One of the most important characteristics of an economist is its ability to abstract from reality in a complex environment and endless relationships amongst actors, institutions, households and time. Therefore, quantitative methods help you to model or caricature the complex reality in models that express events forming consolidated theories. Furthermore, it allows quantifying the relations theories formalized taking as a starting point. Based on this assertion mathematics has become an important tool for the economist and evaluate this summer part of the book entitled entitled "An Introduction to Mathematical Analysis for Economic Theory and Econometrics, by Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman, Princeton University Press, 2009.
ECO 110 - APPLIED MATHEMATICAL METHODS TO ECONOMICS
A – SYLLABUS
Part 1 – Logic: Statements, Sets, Subsets
and Implications; Statements and Their Truth Values; Proofs, a First Look;
Logical Quantifiers; and, Taxonomy of Proofs.
References:
Corbae, Stinchcombe e Zeman
(2009, chap. 1)
Part 2 – Set Theory: Products, Relations,
Correspondences and Functions; Equivalence Relations; Optimal Choice for finite
Sets; Direct and Inverse Images, Compositions; Weak and Partial Orders,
Lattices; Monotonic Changes in Optima: Supermodularity and Lattices; Tarski’s
Lattice Fixed-Point Theorem and Stable Matchings; Finite and Infinite Sets; The Axiom of Choice
and Some Equivalent Results; Revealed Preference and Rationalizability; and, Superstructures;
References: Corbae, Stinchcombe e
Zeman (2009, chap. 2) e Elon (2012, chap.1)
Part 3 – The Space of Real Numbers: Basic
Properties of Rationals; Distance, Cauchy Sequences, and the Real Numbers; The
Completeness of the Real Numbers; and, Supremum and Infimum;
References: Corbae, Stinchcombe e
Zeman (2009, chap. 3) e Elon (2012, chap. 2)
Part 4 – The Finite-Dimensional Meric Space of Real Vectors: The Basic Definitios for
Metric Spaces; Discrete Spaces;
as a Normed Vector Space; Completeness;
Closure, Convergence; and Completeness; Separability; Compactness in
; Continuous Function in
; Lipschitz and Uniform Continuity;
Correspondences ant the Theorem of the Maximum; Banach’s Contraction Mapping
Theorem; and, Connectedness;
References: Corbae, Stinchcombe e Zeman (2009, chap. 4)
Part 5 – Finite-Dimensional Convex Analysis: The Basic Geometry of
Convexity; The Dual Space of
; The three Degrees of Convex Separation; Strong
Separation and Neoclassical Duality; Boundary Issues; Concave and Convex
Functions;; Separations and the Hahn-Banach Theorem; Separation and the Karush-Kuhn-Tucker
Theorem[1];
Interpreting Lagrange Multipliers; Differentiability and Concavity; Fixed-Point
Theorems and General Equilibrium Theory; and, Fixed-Point Theorem for Nash
Equilibria and Perfect Equilibria;
References: Corbae, Stinchcombe e
Zeman (2009, chap. 5)
Part 6 – Metric Spaces: The Space of
Compact Sets and the Theorem of the Maximum; Space of Continuous Functions;
, the Space of Cumulative
Distribution Functions; Approximation in
when
is compact; Regression Analysis as Approximation Theory; Countable
Product Spaces and Sequence Spaces; Defining Functions Implicitly and by Estimation;
The Metric Completion Theorem; and, The Lebesgue Measure Space;
References: Corbae, Stinchcombe e Zeman (2009, chap. 6)
B – REFERENCES
CORBAE, D.; STINCHCOMBE, M.; ZEMAN,
J.; An Introduction to Mathematical Analysis for Economic Theory and Econometrics,
Princeton: Princeton University Press, 671p., 2009.
LIMA, E.; Análise Real – volume 1: Funções de uma Variável, 11ª edição,
Rio de Janeiro: IMPA - Instituto de Matemática Pura e Aplicada, 198p., 2012
C- GRADES
Three exams as follows:
(i)
20% - itens 1 and 2; February 07
(ii)
30% - itens 1, 2, 3, and 4 (cumulative); February 26, and
(iii)
50% - itens 1, 2, 3, 4, 5, and 6 (cumulativE); March 19.
The candidates could follow notes and exercises in this blog:
http://mathematical-economics.blogspot.com.br/
[1] We recognize Karush’s contribution on Theorem.
No comments:
Post a Comment