14.102
Syllabus

Home Contact Info Syllabus Lecture Notes Problem Sets

 

 

 

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

nab@mit.edu

E52-243d

Office hours: by appointment

 

Ufuk Akcigit

uakcigit@mit.edu

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 Ch. 21)     (2 classes)                                          

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 Blume, Ch. 7)

Systems of Linear Equations, Non-linear Systems

Matrices, Linear Maps

(Simon and Blume Ch. 16)

Quadratic Forms, Symmetry, Positive Definite Matrices

(Simon and Blume Ch. 23)

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 Taylor expansions

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