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# Mathematical Economics I ECON 703

UW

GPA 3.6

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This 4 page Class Notes was uploaded by April Jerde on Thursday September 17, 2015. The Class Notes belongs to ECON 703 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 58 views. For similar materials see /class/205166/econ-703-university-of-wisconsin-madison in Economcs at University of Wisconsin - Madison.

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Date Created: 09/17/15

University of WisconsinMadison Department of Economics Econ 703 Prof R Deneckere Fall 2004 COURSE PLAN Mathematics for Economists I Enrollment Requirement All rst graduate students in economics are required to take this course Waivers will be given only if a student has previously taken a course in analysis and one in optimization and obtained satisfactory course grades in each II Prerequisites One year of multivariate calculus and one semester of linear algebra Students should be intimately familiar with this material and review it over the summer prior to entering graduate school Good textbooks that cover the relevant material and lend themselves well to selfstudy are Apostol T Calculus Volumes I and II Blaisdell Publishing Company Waltham Massachusetts 69 Munkres J Elementary Linear Algebra AddisonWesley Reading Massachusetts 1964 III Of ce Hours By appointment or drop in the day of class My o ice phone number is 2636724 My o ice location is Social Science 6422 You can reach me via email at rjdeneckfacstaffwiscedu IV Reading Materials The required teXt for the course is Sundaram R A First Course in Optimization T heory Cambridge University Press Cambridge 1996 The following two teth are not required but are highly recommended Simon C and L Blume Mathematics for Economists WE Norton amp Co New York 1994 Rudin W Principles ofMathematicalAnalysis Mc GrawHill New York 1976 The Simon and Blume teXt provides a more elementary exposition of much of the material in Sundaram The Rudin teXt is a classic treating Analysis at the undergraduate level Students wishing to see a lengthier and somewhat more elementary analysis teXt may also wish to consult Marsden J Elementary Classical Analysis WH Freeman and Company San Francisco 1974 The background material on set theory and logic can be found in Munkres J Topology 39 A First Course Prentice Hall Englewood Cliffs New Jersey 1975 Chapter 1 V Grading The course grade will be a weighted average of the grades on the midterm 40 and the nal 60 VI Course Outline Below the required readings from Sundaram s teXt are indicated with a The other readings provide supplementary material that is highly recommended but not required Week 1 Elements of Set Theory and Logic Fundamental Concepts Functions Order and Equivalence Relations The Real Numbers Finite Sets Countable and Uncountable Sets Induction and Recursion Sundaram AppendiX A and B pp 315331 Simon and Blume AppendiX A1 pp 847855 Rudin Chapter 1 pp 121 Munkres Chapter 1 pp 378 Week 2 Properties of R Metric spaces Sequences in R Lim Inf and Lim Sup Limits Sequences in R Limit Points Limits Vectorspaces Norms Metric Spaces Sundaram Sections 11 and 12 pp 124 Sundaram AppendiX C pp 330348 Simon and Blume Chapter 10 and 12 pp 199236 and 253272 Rudin Chapter 3 pp 4778 Week 3 Topology ofR Basic open sets Open sets Closed Sets Compact Sets Connected Sets ConveX Sets Simon and Blume Ch 29 pp 803821 Rudin pp 2446 Week 4 Continuity and Differentiability of Functions Continuity Discontinuities Monotonic Functions Upper and Lower Semicontinuity Lipschitz Continuity Linear Transformations Differentiation Sundaram Section 14 pp 4150 Simon and Blume Chapter 13 pp 273299 Simon and Blume Sections 141144 pp 305312 Rudin Chapter 4 pp 83102 Week 5 Differential Calculus Partial and Directional Derivatives Chain Rule Higher Order Derivatives Simon and Blume Sections 145149 pp 313333 Rudin Chapter 5 pp 103119 Week 6 Functions of Several Variables Some Important Results Intermediate and Mean Value Theorems Taylor s Theorem Contraction Mapping Theorem Inverse and Implicit Function Theorem Sundaram Sections 15 and 16 pp 4966 Simon and Blume Chapter 15 pp 334374 Rudin Chapter 9 pp 204238 Week 7 Existence of Solutions to Optimization Problems Unconstrained Optimization Midterm The Weierstrass Theorem Upper 39 39 39 and the C quot 39 v i ua Theorem First Order Conditions Second Order Conditions Sundaram Chapters 24 pp 74111 Simon and Blume Chapter 17 pp 396410 Week 8 Local Theory of Constrained OptimizationI Equality Constraints The Theorem of Lagrange Constraint Quali cations Second Order Conditions Sensitivity Analysis Sundaram Ch 5 pp 112144 Simon and Blume Chs 18 and 19 pp 411482 Week 9 Local Theory of Constrained OptimizationI Inequality Constraints The KuhnTucker Theorem Mixed Constraints Sundaram Ch 6 pp 145171 Week 10 Global Theory of Optimization Concavity Saddle point Theorem Concave Functions Conjugate Functions Duality Constrained Optimization Sundaram Ch 7 pp172202 Simon and Blume Ch 21 pp 505543 Week 11 Generalized Concavity Quasiconcavity Pseudoconcavity Concave Transformable Functions Sundaram Ch 8 pp 203223 Week 12 Parametric Continuity Correspondences and the Maximum Theorem Fixed Point Theorems Sensitivity Analysis Sundaram Ch 9 pp 224241 Week 13 Superrnodularity and Parametric Monotonicity Superrnodularity Parametric Monotonicity Tarski xed point theorem Sundaram Chapter 10 pp 253267 Week 14 Dynamic Programming The Maximum Principle Bellman Equation Contraction Mappings Existence of an Optimal Strategy Continuity and Differentiability Properties of an Optimal Strategy Dependence upon Parameters Sundaram Chapters 1112 pp 268314

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