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All incoming students are encouraged to attend Math Camp in August before classes start. Students who do not attend Math Camp are still responsible for the material that will be covered there; professors will assume in classes that students are familiar with it.
Math Camp August 2012
Course Objective
The primary objective of this course is to provide incoming graduate students with the mathematical foundations necessary for the first year sequence of theory and econometric courses. Your success in our program depends on how comfortable you are with the needed mathematical tools.
This course is designed on the presumption that students will have already been exposed to the majority of this material in previous studies. Thus the scope of the material to be covered is much larger than one would encounter in an ordinary mathematics course.
Who Should Take this Course?
Every incoming graduate student (MA and PhD) is strongly encouraged to take this course. There is no charge for taking the course. If you do not take this course, you may find the first year courses significantly more difficult than your classmates and thus risk falling behind. You are responsible for knowing the material contained in this syllabus prior to your graduate studies in Fall 2010 whether or not you attend Math Camp.
General Information:
Instructors: TBA
Dates: August 6 - 23, 2012 (Monday through Thursday only)
Time: 6 - 9pm plus 2 hours before class (starting at 4pm) for additional problem solving
Location: Dealy Hall, conference room
Text Books
A.C. Chiang and K. Wainwright, Fundamental Methods of Mathematical Economics, 4th edition, McGraw Hill. (current Math I text)
D. Salvatore and D. Reagle, Schaum’s Outlines, Statistics and Econometrics, 2nd Edition
Other Useful Books
E. Dowling, Schaum’s Outlines, Introduction to Mathematical Economics (recommended in Math I and Math II)
Course Outline: General Topics
Topic 1 Linear Models and Matrix Algebra
Topic 2 Derivatives, Differentials, Integrals
Topic 3 Optimization with Equality and Inequality Constraints
Topic 4 Probability and Statistics
Syllabus (subject to revision)
Linear Models and Matrix Algebra
Matrices and Vectors Chiang 4.1 - 4.6
Matrix and Vector Operations, Commutative, Associative and Distributive Laws, Special Matrices, Transposes and Inverses
Nonsingularity and Cramer’s Rule Chiang 5.1 - 5.5
Conditions for Nonsingularity and Testing for it, Determinants, Cramer’s Rule
Derivatives, Differentials, Integrals
Limits and Continuity Chiang 6.2 - 6.4
What is a Derivative?, The Concept of Limit
Differentiation Rules Chiang 7.1 - 7.4
Rules of Differentiation for one, two and more variables, Partial Differentiation
Differentials and Total Derivatives Chiang 8.1 - 8.4
Differentials, Total Differentials, Rules, Total Derivatives
Exponential and Logarithmic Functions Chiang 10.1 - 10.5
Exponentials, Logarithms, Derivatives of Exponential and Logarithmic Functions
Integral Calculus Chiang 14.2 - 14.4
Indefinite Integrals, Basic Rules of Integration, Rules of Integration. Definite Integrals, Improper
Integrals
Optimization with Equality and Inequality Constraints
Relative Maximum and Minimum Chiang 9.2 - 9.5
First Derivative Test, Second and Higher Derivatives, Second Derivative Test, Maclaurin and Taylor Series
Optimization Chiang 11.1 - 11.3
Differential Version of Optimization Conditions, Extreme Values, Quadratic Forms
Optimization with Equality Constraints Chiang 12.1 - 12.3
Lagrange Multiplier Method, Second Order Conditions
Optimization with Inequality Constraints Chiang 13.1 - 13.2
The Kuhn Tucker Theorem
Probability and Statistics
Descriptive Statistics Salvatore and Reagle 2.1 - 2.4
Probability and Probability Distributions Salvatore and Reagle 3.1 - 3.5
Statistical Inference: Estimation Salvatore and Reagle 4.1 - 4.4
Statistical Inference: Testing Hypotheses Salvatore and Reagle 5.1 - 5.4
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