Year Two MORSE
Module Guide
Compiled by Iain Carson
Modified by Daniel Wilson-Nunn
Summer 2013
Version 3
Contents
0 Introduction
1 Core Modules
1.1 ST202 - Stochastic Processes . . . . .
1.2 ST208 - Mathematical Methods . . . .
1.3 ST218 - Mathematical Statistics A . .
1.4 ST219 - Mathematical Statistics B . .
1.5 EC220 - Mathematical Economics 1a .
1.6 IB207 - Mathematical Programming II
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2 List
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
(A)
EC204 - Economics 2 . . . . . . . . . . . . .
EC221 - Mathematical Economics 1b . . . .
IB211 - Simulation . . . . . . . . . . . . . .
ST221 - Linear Statistical Models . . . . . .
ST213 - Mathematics of Random Events . .
MA244 - Analysis III . . . . . . . . . . . . .
MA225 - Differentiation . . . . . . . . . . .
MA222 - Metric Spaces . . . . . . . . . . .
MA250 - Introduction to Partial Differential
3 List
3.1
3.2
3.3
3.4
3.5
3.6
(B)
IB109 - Foundations of Accounting and Finance .
IB206 - Introduction to Business Studies . . . . .
IB217 - Starting a Business . . . . . . . . . . . .
MA117 Programming for Scientists . . . . . . . .
MA209 - Variational Principles . . . . . . . . . .
MA246 - Number Theory . . . . . . . . . . . . .
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0
Introduction
I have gone to as much effort as I can to ensure that the information in this guide is still serviceable, and that details are accurate. I will reiterate what Iain said last year in that if you have
taken a module, and had a very different experience to that in this document, let us know and
we can update this guide. Or indeed if you have taken a module that there is no information
on in this document, again let us know so that we can help future generations of MORSE and
MathStats students.
Summer 2013
Daniel Wilson-Nunn
This guide will go out of date every year, and so must be updated regularly. I cannot guarantee
that future execs will be diligent about this, so please check when this was last updated and see
if you can trust the comments given!
As always, use this guide at your own risk: the comments are only opinions, and are based on
an unreasonably small sample size. As such, your opinion of the module might be completely
different to what is written here. If it is, then please get in touch with a paragraph of your own
about the module, and it will be included in here too! Similarly, if you have taken a module
which is not mentioned in this guide, then please let us know your thoughts about it.
Iain Carson
Summer 2012
Regulations
The following is taken directly from the MORSE Handbook:
The normal load in the second year is 120 CATS points. The maximum load is 150 CATS.
Candidates for Honours are required to take the core modules, at least 36 CATS from
List (A), and an appropriate number of modules from List (B).
Candidates for Pass degrees are required to take the core modules and 12 CATS from List
(A). At the discretion of the Chair of the Statistics Department, the total load for such
students may be increased up to a maximum of 120 CATS.
Students cannot take ST335 Finance and Financial Reporting
ii
1
1.1
Core Modules
ST202 - Stochastic Processes
Term 1
12 CATS credits
This is an intuitive module whilst having lots of applications and forms the basis for many
modules in future years. There are also quite a few calculation bits so if you enjoy dealing
with actual numbers, you’ll enjoy it. The module is heavily dependent on definitions etc. to
introduce concepts so its important to understand and learn them early on so that you do well
in the class test and follow the module. The class test is based on a question from a worksheet
or exam question (usually calculations and vital concepts) so its important to turn up to the
seminars. The exam itself is slightly less calculations and more proofs but nevertheless is still
manageable. Overall, this is a useful module for future years and is quite fun!
This module leads to ST333 - Applied Stochastic Processes.
Rajinder Poonian
This module is quite stimulating, and is apparently useful for later modules in finance, as well as
those which involve Markov chains, and of course ST333 - Applied Stochastic Processes.
There are lots of unassessed exercise sheets which will allow you to practise ahead of the class
test and exam.
Iain Carson
1
1.2
ST208 - Mathematical Methods
Term 1
12 CATS credits
This is the follow up module to ST108 Applications of Algebra and Analysis in first year. Again
it is lectured by Heather Humphries, and again it is well lectured. She appreciates that the
mathematical concepts in the module don’t come easily to most MORSE students so takes the
time to go over them properly, relating them to things easier to understand. This course is also
much less reliant on proofs and theorems, instead concentrating on applications of the theory
in the lecture notes. It also covers topics which should already be familiar: linear algebra,
differentiation and integration. There is a question sheet provided each week, and in addition to
the three lectures per week, there is a very helpful weekly problem class where you can speak to
Heather about any problems with the question sheets or with any of the course material.
As with ST108 - Applications of Algebra and Analysis, there are two tests over the term: one
half-way through the course and one at the end of the course, and again in both you are allowed
an A4 crib sheet. The difference in this module is that in addition to the tests there is also a
final exam in the summer, which is closed-book.
However, the exam is very similar to the exercise sheets, in that there is very little theory, and
what theory there is can be replicated straight from the lecture notes, so once you are confident
with the applied material, the exam should be relatively straightforward.
If you like the linear algebra, metric spaces, and differentiation topics covered in this module,
you may want to look at doing the corresponding mathematics modules MA251 - Algebra I,
MA222 - Metric Spaces, and MA225 - Differentiation, for the mathematics modules are just
more in-depth work of this module!
This module leads to: ST323/ST412 - Multivariate Statistics.
Rajinder Poonian
This module is an introduction to various mathematical fields. If you like any of these (differentiation, linear algebra and metric spaces), then you can take their corresponding modules
offered by the mathematics department in year two, or in some cases in later years.
The style of the course is very similar to ST108 Applications of Algebra and Analysis.
Iain Carson
2
1.3
ST218 - Mathematical Statistics A
Term 1
12 CATS credits
This module is very technical, and quite a number of students find it really hard. Essentially,
it’s a direct follow-on from ST115 - Introduction to Probability. It covers more distributions in
more depth, and extends them to the bivariate and multivariate cases.
Expect to do more proofs than last year, and to understand earlier concepts like the Weak
Law of Large Numbers in much more detail. Expect also to do lots of calculus! As such, the
lecturing style is much denser, with very little chit-chat about practicalities compared with year
one.
The assessment method is 100% exam, but there are four exercise sheets and seminars to help
you to understand the material along the way.
This module leads on to sister module ST219 - Mathematical Statistics B, which is also core.
Iain Carson
3
1.4
ST219 - Mathematical Statistics B
Term 2
12 CATS credits
This module covers the other side of mathematical statistics, after ST218 - Mathematical Statistics A. It’s completely different, but at the same time still relies on previous statistical knowledge.
You will be doing statistics concerned with hypothesis testing, constructing confidence intervals,
and finding maximum likelihood estimators, as well as their associated properties.
As a whole, I found that this module went at a much slower pace and was far less technical than
ST218 - Mathematical Statistics A.
The assessment method is 100% exam, but again, there are four unassessed exercise sheets and
corresponding seminars as well.
This module leads on to the third and fourth year statistics courses.
Iain Carson
4
1.5
EC220 - Mathematical Economics 1a
Term 1
12 CATS credits
This module currently focuses on just two topics, decision theory and game theory, as well as the
concepts briefly introduced in EC106 - Introduction to Quantitative Economics, expanding upon
them. The content is fairly intuitive and easy to follow, but the mathematical notation used
can be quite confusing, though it is rarely used outside the lecture notes and is not examinable.
Since you will be tested on applying theories and methods, it is important to attend the seminars
and attempt the worksheets. Confusingly, methods and answers between lecturer and seminar
leader have differed in previous years.
Material covered in ST218 - Mathematical Statistics A may help in some parts of the decision
theory aspect, and revising material from MA132 - Foundations might also help here too.
MORSE students do not need to take the class test, for it is not counted. However, for nonMORSE students, this module is worth 15 CATS credits, and the class test is counted.
Rajinder Poonian
This module is hard to score well on. Most of the principles involved are relatively straightforward, but when you start looking at them closely, there can be lots of paradoxes, irregularities
and contradictions. Quite a lot of lecture time is spent discussing the problems with and shortcomings of solution concepts.
There is a lot of complicated notation in the module which is hard to get your head around, let
alone manipulate.
Most of the module is on game theory, but there is also a bit on decision theory at the start of
the module.
For MORSE students, the exam is worth 100%.
Iain Carson
5
1.6
IB207 - Mathematical Programming II
Term 1
12 CATS credits
Like IB104 - Mathematical Programming I, this module is a mix of all sorts of different areas
of mathematical programming. Yet the coursework is fairly similar to the one you get in first
year, and just builds on it slightly with the inclusion of dynamic programming and Dijkstra’s
algorithm.
As before, you will be studying linear programming, duality theory and graph theory. Not only
does this module extend these topics in many different ways, but there are also new subjects
introduced, such as convexity (following on from ST208 - Mathematical Methods) and dynamic
programming. You will also see more applications than were given last year, in particular to the
airline industry.
This module leads to IB352 - Mathematical Programming III and IB391 - Decision Analysis.
Iain Carson
6
2
2.1
List (A)
EC204 - Economics 2
Terms 1 and 2
30 CATS credits
This module is designed to teach core economic concepts to students on joint degrees such as
PPE and MORSE, and it follows on quite nicely from EC106 Introduction to Quantitative
Economics. The module is split into two halves, with microeconomics taught in the first term
(general equilibrium theory, game theory), and macroeconomics in the second. There is one
2000-word essay per term worth 10% each, and a final summer exam worth 80%. There are
also fortnightly seminars which go through problem set questions, and can be quite useful. The
seminars try to bring the study of economics to life more than most, so be prepared to get fully
involved in these. The exam is mainly written, though the mathematical content has increased
since 2008. There is also a little content overlap with EC220 Mathematical Economics 1a.
Rajinder Poonian
7
2.2
EC221 - Mathematical Economics 1b
Term 2
12 CATS credits
This module deals with and expands upon competitive equilibrium, which was briefly introduced
in EC106 - Introduction to Quantitative Economics. This course features a lot of mathematical
notation, and can be quite confusing at times. This course is excellent for students who like
following set mathematical methods and applying them to similar problems as most problem
sheets are like this. There is a test at the end of term 2 for this module worth 20%. The lecture
notes go into a lot of detail, but you will need to do the worksheets and go to seminars to go
through enough examples.
The Lagrangian multiplier from EC106 - Introduction to Quantitative Economics and ST208
- Mathematical Methods appears many times in this module, and can come up in all exam
questions, so knowing this is essential.
MORSE students do not need to take the class test, for it is not counted. However, for nonMORSE students, this module is worth 15 CATS credits, and the class test is counted.
Rajinder Poonian
This module builds on the Edgeworth box economies, utility functions and constrained optimisation principles encountered in EC106 - Introduction to Quantitative Economics. You will also
come to understand the
rst and second fundamental theorems of welfare economics.
Lots of the intuition for this module is graphical, and is then put to use with lots of maths and
computation, particularly concerning Pareto optimal and technologically efficient points, and
Walrasian equilibria.
The examination is worth 100% of the module.
This module leads onto EC301 and EC341 Mathematical Economics II, and other third-year
economics modules.
Iain Carson
8
2.3
IB211 - Simulation
Term 2
12 CATS credits
Simulation is the nicest of all the coursework option modules available to second years, with a
very interesting content, clear notes, and weekly support classes. The course centres on the use
of a program called SIMUL8, which although difficult to grasp at first, becomes very easy to
use and manipulate as time goes by. The seminars build up more complex simulations as the
weeks go by, and if attended, make the coursework much easier. The coursework itself is divided
into the construct of a model in a group, consisting of 40% of the module mark, and then an
individual analysis for the remaining marks. The only issue with taking this module is the fact
that the deadlines are at similar time to the other coursework options, and therefore good time
management is needed to not leave it to be rushed.
Rajinder Poonian
This module is quite straightforward, and really useful. You will learn to use the software
SIMUL8 and Statfit, which are used in the business world to analyse problems and test courses
of action.
Just as you would in the real world, you will need to find a proper project to work on and
optimise, either off or on campus. This could be something like looking at the queuing systems
in the campus food outlets, or analysing how we students use systems in the library.
This project is worth 100% of the module, and is split into a group task of building the model,
and then an individual report based on finding useful results from the model which you have
built.
There is just one lecture per week, two hours in length. The one-hour seminar is much more
important, as this is where you will be using the software, both individually and in your
group.
The module IB320 - Simulation is in fact the same module, so unfortunately you can’t do both!
Iain Carson
9
2.4
ST221 - Linear Statistical Models
Terms 2 and 3a
12 CATS credits
This module was taught for the first time this year (2012/13) and was very well organised and
structured compared to some other modules. There were 2 lecturers who each taught different
topics. The first eight weeks of the course focuses on linear statistical models and gives lots
of properties and examples of these, mainly based on multivariate random variables. The last
two weeks focus on time series modelling and was taught by the other lecturer. The module is
taught at the end of term 2 and the start of term 3 with 3 lecturers per week and one computer
class per fortnight.
There are two pieces of coursework for this module, either side of the Easter holiday each worth
15% using the computer program R with a deadline a week after it is given out so can be quite
time constrained, but isn’t particularly difficult in terms of content once you’ve got your head
around the computer program.
Overall this is one of the more accessible statistics modules in terms of content, and gives some
nice applications of the more complex content from other modules such as ST218 Mathematical
Statistics A and ST219 Mathematical Statistics B.
Mel Scrutton
10
2.5
ST213 - Mathematics of Random Events
Term 2
12 CATS credits
This isn’t the nicest of Statistics modules, but unfortunately it is core for all Statistics students.
Its quite abstract and if you liked Analysis 2, its very much like that (i.e. staring at the
question, wondering what to do exactly). Try to pay attention as much in lectures as there are
the occasional times where you do understand something (plus a mental image is always good
for exam time). The big tip for this module is just to learn all the definitions and theorems
thoroughly to get the easy marks, and then play around with them to see if you get anywhere.
It starts off at a slow pace, telling you things which youve already been told 5 times, but then
gets very hard all of a sudden, and extra reading and work especially on weekly worksheets is
necessary to really understand what is needed.
However, you’ll find that ST213 - Mathematics of Random Events is taking ideas and putting
them into a probability framework, and it actually becomes easy if you have a firm grasp of
the topics in the following modules: MA132 - Foundations (set theory), MA131 - Analysis I
(convergence of sequences), ST115 - Introduction to Probability, MA244 - Analysis III (step
functions and regulated functions), and MA222 - Metric Spaces (bases, subbases, open sets and
pre-images).
Rajinder Poonian
Lots of people think that this is the hardest module in the whole of MORSE. You will be
faced with a load of mathematical symbols, concepts and theorems, and will be expected to
grapple with them without properly understanding where they have come from or what their
real purpose is.
As Rajinder has said, it starts quite slowly, but the pace soon becomes quick, to the point of
being overwhelming.
This module leads on to ST318 - Probability Theory and MA359 - Measure Theory.
Iain Carson
11
2.6
MA244 - Analysis III
Term 1
12 CATS credits
If you are planning to do any maths modules, I would advise to do this one the most since it
is well taught and very manageable. It is also a prerequisite for pretty much any future maths
module. I would think it is slightly easier than the current syllabus of MA131 - Analysis II, for
there is some talk of switching the syllabus of MA244 - Analysis III and MA131 - Analysis II.
The course is quite interesting and it is nice to get the exam out of the way before all the June
ones.
The assignments are quite manageable, but like in Analysis I and II will need more work in
some places than others. This year [2010], with marks not being released yet, was a very nice
paper in my opinion with each question consisting of several small parts which guided you well.
There are support classes available too.
The concept of step functions and regulated functions come in very handy in ST213 - Mathematics of Random Events when comparing with (simple) random variables.
This module leads to: MA222 - Metric Spaces, MA225 - Differentiation, MA359 - Measure Theory, MA3F4 - Linear Analysis, MA3G1 - Theory of PDE’s and many others.
Rajinder Poonian
12
2.7
MA225 - Differentiation
Term 2
12 CATS credits
This is also a second year Maths course taken by Statistics students in their third year. Even
though it is called Differentiation, it covers numerous topics such as metric spaces, continuity,
and other concepts from first year analysis, applied to more than one dimension. It has to be
said that some parts of the course are a lot more applied than others.
The course is 100% exam, but there are assignments handed out weekly. They are not compulsory but I would strongly advise working through them, as questions very similar to those in
assignments featured prominently in the exam. Another thing to bear in mind is that MA244
Analysis III is a prerequisite for this module.
Rajinder Poonian
13
2.8
MA222 - Metric Spaces
Term 2
12 CATS credits
This is a very abstract module designed only for hardcore mathematicians, but made easy
if you draw a lot of diagrams. It can even be the easiest module provided you are the sort
that doesn’t mind getting messy and drawing pictures in your work. Interestingly, the basics
of this module provides the largest stumbling block, but for those who have taken ST208 Mathematical Methods, the lecturer would have gone through the basics in a comprehensive
manner, which makes this module even easier. There are a certain amount of definitions which
need to be understood, and the techniques for solving some questions may be different from
what one has encountered before, but they share many similarities with ST213 - Mathematics
of Random Events, which is a compulsory module for MORSE students. So if you like ST213 Mathematics of Random Events, you may as well do this module.
There are 2 tests which are worth 15 percent altogether. The lecture notes are quite helpful, as
well as the recommended textbooks, but you need to do worksheets to even have a chance of
understanding it.
Rajinder Poonian
14
2.9
MA250 - Introduction to Partial Differential Equations
Terms 1b and 2a
12 CATS credits
No students who have taken this module have been able to provide an opinion of this module
yet.
15
3
3.1
List (B)
IB109 - Foundations of Accounting and Finance
Terms 1 and 2
24 CATS credits
Impressions I get from this module is that it is very manageable, and obviously involves a lot
of number crunching. There is a test in January which is multiple choice. It is well taught but
not at a nice time! Lecture notes are very good to learn from, if you cant or wont make the
early starts. Accounting isn’t known for being the most interesting of areas, but is obviously
very practical. However beware in taking this module if you are going down the Actuarial route,
as it will prevent you from taking ST335 - Finance and Financial Reporting, which gives an
exemption for CT2.
While this is a Year 1 module, MORSE students are only allowed to take it in their second year.
Rajinder Poonian
16
3.2
IB206 - Introduction to Business Studies
Term 3a
6 CATS credits
Four topics are covered in the module: Marketing, Human Resources, Accounting & Finance
and Operations Management. All are run by different lecturers. The module is very interesting
(with small case studies as examples usually) and is easy to understand since quite a lot is based
on common sense. The module is assessed by a two-hour multiple choice paper, but the answers
can often be confusing. Past papers are supplied with no answers. You also get penalised for
incorrect answers. Since it is held in term 3 it can disrupt or provide a break from revision, so
you should keep this in mind. Another thing to bear in mind is that this module is now only for
second year students. Many real life examples are provided, making understanding relatively
straightforward.
Rajinder Poonian
This is a good introduction to a few areas of business, and since each part only lasts one week,
it’s never long until you move on to a new area and a new lecturer if you don’t like the current
ones.
This module leads on to many options run by the business school, but especially IB253 - Principles of Finance I and then IB254 - Principles of Finance II.
There is quite a lot of rote learning of acronyms and names of categories of things like methods
of production, for this module. Yet very often these concepts are also seen put into practice albeit briefly - using videos, case studies and everyday examples.
Iain Carson
17
3.3
IB217 - Starting a Business
Term 2b
6 CATS credits
This module is really more of a filler than anything else; useful if you need to boost your CATS
level, or obviously if you are considering starting up your own business at the end of university.
Unsurprisingly it covers all the aspects of business that you need to know if you are starting up
your own company, from generating ideas for the business to creating financial statements for
the company. Only the basics of each concept are covered, due to the course only running for
15 lectures.
This module, like IB211 - Simulation and ST215 - Forecasting and Control, is assessed by
coursework, in the form of a business plan based on one of your own ideas. If you are thinking
of doing this module it would certainly be wise to have an idea of what you want to do either
before the lectures begin or within the first couple of weeks because the lecturer moves quite
quickly through the material due to the time constraints, so you are in a much better position
if you keep up with the lectures, and also if you have any problems with your plan it is a lot
easier to sort them out earlier on in the course, because while the lecturer is very accessible, he
is likely to have lots more queries to deal with later in the term so the earlier you see him you
the more time he has to help you.
If you are thinking of taking any accounting/finance modules in your third year, or are planning
on taking IB206 - Introduction to Business Studies and haven’t done anything similar before
then the finance part of this course I think provides quite a good crash course in financial terminology and concepts. One thing to note is that, like IB211 - Simulation and ST215 - Forecasting
and Control, the coursework is done over the Easter holidays and based on my own experience
it was very difficult to do all 3 at the same time so I recommend you manage your time effectively.
Rajinder Poonian
18
3.4
MA117 Programming for Scientists
Term 2
12 CATS credits
This module is about learning Java and is 100% assessed by computer code coursework. There
are three main projects to be done, with one additional ‘test’ program to be done first, in order
to familiarise you with the system.
There is just one lecture per week, as well as one two-hour programming session. During these
sessions, there is set work to begin with, which teaching assistants will support you on, but as
the module progresses, the time will be given over to work on the assessment.
Once you are familiar with the style of language and code which you must learn to deal with,
then this module is relatively straightforward.
Lecture slides are usually printed out by the lecturer, and there are good online resources
too.
You can take this module in either year one or year two.
Iain Carson
19
3.5
MA209 - Variational Principles
Term 3a
6 CATS credits
This is a relatively straightforward module for those who are interested in maths, but don’t
want to do a whole 12 CATS on it. It is very worthwhile if you are interested in integration,
differentiation and optimisation problems, going deeper into the theory, with the exam not
having heavy proofs.
It is a well taught module, and there are worksheets not for credit. The content has not changed
much in the past 10 years so there is plenty of material to look back on.
Rajinder Poonian
This module is very methods-focused, and is quite satisfying. You will learn about optimisation from the point of view of physics and mathematics, so in a way it complements IB104 Mathematical Programming I and IB207 - Mathematical Programming II.
The key difference between the two approaches to optimisation is mainly in the generality. In
this module, the results will usually apply widely. For instance, it will be shown that the circle
is the two-dimensional shape which maximises area on constraint of perimeter - a result which
holds quite generally, no matter how small or great the perimeter in question.
Some of the methods encountered will build on concepts already covered, such as Lagrange
multipliers met in EC106 - Introduction to Quantitative Economics and ST208 - Mathematical
Methods. Yet this module will also prove these results, and apply them in a wider variety of
situations.
The assessment is 100% by exam.
Iain Carson
20
3.6
MA246 - Number Theory
Term 3a
6 CATS credits
The module handbook tells you most of what you need to know, since you work from workbooks. Often seen as enjoyable at first, but as always with maths modules, you need persistence
for more abstract things. Also there is a lot of new notation, which you have to get to grips
with to do well on the weekly tests. Surprisingly, if you are the person that prefers to go for
Mathematical Olympiads and competitions in your secondary school days, this module will just
be a snap of the fingers.
Rajinder Poonian
There is one scheduled lecture for this module, but this is just to go through the administrative
side of the module.
The size of the book which you need to work through for this module is initially quite scary.
There are five parts, the first four of which are assessed by weekly class tests, which are altogether
worth one quarter of the module. There is also a ‘zeroth’ part of the book, which should usually
be done before the course begins.
Since this module is entirely self-taught, be prepared for it to take a lot of your time, which
can be really annoying since it takes place in term three, when you’ll need to spend most
of your day revising for impending exams. The topics covered are in linear congruences and
modulo arithmetic, Euler’s φ-function and the Chinese remainder theorem, discrete logarithms
and primitive roots, and continued fractions.
You can take this module in either year one or year two.
Iain Carson
21
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