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 ii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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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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 Summer 2013 Daniel Wilson-Nunn This guide will go out of date every year, and so must be updated regularly.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 All material contained within this guide belongs to Warwick MORSE Society. The views and opinions expressed in this guide are soley those of the original authors and other contributors. These views and opinions do not necessarily represent those of Warwick MORSE Society.