About the MSc Preliminary course
Aim of the course
Prerequisite of the course
Rooms and times
Course outline
Reading list

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About the MSc Preliminary course.
This course is an essential prerequisite for all students taking the MScs in Economics, MSc Development Economics, MSc in Finance and Development, and the MSc Political Economy of Development. 

The preliminary course is broken into two parts.

• Mathematics component - from 14th to 22nd of September 2009
  
• Statistics and computing components - from 23rd to 30th September. 

The 1st of October is a revision day.  On the 2nd of October, there will be a three-hour examination.  Attendance at the pre-sessional course is mandatory.  Performance on the exam will act as an indicator as to the students’ ability to complete the MSc.

• use matrices for simple manipulations
• solve system of equations using matrix algebra
• understand derivates and partial derivatives
• use Jacobian determinants to test for functional dependence
• understand differentials, total differentials and total derivatives
• use exponential and logarithmic functions to analyse growth
• find unconstrained optima of functions with one or more choice variables
• find constrained optima using the Lagrange multiplier and substitution methods
• use these techniques to solve problems in economics.
  

Prerequisite of the course.
This course revises material usually taught in an undergraduate degree.  It will be assumed that all students are familiar with elementary algebra and calculus, including:

• Functional relationships and graphs
• Equations and inequalities
• Solutions and linear and quadratic equations
• Solution of simple simultaneous equations
• The concepts of a derivative and rules for differentiations

Revision booklets available from the mathcentre are useful if you need a quick reminder. 

Rooms and Times.
Sept. 14th to Sept. 22nd 2009 inclusive (7 days).
10 a.m. to 1 p.m.
Room V211
Vernon Square

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Course outline.
Click here to download the Course outline/Reading list.

1. Matrix algebra. Matrix, Elements of a matrix, Dimension, Row vector, Column vector, Scalar. Equality of matrices, Addition, subtraction, scalar multiplication, matrix multiplication, conformable matrices, rules of matrix operations. Transpose, Properties of transpose, Symmetry, Identity matrix, i vector, Null matrix, Diagonal matrix, Idempotent matrix. Quadratic form, Positive definite and negative definite matrices. Determinants, minors, cofactors. Properties of determinants, alien cofactors, non-singular and singular matrices. Linear dependence and independence, rank of a matrix, non-singular and singular matrices. Inversion, properties of inverse, solution to a system of non-homogenous linear equations. Cramer’s rule.
   
2. Calculus. Rules of differentiation for functions of single variable, constant function rule, power function rule, sum difference rule, product rule, quotient rule, Monotonic functions, monotonic increasing (decreasing) functions, inverse function rule, inverse function rule generalised. Partial differentiation, Jacobian determinants. Differentials, rules of differentials, total derivatives, derivatives of implicit functions, economic examples.
   
3. Exponentials and Logarithmic Functions. Exponential functions, logarithmic functions, natural exponential and logarithmic functions, rules of logarithms, derivatives of exponential and logarithmic functions, economic applications
4. Optimization. Relative extrema of a function of one choice variable, first derivative test for a relative extremum, second derivative test, necessary versus sufficient conditions, inflection points, nth derivative test for relative extrema or inflection points. Optimum values of functions containing two or more choice variables, first-order conditions, sufficiency and necessity, economic applications.
   
5. Constrained Optimization. General statement of constrained optimization
   Solutions by direct substitution and the Lagrange multiplier method, Interpretation of the Lagrangian multipliers, Comparative static applications. Second order conditions, bordered Hessian.

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Reading list.
The topics listed above are covered in almost all introductory mathematics textbooks for economists.  Many of you will have books from your undergraduate degrees that cover the topics.  The following are some recommended books you may refer to for the course:

• Chiang, A. C. and K. Wainwright (2005) Fundamental Methods of Mathematical Economics, Forth Edition. McGraw-Hill.

This textbook covers all the required topics in introductory and intermediate level mathematical economics with rigor and detail.  However students with less exposure to mathematics may find some of the expositions difficult.

• Thomas, R. L. (1999) Using Mathematics in Economics, Second Edition. Addison-Wesley.
• Jacques, I. (2009) Mathematics for Economics and Business, 6th Edition, Prentice Hall.

These textbooks are popular amongst students, because of the more accessible exposition in explaining mathematical techniques.  However both books only cover part of the material on matrix algebra that is required for this course.

• Dowling, E. T. (2000) Introduction to Mathematical Economics, Third Edition. McGraw-Hill.

This textbook provides problems with step-by-step detailed solution.  While it may not be sufficient as a stand-alone textbook, it is a useful supplementary source for exercise and revision.

• Abadir, K. M. and J. R. Magnus (2005) Matrix Algebra, Cambridge U. P.

This book offers a comprehensive overview of matrix algebra with exercises – another textbook ideal for further problem solving and revision.