M.Phil. Maths Crash CourseThis page contains details of the first week of the 2009 M.Phil. Maths Crash Course (taught by Chris Wallace). For further details and information about the second week, see the mathematics methods course page. Jump ahead to the relevant section:
Quick DownloadsYou can download my lecture slides for this course using the links below. All documents are in .pdf format. Most modern web browsers are equipped with an Acrobat reader to access these files. Visit Adobe for more details.
Course OutlineThe course outline containing all the details on this page is available here. This is the document you were sent in the introductory pack during the summer. You should also have been sent the Preparatory Work document, which provides pre-course reading along with exercises and answers. Course ObjectiveThis course is intended for those taking the M.Phil. in Economics at Oxford University. The course covers the main mathematical pre-requisites for the M.Phil. All incoming students for the M.Phil., unless they have a very good background in mathematics and statistics, are advised to attend. PRS students may also find the course useful, and are welcome to attend if they wish. TeachingThis week's lectures are on the following days:
There will be a twenty minute coffee break at 10.30 each day. The first lecture takes place in the Lecture Theatre at the Manor Road Building. The remaining lectures will be held in Seminar Room A. The associated classes take place in the Lecture Theatre on the first day and Seminar Room A subsequently, on the same days as the lectures, between 4.30pm and 5.30pm. ExercisesExercises will be distributed during the lectures. You can also download Exercises 1-3 together in a single file. These will be reviewed in the afternoon class, so you should work on them during the day. Solutions will be distributed during the class, and you will be able to download Answers 1-3 after the course is over.ContactI can be reached at Trinity College or at the Department of Economics. Email is best. ReadingThere are many good introductory textbooks: for the first four topics, you may wish to try:
For probability and distributions, try:
A more advanced treatment of all five topics may be found in:
Topic OutlineThe first week's lectures cover five topics. A brief guide to the content follows. Topic 1: Sets and SequencesSets and sequences: open, closed, bounded, compact, and convex sets, supremum and infimum, convergence, continuity. Topic 2: Functions of One or More VariablesIntermediate Value Theorem. Bolzano and Brouwer fixed point theorems. Taylor and Maclaurin expansions, mean value theorem, L'Hopital's Rule. Weierstrass' theorem, homogeneous functions, Euler's theorem, homothetic functions, repeated integrals, differentiating integrals. Topic 3: Equations and MatricesEquations and matrices, linear systems, Cramer's rule, rank, eigenvectors and eigenvalues. Topic 4: Comparative StaticsCalculus with several variables, total differential and derivative. Implicit differentiation, implicit function theorem, comparative statics. Topic 5: Probability and DistributionsProbability and some important distributions (Poisson, log-Normal, gamma), moments, Jensen's and Chebychev's inequalities, conditional probability, Bayes' theorem. |