This is a work-intensive applications-oriented course on advanced mathematical methods for economics. The course is directed toward first-year Ph.D. students. It focuses on the methods of dynamic optimization, such as optimal control and dynamic programming, and their mathematical prerequisites, such as integration and difference/differential equations. The objective is to develop students' understanding of how to frame dynamic modeling ideas and how to make intelligent use of advanced computer software (such as Maple or Matlab) to facilitate the modeling process.
The final grade will be based on two exams, with a weight toward the final grade of 40 percent each, and a set of homework assignments with a combined weight of 20 percent.
Every student is responsible for checking his/her email and the course webpage regularly before and after class, as course information is transmitted via email and the course webpage (see below). Make sure your instructor knows your email address from day one. If you have any problems, concerns, or suggestions, please contact your instructor via email. You will get a response typically in much less than 24 hours. That includes weekends and holidays.
Computer Use: Students are expected to be familiar wtih the MTSU computing environment and mathematics software packages, such as Maple, in the first couple of weeks. The Getting Started web page provides a convenient summary of some basic facts on both.
Prerequisites: Familiarity with the topics of Econ 6100 Mathematical Methods for Economics.
Textbook: The course will not follow a textbook. Students are expected to carefully study the lecture notes that are made available on line and to read the relevant material in textbooks and reference works listed below.
Course webpage To view the lecture notes, problem sets, and other material on the course webpage, you will need both a userid and a password. Both are available from the instructor at the beginning of the course.
Office hours: We 4:00 through 6:00, by E-mail or by appointment. Check all questions and problems first via e-mail.
Special Note: Students with a disability that may require assistance or accommodation, or with questions related to any accommodations for testing, note takers, readers, etc., should contact the instructor as soon as possible. Students may also contact the Office of Disabled Students Services (898-2783) with questions about such services.
1. Basics of Mathematical Statistics
2. Difference Equations
3. Differential Equations
4. Dynamic Optimization in Continuous Time
5. Dynamic Optimization in Discrete Time
6. Elements of Advanced Matrix Algebra
Abadir, Karim M., and Jan R. Magnus, Matrix Algebra. Cambridge
University Press, 2005.
Adda, Jerome, and Russell Cooper, Dynamic Economics: Quantitative Methods and Applications. MIT Press 2003.
Baldani, Jeffrey; Bradfield, James, and Robert Turner, Mathematical Economics. 2nd ed., Thompson-South Western, 2005.
Carter, Michael, Foundations of Mathematical Economics. MIT Press 2001.
Caputo, Michael R., Foundations of Dynamic Economic Analysis. Cambridge University Press, 2005.
Chiang, Alpha C. and Kevin Wainwright, Fundamental Methods of Mathematical Economics, 4th ed., Mc-Graw Hill-Irwin, 2005.
Chiang, Alpha C., Elements of Dynamic Optimization. Mc-Graw Hill, 1992.
Dowling, Edward T., Introduction to Mathematical Economics. 3rd edition, Schaum's Outlines Series. McGraw-Hill, 2001.
De la Fuente, Angel, Mathematical Methods and Models for Economists. Cambridge University Press, 2000.
Gandolfo, Giancarlo, Economic Dynamics. Springer 1997.
Hoy, Michael; Livernois, John; McKenna, Chris; Rees, Ray, and Thanasis Stengos, Mathematics for Economics. 2nd edition, MIT Press, 2001.
Kamien, Morton I. and Nancy L. Schwartz, Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management. North Holland, 1981.
Kendrick, David A., Mercado, Reuben P., and Hans M. Amman, Computational Economics. Princeton University Press, 2006.
Klein, Michael W., Mathematical Methods for Economics. 2nd edition, Addison-Wesley, 2002.
Ljungqvist, Lars, and Thomas J. Sargent, Recursive Macroeconomic Theory. 2nd ed. MIT Press, 2004.
Lynch, Steven, Dynamical Systems with Applications Using Maple. Birkhäuser, Boston, 2001.
Medio, Alfredo, and Marji Lines, Nonlinear Dynamics: A Primer. Cambridge University Press, 2001.
Mikosch, Thomas, Elementary Stochastic Calculus. World Scientific, 1998.
Miranda, Mario J. and Paul L. Fackler, Applied Computational Economics and Finance. MIT Press, 2002.
Parlar, Mahmut, Interactive Operations Research with Maple. Birkhäuser, Boston, 2000.
Rose, Colin, and Murray D. Smith, Mathematical Statistics with Mathematica. Springer, 2002.
Searle, Shayle R. Matrix Algebra Useful for Statistics. John Wiley, New York, 1982.
Sethi, Suresh P., and Gerald L. Thompson, Optimal Control Theory: Applications to Management Science and Economics. 2nd ed., Springer, 2000.
Shone, Ronald, Economic Dynamics: Phase Diagrams and Their Economic Application. Cambridge University Press, 1997.
Simon, Carl, P., and Lawrence Blume, Mathematics for Economists. Norton, 1994.
Sydsaeter, Knut, and Peter J. Hammond, Mathematics for Economic Analysis. Prentice Hall, 1995.
Turkington, Darrell A., Mathematical Tools for Economics. Blackwell Publishing, 2007.
last revised: August 7, 2009