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  Grad   Ferrall  QED 
Department of Economics, Queen's University, Kingston, Ontario K7L 3N6, Canada
Tel: (613) 533-6658     Fax: (613) 533-6668
[Feedback] [ 01 August 2004 ]
 

GRADUATE METHODS REVIEW
& INTRODUCTION TO QED RESOURCES

Christopher Ferrall & Jeremy Lise
 
September 8-10, 13-14, 20, 27, 2004
 
Exit Exam Announcement [PDF]
KEY TO ENTRY EXAM [PDF] 		 

OBJECTIVE

The course reviews and exercises mathematics and statistics used in the graduate program. The sessions run by Jeremy Lise introduce computer tools and resources available to students.

SCHEDULE

Incoming graduate students will be split into two groups, A and B. On days two and three (Sep. 9-10) the two groups meet separately, alternating between sessions led by Professor Ferrall in the Hand-Purvis Conference Room (Dunning Hall 2nd floor) and Mr. Lise in the Electronic Classroom (Dunning Rm 350). These split sessions all occur in the afternoons (1:00-5:00PM). On the first day, in the mornings of days 2-3, and two days the next week (Sep 13-14) all students meet with Professor Ferrall. The schedule is available at http://calendar.yahoo.com/qed_workshop.

Schedule of Sessions with Prof. Ferrall

Wednesday
Session 1 : A & B
Welcome and Introduction
Entry Exam
Thursday
Session 2: A & B at 9:00am
Brief Review of Entry Exam
Proofs and Properties of Sets
Functions
Differentiation
Linear Systems
Session 3: [A at 3:15pm]   [B at 1:30pm]
Gradients & Hessians
Implicit Function Theorem
Inverse Function Theorem
Friday
Session 4: A & B at 9:00am
Optimization
Session 5: [A at 1:30pm]    [B at 3:15pm]
Probability & Statistics
Monday (Sept. 13)
Session 6: A & B at 2:30pm
Optimization II
Tuesday (Sept. 14)
Session 6: A & B at 2:30pm
Loose Ends
Monday (Sept. 20)
Session 7: A & B at 2:30pm
Question Period
Monday (Sept. 27)
Session 8: A & B at 2:30pm
Exit Exam

FORMAT

The methods review is aimed at MA students, although PhD students will likely find some or all of the sessions helpful. (The PhD Methods course which starts later is required of all incoming PhD students.) PhD students who did their MA at Queen's are welcome but not required to participate. Other PhD students should attend the first day and at a minimum should attend the computer sessions with Mr. Lise.

As there is limited time for this review, and there are many sources for basic mathematics for economists (see references), lecture elements of this course are kept to a minimum. In the first session an exam will be given to assess your understanding of mathematics used in the core graduate courses. Subsequent sessions will include both lectures and problem solving. An "exit" exam will be given in the last session.

REQUIREMENTS

To attend the course, students must actively participate in the course and develop a notebook of work related to the course. Student notebooks are expected to contain the following material:
The entry exam
The self-assessment "entry" exam given in the first session will be handed in, marked, and returned to the student.
The exit exam (September 27)
The exit exam will be given during the last session. Students will be allowed to refer to their notebook during this exam. The exit exam and the notebook will be handed in at this session. A review session will be held on September 20.
Notebook
The content and format of the notebook is up to the student, but along with the exams, the notebook should demonstrate to me that you have reviewed the requirements for entry into the graduate program and you have spent some time working on weak spots in your background. Find below a list of suggestions.

ASSESSMENT

  • The entry exam will be read and returned as soon as possible to students. Students will receive feedback on whether they seem prepared for core courses in the MA program and which topics they might wish to focus on.
  • The notebooks (including the exit exam) will be read to see whether students have put in sufficient work during the review course relative to their entry exam. At this point most students will be finished with the review. However, if a notebook suggests serious weaknesses, the student will meet with Professor Ferrall to discuss ways to strengthen them before exams in their core courses.
  • At the end of this process assessments of student work and their preparation for the program will be given to the Graduate Studies Coordinator (Prof. Abbott) using this form: 

REFERENCES

The QED_GRAD_CDROM

Upon arrival in Kingston students will receive a CD-ROM with notes, shareware and licensed programs used in the QED, and other resources.

Math Prep at McMaster University

John Leach and Marc-Andre Letendre (PhD, Queen's 1999) have extensive notes available at http://socserv.socsci.mcmaster.ca/prepmath/
.

Books You Might Consider Buying

None of these textbooks are required for this course.
 
Foundations of Mathematical Economics by Michael Carter (MIT Press), available from Amazon CA
 
 
Mathematics for Economics by Carl P. Simon and Lawrence Blume (WW Norton), available (cheaply!) from Chapters/Indigo.
 
 
Mathematical Methods and Models for Economists by Angel de la Fuente.
An advanced textbook, suggested for PhD students. Available (cheaply!) from   Chapters/Indigo.
 
 
Numerical Methods in Economics, by Kenneth L. Judd .
Recommended for PhD students and MA students planning a PhD, available from:  Chapters/Indigo.

THINGS TO INCLUDE IN YOUR NOTEBOOK

 The material in your notebook should be written out (no photocopies). Rather than simply copying from a text or from our class discussions, organize the material in your own in order to improve your understanding. This list a guide not a strict requirement. Rather than including everything, focus on areas items that you need to work on. If coming into this class you could crank through a Lagrangian problem but didn't know how to determine whether two random variables are independent, then your notebook can skip details about Lagrangians but lots of material about distributions.
Organization: Pick a system that works for you, but, for example, divide your notebook into topics and items within topics.
Topics: linear/matrix algebra, calculus, statistics and econometrics, economics
Items: definitions, theorems, examples and counter-examples
Definitions
Algebra
matrix operations (addition, multiplication, inverse, transpose, etc.); determinant, rank, row/column space, null space, eigen value, eigen vector
Calculus:
continuity, (strict-) (quasi-) concavity/convexity, derivative, integral, gradient, Jacobian, Hessian
Statistics:
random variable, density, distribution, independence, moment (mean, variance, covariance etc.), estimator, consistency, unbiasedness, efficiency (best), likelihood; distributions (normal, t, chi-square, F, binomial, etc.), significance level, hypothesis testing, confidence intervals.
Economics:
functional forms, demand/supply, risk, Pareto optimality, equilibrium concepts, etc.
Theorems and Results
Algebra:
Calculus:
Taylor expansion; Inverse Function Thm; Implicit Function Thm; optimization( FONC SONC sufficient conditions, etc), Lagrange, Kuhn-Tucker
Statistics:
Gauss-Markov Theorem, Central Limit Theorem(s), properties of normal variables,
Examples
Algebra:
solved systems, determinants, spaces, eigenvalues, etc.
Calculus:
common derivatives and integrals, write out a Taylor expansion, illustrate FONC, SONC, etc.,
Statistics:
compute sample means, variances, OLS estimates, for small samples; conduct hypothesis testing and confidence intervals