and feedback given.
The module takes a student-centred approach to summative assessment, allowing students to choose their own method of tackling problems, developing and implementing their own strategies.
The summative assessment components are:
i. Problem statement assignment (30%): students will be given an individual problem based around an appropriate topic; they will develop a strategy to collect information that leads to a keener understanding of the problem, culminating in a clear statement of the problem. A written report (approximately 1500 words) will detail their findings and the strategy they intendto employ in order to solve their problem, (week 10). This will assess learning outcomes 1, 2, 3, 5 and 6.
ii. Implementation (40%): students will develop a computer programme that provides a solution to the problem in assignment i. The programme will follow the strategy identified in the previous assignment (week 18). This will assess learning outcomes 2, 3 and 8.
iii. Group assignment (30%): students will work in groups tackling a given unfamiliar problem in the broad context of the mathematical and physical sciences. Groups will develop a fully justified solution to the problem in a short (15 minute) presentation and report (2000 words), (week 23). This will assess learning outcomes 1, 2, 3, 4, 6 and 7.
In order to pass this module students must achieve a grade 18 or better in each summative assessment component and a grade 16 overall.
Assessment Weighting
Coursework: 100%
Learning Materials
Your online reading lists can be accessed from the My Study area of UniHub. They highlight essential and recommended reading for all modules you are registered on.
Total Notional Learning Hours
300
Module Title / Financial Mathematics
Credit / 30
Aims
This module explores the mathematics that underlies financial processes and financial decision making, and complements the study of these areas in economics and accounting. Specific areas include probability, extending interest ideas to annuities and bonds, modelling financial data using time series models and Markov chains, applying discrete methods for option pricing, and using utility to make decisions in risky environments.
Learning Outcomes
Knowledge
On completion of the module the successful student will be able to:
1.state the properties of basic single and joint distributions;
2.make decisions in risky environments using utility;
3.analyse and use Markov chain models including random walks.
Skills
This module will call for the successful student to:
4.calculate present and future values, and evaluate annuities and bonds;
5.model financial data using time series methods, and critique those methods;
6.apply discrete methods for options pricing and two-stock portfolio selection;
7.work as a member of a small team.
Syllabus
•Payments, repayments, annuities and bonds
•Probability distributions, joint distributions and covariance
•Vectors and matrices
•Decision making under risk and utility
•Time series and seasonality
•Random walk models and Markov chains
•Option pricing
•Stock portfolio selection
Learning, Teaching and Assessment Strategies
A one-and-a-half-hour session each week will introduce, explain and consolidate the various techniques, and will include exposition, discussion and supervised exercises. Each session will identify a selection of graduated exercises which the student should attempt before the next session.
A one-hour workshop in alternate weeks will explore problem-based activities, provide detailed solutions to some of the work set in lectures, and provide opportunity for discussion of problems and approaches.
A one-hour computer laboratory session in alternate weeks will employ commercial computer software and provide the student with the opportunity to develop both their understanding and their skills in using software to solve problems.
The module’s on-line environment will contain all lecture slides and any additional learning material required for this module.
Assessment Scheme
Formative assessment includes samples of the tests and exam made available on myUniHub and discussed in seminars, and a practice submission opportunity for the group coursework to give students experience of the submission mechanism.
Summative assessment consists of three components:
Tests, 30% Two 45-minute multiple-choice tests enable students to monitor their progress (weeks 9 and 18). The questions are designed to provide formative feedback for the examination by diagnosing common errors and helping students to focus their revision. Learning Outcomes 1-6.
Group coursework, 20%A practical small-group coursework analysing share prices throughout the year enables students to explore the practical application of various of the module techniques, and is assessed by an evaluative report of around 8-20 typed A4 pages submitted online (week 22). Learning Outcomes 2, 5 and 7.
Examination, 50% A three-hour unseen examination, with a choice of questions, tests theoretical knowledge and problem-solving techniques (exam period). Learning Outcomes 1-6.
In order to pass this module, students must achieve a grade of 18 or better in the group coursework and examination.
Assessment Weighting
Coursework: 50% Examination: 50%
Exam Duration
Examination, 3 hours
Learning Materials
Your online reading lists can be accessed from the My Study area of UniHub. They highlight essential and recommended reading for all modules you are registered on.
Total Notional Learning Hours
300
Module Title / Simulation and Decision Making
Credit / 15
Aims
Understanding and implementation of decision making is crucial as it will lead to a better decision. This module introduces students to methods and tools to assist them in the decision making process by focusing on simulation tools which can be used interactively. Students will be encouraged to construct different scenarios using simulation games and software
Learning Outcomes
Knowledge
On completion of this module the successful student will be able to:
1. analyse a decision matrix and interpret it to inform the decision making process;
2. demonstrate an understanding of the large number of decision factors and their relative significance in decision making;
3. demonstrate a critical appreciation of the assumptions, implications, and limitations of decision analysis;
4. demonstrate an understanding of the use of simulation and differentiate between discrete and continuous simulation models.
Skills
This module will call for the successful student to:
5. explain how simulation is used to explore the dynamic behaviour or operation of complex commercial, industrial, or technical systems or subsystems.
6. demonstrate an understanding of how discrete event model is composed of a network of interrelated queues.
7. create and run a programme on Simul8.
8. critically evaluate the effect of constraints on the decision choices
Syllabus
• Decision Making and its Importance
• Decision Matrices (Evaluation of different options and prioritization)
• Decision Analysis
• Implementation of Decision Making
• Decision Making Constraints
• Discrete Event Simulation
• Use of appropriate specialist simulation software
Learning, Teaching and Assessment Strategies
The nature of mathematics learning is that it is cumulative, and so in order to complete this module successfully students are expected to be actively and continuously involved in all the learning, teaching and assessment methods employed, to develop their appreciation of, and skills in, the application of mathematics.
Each week there will be a one and a half hour lecture and one and a half hour workshop. Lectures are designed to introduce the topics covered in the syllabus and emphasise the important areas.
A one and a half hour weekly workshop will be run which will be the combination of both seminar and lab. Workshops will provide students with the opportunity to discuss topics covered in the lecture in more detail. Workshops will also help students to learn simulation software like Simul8 and Excel and students will be taught how to create and run programmes in such specialist simulation software.
Students are expected to be prepared for lectures and workshops in advance by completing their readings before attending classes. During the course of the module, students will be given opportunities to receive verbal feedback on their work.
The module’s online environment will contain all the lecture slides and any additional material as appropriate for each unit.
Assessment Scheme
Formative feedback will be provided to students in workshops on the given activities.
Summative assessment consists of two components selected in order to ensure students demonstrate an overall understanding of relevant concepts and techniques as well as the ability to apply and critique them in appropriate contexts.
The summative assessment components are:
i. One hour online test (50%) taken in the computer laboratory working with the software packages introduced in the teaching sessions to create and run programme and also to analyse data and interpret their results (week 7). This will address learning outcomes 4, 5 and 7.
ii. Group Coursework (50%). Students will be given data to analyse and produce a report (between 6-8 typed A4 pages) discussing their findings (at the university’s coursework deadline). Learning outcomes 1, 2, 3, 6 and 8.
In order to pass this module, students must achieve a grade 18 or better in each summative assessment component and a grade 16 overall.
Assessment Weighting
Coursework 100%
Learning Materials
Your online reading lists can be accessed from the My Study area of UniHub. They highlight essential and recommended reading for all modules you are registered on.
Total Notional Learning Hours
150
Module Title / Financial Data Analysis
Credit / 30
Aims
This module aims to enhance students’ knowledge and understanding of financial data analysis techniques used in the financial services. The module uses mathematical and statistical techniques to develop an understanding of the models underlying finance, and statistical and probability methods used in analysing financial data. Throughout the module, computer packages are used to develop a deeper understanding of the techniques.
Learning Outcomes
Knowledge
On completion of the module the successful student will be able to:
1.demonstrate a systematic understanding of how financial data analysis may be used to support economic and financial arguments and draw conclusions.
2.review and contrast a variety of techniques for data exploration, analysis and summary;
3.identify appropriate techniques to model data in a broad range of financial settings, demonstrate judgement in selecting and applying methods appropriately, and justify these decisions;
4.identify the relationships that may exist between variables, and critically evaluate techniques for exploring these using appropriate computer packages;
5.model financial data using an appropriate statistical computer package and reflect on its suitability;
Skills
This module will call for the successful student to:
6.critically evaluate financial concepts and data and reach sound judgements and decisions;
7.analyse and appraise data and information in order to make informed financial decisions;
8.locate, extract, consolidate and analyse financial data from multiple sources;
9.work effectively as part of a team;
10.communicate financial ideas, problems and solutions effectively to a non-specialist.
Syllabus
•Mathematical and probabilistic techniques used in financial modelling
•Financial mathematics; including forms of interest and foreign exchange and their application in finance and investment appraisal, including present value, continuous compounding and bond valuation.
•Index numbers and their use and application in Finance, with detailed examination of stock indices and tracker funds.
•Differential calculus and linear programming
•Descriptive statistics and probability
•Modelling relationships within financial data, using correlation, regression and the capital asset pricing model
•Using a sample to estimate the mean of a population
•Testing hypothesis
•Time series and forecasting techniques used to model financial data, stock prices, commodities and exchange rates.
•Excel, SPSS and Minitab.
Learning, Teaching and Assessment Strategies
Each week students are expected to attend and participate in a one-hour weekly lecture in addition to a one-and-a-half hour weekly workshop which will be a combination seminar and lab session.
Lectures will be used to explore key concepts in the syllabus, investigate relevant issues and outline scope for private study. Seminars will be used to analyse key issues in greater depth as well as to provide opportunities for developing skills in computation, interpretation and evaluation of data. Laboratories will be used to develop skills in the use of the computer packages Microsoft Excel, SPSS and Minitab to analyse data and interpret statistics.
The online module page accessed through the My Learning portlet on the My Study page on Unihub contains additional learning material as appropriate for each topic. These include online lectures, additional material to support practice of techniques and formative assessment tasks to help students prepare for the summative assessment.Utilisation of, and progress with, the additional material will be monitored by the teaching team. In addition, students will have access to advice and support through a timetabled advice service.
Assessment Scheme
Formative assessment and feedback: Students are expected to take an active part in their learning, and contribute to discussion and debate of module activities during workshops. Formative feedback will be provided during workshops on formative activities, and other learning activities such as self-check activities that are specifically designed to provide guidance and feedback.
Students are also encouraged to participate in the discussions on the online module page.
Summative assessment consists of three components selected in order to ensure students demonstrate an overall understanding of relevant concepts and techniques as well as the ability to apply and critique them in appropriate contexts. The three assessment components are:
Group Coursework: 30%This will assess students’ ability to conduct a financial data analysis activity involving construction of a financial index and to critically analyse and discuss the results using a computer package. (Learning Outcomes 1 to 10). Groups will be required to write a group report and an individual reflection on the process submitted in week 12.
Individual Coursework: 30% This will be a time series and forecasting individual (data modelling) exercise in an appropriate package modelling financial data submitted in week 20. (Learning Outcomes 1-8 and 10).
Unseen Examination (2 hour): 40%The end-of-year examination will assess the understanding of concepts and the ability to critically evaluate the theories and methods.(Learning Outcomes 1- 8 and 10).
Assessment Weighting
Coursework 60% Examination 40%
Exam Duration
Examination, 2 hours
Learning Materials
Your online reading lists can be accessed from the My Study area of UniHub. They highlight essential and recommended reading for all modules you are registered on.