The National Centre for Econometric Research (NCER) will hold a Short Maths Course at QUT, from Wednesday 27 to Saturday 30 April. If you are interested in attending, please contact the Administration Coordinator.
All sessions will be held in the Dennis Gibson Room, Z1064, Gardens Point Campus.
Course Overview
The short course in mathematics for economics and finance aims to provide the core principles of comparative static analysis and simple static optimisation. It is aimed at providing first-year postgraduate students with the necessary mathematical skills to read the current literature, but would also be beneficial to students of more advanced standing, academic staff and members of the private sector who would benefit from refreshing their knowledge of mathematics. The course will be pitched at the level of the classic textbook "Fundamental Methods of Mathematical Economics" by Alpha C Chiang and will loosely follow Parts 3 and 4 of this text. The course will be taught by Kenneth Lindsay who is a professor of mathematics at the University of Glasgow.
Course Convener
Professor Kenneth Lindsay, Department of Mathematics, University of Glasgow.
Kenneth Lindsay received an undergraduate degree in Mathematics and Natural Philosophy from the University of Glasgow, Scotland, and a D.Phil in Continuum Mechanics and Thermodynamics from the University of Oxford (Merton College). His early work concerned aspects of nonlinear wave propagation leading to shock wave formation. Later work involved the use of spectral analysis and energy methods to study the stability of fluid convection driven by heating and other destabilising mechanisms followed later by work in linear and second order elasticity based on the use of integral transform methods. His most recent research is concerned with the use of mathematics in Neuroscience and in Finance. The important theme unifying what appear at first sight to be very different disciplines is the inherent stochastic nature of the underlying problems which involves the mathematics of point processes (discrete processes) and stochastic calculus (continuous processes).
Course Notes/Exercises/Solutions
Download course notes (zip, 514kb)
Download Exercises on Differential Calculus (pdf, 133kb)
Download Solutions to Exercises (pdf, 123kb)
Course Schedule
Day 1 - Wednesday 27 April
| Session | Topic |
|---|---|
| # 1 (9am - 10:30am) |
Notion of Continuity and Differentiability of a Function Rate of Change and the Derivative The Derivative and the Slope of a Curve The Concept of a Limit Differentiation of the power function from first principles Show that the derivative of the sum is the sum of derivatives Differentiation of polynomials Computation of tangent lines to polynomial curves |
| # 2 (11am - 12:30pm) |
Radian measure Simple trignometric functions and their derivatives The exponential function and its derivative The logarithm function and the natural logarithm and their derivatives |
| # 3 (3pm - 4:30pm) |
Tutorial/Problems |
Day 2 - Thursday 28 April
| Session | Topic |
|---|---|
| # 1 (9am - 10:30am) |
Limit Theorems - ie product and quotient rules and examples of their use Chain rule for differentiating composite functions Examples in the use of the chain rule Higher derivatives Extremal and stationary values of functions of a single variable Taylor's theorem on the expansion of functions |
| # 2 (11am - 12:30pm) |
Modelling with polynomial and exponential functions |
| # 3 (3pm - 4:30pm) |
Tutorial/Problems |
Day 3 - Friday 29 April
| Session | Topic |
|---|---|
| # 1 (9am - 10:30am) |
Partial Differentiation for functions of two variables Extension to functions of many variables The chain rule for partial differentiation Implicit differentiation Taylor's theorem for functions of many variables |
| # 2 (11am - 12:30pm) |
Differentials Total Differentials Rules of Differentials Total Derivatives Absolute Value Algebra of Inequalities |
| # 3 (3pm - 4:30pm) |
Tutorial/Problems |
Day 4 - Saturday 30 April
| Session | Topic |
|---|---|
| # 1 (9am - 10:30am) |
Extremal and stationary properties of functions of several variables The Hessian for functions of several variables The notion of convexity and Jensen's inequality Constrained optimisation The method of Lagrange Multipliers |
| # 2 (11am - 12:30pm) |
Complex numbers and their meaning The fundamental theorem of Algebra The arithmetic of complex numbers DeMoivre's Theorem Polar form of complex numbers Connection between exponential and trignometric functions |
| # 3 (3pm - 4:30pm) |
Tutorial/Problems |
Enquiries and Registration
For QUT members and NCER Corporate Affiliates, this course is free of charge.
For all other participants, the there is a $500 registration fee. Please make your payments via QUTPay.
For further details please contact the NCER Administration Coordinator:
Angela Fletcher
Queensland University of Technology
Email: a.fletcher@qut.edu.au