Contents: The first goal of the course is to teach the key mathematical tools that are useful for the study of economics. The second goal, is to show real (but relatively simple) mathematical proofs so that you can get familiar with mathematical reasoning. This should be helpful to understand proof arguments in micro- macro or econometric classes.
Section 1: Introduction to Linear Algebra
a. Linear models, systems of linear equations
b. Vector space and subspaces
c. Matrices, rank, determinant
d. Linear mappings
e. Eigenvalues and eigenvectors
f. Symmetric matrices, quadratic forms
Section 2: Calculus of Several Variables
a. Basic topology: Limits and open sets, compact sets
b. Calculus of several variables: partial derivatives, differentiability, chain rule, special determinants and matrices (Jacobian, Hessian)
c. Convex and concave functions of several variables
d. Homogeneous functions, implicit functions and derivatives
Section 3: Optimization – Comparative Static Analysis
a. Unconstrained optimization
b. Constrained optimization: Equality constraints- the Lagrange problem,
c. Constrained optimization: Inequality constraints- the Kuhn – Tucker problem
d. Concave programming
e. Comparative statics, envelope theorems
f. Economic applications
Bibliography:
· G. Sarafopoulos, N. Mylonas, Linear Algebra, Optimization and Dynamics for Economics (in Greek), Ed. Tziolas,2019 (Primary textbook)
· E. Dowling, Intoduction to Mathematical Economics, McGraw – Hill (Shaum’s series),2001
· M. Hoy et al. Mathematics for Economists, Addison Wesley,2001
· S. Lang, Introduction to Linear Algebra, UTM-Springer, 1986
· Simon – L. Blume, Mathematics for Economists, Norton Co.,2004
[test-short]
