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ECONOMICS 386 APPLICATIONS OF MATHEMATICS TO ECONOMICS I
Semester: Fall 2016
Section A1: Tuesday and Thursday 12:30 – 1:50 PM
Location: V 103
Instructor: Professor Xuejuan Su
Office hours: Wednesday 1:30-3:00 pm at 9-22 Tory Building or by appointment Email address: [email protected]
Office phone: (780) 492-4198
Required Textbook: Essential Mathematics for Economic Analysis (4th Edition). Authors:
Knut Sydsaeter, Peter Hammond, and Arne Strom. ISBN: 9780273760689. Price around $90 (the exact amount depends on the vendor). Used books are ok.
Course Overview
The purpose of this course is to provide you with a toolbox of mathematical techniques and concepts that are used in modern economic and econometric analysis. By the end of the course, you should be able to:
1. Solve quadratic equations and systems of linear equations with multiple unknowns;
2. Work with basic functions such as logarithmic, exponential and power functions and be familiar with their properties;
3. Calculate derivatives and integrals involving functions that are commonly used in economic analysis;
4. Set up and solve basic unconstrained optimization problems;
5. Set up and solve basic constrained optimization problems;
6. Understand the basics of linear algebra, including matrix operations, geometric interpretation of vectors, as well as singularity, determinant, and the inverse of a matrix.
Prerequisites
ECON 281, 282, 299; and Math 125 or equivalent. This prerequisite will be enforced.
Course Materials
Announcements, handouts, practice problems, and previous sample exams (as representative evaluative course materials) will be posted on Moodle. Please check the announcement section of Moodle frequently. If you have any troubles accessing the Moodle course website, please send an e-mail to the Moodle support staff. They are the only ones that can help you.
Attendance and Class Participation
There is no mandatory attendance requirement in this course, as rational individuals can be expected to make the best decisions regarding their time allocation choices. ☺ However, not coming to class regularly may hinder your ability to do well in this course. This is a hands-on course. To best learn these mathematical tools, you need to keep up with the daily progress of topics and hone your own skills. Since exams will focus on materials discussed in class, attending class regularly will help save your learning effort, better your understanding, and improve your final grade.
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Recording of Lectures:
Audio or video recording of lectures, labs, seminars or any other teaching environment by students is allowed only with the prior written consent of the instructor or as a part of an approved accommodation plan. Recorded material is to be used solely for personal study, and is not to be used or distributed for any other purpose without prior written consent from the instructor.
Grades
Your grade in Econ 386 will be determined by your exam performance. There are two mid- term exams, to be held in class, and a final exam. All exams are cumulative, but more weight is given to the new materials not covered in the previous exam. The use of notes or books is NOT allowed during the exams, and no calculators or other electronic devices can be used. The breakdown of the scores is shown below, together with TENTATIVE exam dates.1
Mid-term Exam I 30 % Date: September 29 (in class) Mid-term Exam II 30 % Date: November 3 (in class)
Final Exam 40 % Date: December 13
Grades reflect judgments of student achievement made by your instructor. These judgments are based on a combination of absolute achievement and relative performance in a class. There are no extra credits or bonus points for this course. The overall grade distribution follows the university guidelines.
Absence from Exams
Following the U of A regulation for excused absences, if a student misses one of the two mid- term exams because of incapacitating illness, severe domestic affliction or other compelling reason (including religious conviction), then the final will count for 70% of the course grade. If a student misses two mid-term exams, then the student is required to write an equivalent exam at a time set by the instructor and the final will count for 70% of the course grade. If the student does not write the assigned make-up exam at the prescribed time, a raw score of zero will be assigned for all missed exams (refer to Calendar, §23.5.6, Point 1).
1 Other deadlines: September 15, 2016, Registration (Add/Delete); October 4, 2016, Fee Refund 50%; and finally, November 30, 2016, Withdrawal (Grade W).
Descriptor
Letter Grade
Point Value Excellent
A+
A A-
4.0 4.0 3.7 Good
B+
B B-
3.3 3.0 2.7 Satisfactory
C+
C C-
2.3 2.0 1.7 Poor
Minimal Pass
D+
D
1.3 1.0
Failure F 0
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A student who has missed a final exam because of incapacitating illness, severe domestic affliction or other compelling reason (including religious conviction) may apply for a deferred exam. A deferred final exam will not be approved if a student, excluding the final exam, has completed less than half of the assigned work (Calendar, §23.5.6, Point 2). Hence if you have written only one term exam you cannot apply for a deferral.
Students with special needs (University Calendar §25.2):
Students with disabilities or special needs that might interfere with their performance should contact the professor at the beginning of the course with the appropriate documentation. Every effort will be made to accommodate such students, but in all cases prior arrangements must be made to ensure that any special needs can be met in a timely fashion and in such a way that the rest of the class is not put at an unfair disadvantage.
Exam arrangements: SAS (Student Accessibility Services) and the student, with the approval of the course instructor, determine exam accommodations. Assessments and/or documentation of the need for accommodation are required. At the beginning of each term, the student meets with instructors to review the exam arrangements which will be used. They provide a “Letter of Introduction” from SAS verifying the nature of the accommodations required due to the disability. A few weeks before each exam, the student completes an “Exam Schedule” form, for SAS, outlining scheduled exam dates, times, etc. At least one week before the exam the student then takes an “Exam Instructions and Authorization” form to the instructor. The instructor is asked to complete the form and enclose it with the exam and arrange to have it delivered or mailed to SAS. In administering exams, SAS follows university protocol and only makes accommodations as required due to the disability. Exams are usually set to overlap with the time the professor has set the in-class exams.
Learning and working environment
The Faculty of Arts is committed to ensuring that all students, faculty and staff are able to work and study in an environment that is safe and free from discrimination and harassment. It does not tolerate behaviour that undermines that environment. The department urges anyone who feels that this policy is being violated to:
• Discuss the matter with the person whose behaviour is causing concern; or
• If that discussion is unsatisfactory, or there is concern that direct discussion is inappropriate or threatening, discuss it with the Chair of the Department.
For additional advice or assistance regarding this policy you may contact the student ombudservice: (http://www.ombudservice.ualberta.ca/). Information about the University of Alberta Discrimination and Harassment Policy and Procedures can be found in the GFC Policy Manual, section 44 available at http://gfcpolicymanual.ualberta.ca/.
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Please read the following notes
“Policy about course outlines can be found in the Evaluation Procedures and Grading System section of the University Calendar.”
“The University of Alberta is committed to the highest standards of academic integrity and honesty. Students are expected to be familiar with these standards regarding academic honesty and to uphold the policies of the University in this respect. Students are particularly urged to familiarize themselves with the provisions of the Code of Student Behaviour (online at http://www.governance.ualberta.ca/en/CodesofConductandResidenceCommunityStandar ds/CodeofStudentBehaviour.aspx) and avoid any behaviour which could potentially result in the suspicions of cheating, plagiarism, misrepresentation of facts and/or participation in an offence. Academic dishonesty is a serious offence and can result in suspension or expulsion from the University.”
Course Topics
• Quadratic equations, absolute values, summations. Chs. 1,2&3.
• Basic functions. Chs. 4&5.
• Derivatives (basics). Taylor series expansion, in one variable. Elasticities.
Unconstrained optimization with single choice variable. Concavity/convexity for sets and functions of one variable. Basics of limits for univariate functions (includes the l’Hopital’s rule). Chs. 6,7,8.
• Integration (by substitution, by parts) for functions in one variable. Ch. 9.
• Continuous compounding of interest/ present values. Ch. 10.
• Total derivatives, partial derivatives, gradients, total differentials, quadratic forms, Hessian (rule for calculating the determinant of a 2x2 and 3x3), concavity/convexity, Taylor series expansion in two variables, homogeneous functions, homothetic
functions, Euler’s rule. Marginal Rate of Substitution. In particular: the implicit function theorem for single equation and for systems. Chs. 11&12.
• Unconstrained optimization with multiple choice variables. Envelope Theorem. Ch. 13.
• Constrained optimization with multiple choice variables. Envelope Theorem. Shadow prices. Ch. 14. The examples on optimization will include comparative statics of optimal choices.
• Matrix algebra, calculating a determinant, singularity, non-singularity (using determinant only), matrix inversion, use matrices to solve linear systems of equations, Cramer’s rule, Leontief’s model. Chs 15-16.
