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MIT Department of Economics
Fall 2005
14.102 Mathematics for Economists
TTh 2:30-4, E51-063
Recitations (see below): F 2:30-4, E51-063
Nathan Barczi
E52-243d
Office hours: by appointment
Ufuk Akcigit
E52-204
Office hours: by appointment
This class will introduce students to the mathematics that underpins the core theory sequence for graduate students in economics. Here we view math as a tool for economists rather than as an art, so more emphasis will be put on examples and procedures and less on rigorous proofs.
Comprehensive lecture notes will be distributed as the course progresses, so we do not require any particular textbook. However, the following texts may prove useful as supplementary materials:
Sundaram,
A First Course in Optimization Theory
Simon and Blume, Mathematics for Economists
Rudin, Principles of Mathematical Analysis
There will be a midterm and a final exam, each counting 45% towards the final grade; there will also be problem sets, handed out approximately every two weeks, counting for the rest of the grade. Students may obtain instructor permission (from Ufuk, Nathan, or Glenn) to skip either half of the course (depending on prior experience) but still receive a grade. Tentatively, recitations will only be held on weeks when a problem set is due, in order to discuss solutions. We have estimated below the number of classes devoted to each section, but these may change depending on how the course progresses.
1. Real Analysis (Rudin Chs. 2-4, Simon and Blume
Unions, Intersections, Complements
Relations and Equivalences
Metrics and Norms
Sequences, Convergence, Limits
Closed and Open Sets, Neighborhoods
Compactness
Sets of measure zero
Convex Sets, Separating Hyperplanes
Domain, Images, Graphs, Inverses
Continuity, Bolzano-Weierstrass Theorem
2. Matrices and Linear Algebra (4 classes)
(Simon and Blume, Chs. 8-11, 26-7)
Matrices and Matrix Operations
Euclidian Vector Spaces, Subspaces
Vectors, Span, Linear Independence
Rank, Determinants, Inverses
(Simon
and
Systems of Linear Equations, Non-linear Systems
Matrices, Linear Maps
(Simon
and Blume
Quadratic Forms, Symmetry, Positive Definite Matrices
(Simon
and Blume
Eigenvectors, Eigenvalues, Decomposition, Basis of a Vector Space
Projections, Idempotency, OLS
3. Functions and Calculus
(Simon and Blume Ch. 13-15, 30) (2 classes)
Differentiability,
linearization and
Derivatives and Jacobians
Implicit Function Theorem
Integration, Integration by Parts, Differentiation of Integrals, Leibniz’s Rule
4. Static Optimization (Simon
and Blume Chs. 16-21, 30) ( 3 classes)
Unconstrained optimization
Constrained Optimization: Lagrange
Constrained Optimization: Kuhn-Tucker
Convexity
The Theorem of the Maximum
Last Modified: 15 September 2005