Mathematical Economic Analysis

Learning Outcomes

This course introduces core mathematical methods used by economists. These are foundational for any advanced study in economics. Students who master the material will be able to understand and solve problems related to:

• sets and methods of proof in economic theory.

• functions and equation in economic modeling.

• composition of functions.

• matrix algebra for linear economic models.

• linear comparative statics (predictions of economic models).

• differential calculus (marginal analysis at multiple margins).

• nonlinear comparative statics (micro and macro applications).

• multivariate optimization (profit maximization; optimal constrained choice).

• computer applications of mathematical methods to economic analysis.

Course Prerequisites

A college-level calculus course is prerequisite to this course. I assume you remember basic differential calculus from the first semester and a little bit about integration. Ideally you also recall some statistics and matrix algebra, but we develop these topics when needed.

Communication

This class will use Canvas. Look there for the syllabus, lecture supplements, and assignments. Canvas announcements are sent by email; students must monitor these announcements and Canvas Conversations (Inbox). Students should also subscribe to the Canvas Discussions. In online interactions, all students are expected to adhere to basic etiquette: be respectful, and quote appropriately.

Classroom Policies (IRW)

The following policies apply to in-person meetings only.

Masks:

Be sure to follow the AU mask guidelines. These are updated on a regular basis, in response to local conditions. Use a high-quality mask (e.g., KN95). Surgical masks are not adequate. When wearing a mask, ensure that it fits correctly. The mask must be snug over both the nose and mouth.

Connected devices:

As a courtesy to other students, do not browse the web or check your email during class. Such activities distract others and reduce your ability to contribute to discussions. In addition, there is evidence that students believe themselves capable of productive multitasking but in fact are not (May and Elder, 2018).

Cell phones:

Please silence your phone before entering the classroom. (E.g., put it on vibrate, or turn it off.) Place it out of sight in a pocket or bag (and not on your desk). If you need to make or take a call, you may quietly leave the classroom. (Please sit near the door if you anticipate such a need.)

Computers:

You may use a computer to take notes or do other course-relevant activity. However, be aware that research indicates that using a computer to take notes can hinder learning (Sana, Weston, Cepeda 2013). This appears to be due to the distraction of multitasking.

Software

This course requires the use of Mathematica, both in the classroom and for homework assignments. There is a free Mathematica tutorial, which you should complete on your own during the first week of class. Homework assignments must be typed in Mathematica and then submitted on Canvas in PDF format. Software crashes or disk crashes are not an excuse for late submission: turn on autosave and additionally use an external backup such as GoogleDrive for Desktop or OneDrive.

Assessment

Mastery of the student learning outcomes (see above) is assessed by means of graded exams, graded homeworks, and ungraded class participation.

Grading

Homework and exams are graded. Your final grade is based on your total weighted points earned. (See below.) There is no "extra credit". Whole grade numerical cut-off points are standard: 90% for A-range grades and 80% for B-range grades. It follows that in principle everyone can attain an A, if every student makes an exceptional effort. In practice, this has not happened.

If numeric scores are unusually low in an otherwise attentive class, I curve the grades. Specifically, if fewer than 15% of the class reaches the 90% cutoff, I will lower all cutoffs proportionally until at least 15% of the grades are A or A-. Grades are not rounded upwards.

Logic and Proofs

Week 0 (read independently)

Review this material on your own. It will not be covered in class.

Sentential Logic

[Velleman-2019-CambridgeUP] ch. 1 (on reserve)

Logic

[Doerr.Levasseur-2021-Lulu] ch. 3

Exponents and Logarithms

Week 0 (read independently)

Review this material on your own. It will not be covered in class.

Functional Forms

[Hoy.etal-2022-MITPress] ch. 2.4.

Review of Functions

Week 1-2

Sets, Numbers, and Functions

[Hoy.etal-2022-MITPress] ch. 2. (Skip pages 48--50. Emphasize mastering section 2.4.)

There are additional optional readings on functions and sets.

Counting and Probability

Week 3-4

Combinatorics

[Grinstead.Snell-2003-AMS] ch.3 https://open.umn.edu/opentextbooks/textbooks/21

Strongly Recommended:

Basic Probability Theory,

[Hansen-2022a-PrincetonUP] Chapter 1

Sequences

Week 5–6

Sequences, Series, and Limits

[Hoy.etal-2022-MITPress] ch. 3

Convergent Sequences

[Binmore-1982-CambridgeUP] ch. 4

Fixed Points

Video: https://www.youtube.com/watch?v=csInNn6pfT4&t=125s

Continuity (Univariate Functions)

Week 7

Continuity of Functions

[Hoy.etal-2022-MITPress] ch. 4

Derivatives and Differentials (Univariate)

Week 7

Univariate Derivatives, Differentials, Taylor Series

[Hoy.etal-2022-MITPress] ch. 5

Recommended:

Taylor Series

Video: https://www.youtube.com/watch?v=KoCk1krAX2M

Midterm

Week 8

Scheduled for 5 March 2024. (Does not cover Taylor series.)

Optimization (Univariate)

Week 9-10

Univariate Optimization

[Hoy.etal-2022-MITPress] ch. 6

Elementary Equation Operations

Week 10-11

Linear Equations and Vector Spaces

[Hoy.etal-2022-MITPress] ch. 7

Matrices

[Hoy.etal-2022-MITPress] ch. 8

The Comparative Statics of Linear Models

Week 11

Determinants and Inverses

[Hoy.etal-2022-MITPress] ch. 9

Multivariate Calculus and Nonlinear Comparative Statics

Week 12

Multivariate Calculus

[Hoy.etal-2022-MITPress] ch. 11

Comparative Statics

[Hoy.etal-2022-MITPress] ch. 14.1, 14.2

We may not have time to discuss chapter 14.

Quadratic Forms and Eigensystems

Week 13

Topics in Linear Algebra

[Hoy.etal-2022-MITPress] ch. 10

We may not have time to discuss eigensystems.

Multivariate Optimization

Week 14

Multivariate Optimization

[Hoy.etal-2022-MITPress] ch. 12

FONCs for Constrained Multivariate Optimization

[Hoy.etal-2022-MITPress] ch. 13.1

Second-Order Conditions for Constrained Multivariate Optimization

[Hoy.etal-2022-MITPress] ch. 13.2

Academic Support and Access Center (ASAC) MGC 243, 202-885-3360.

All students may take advantage of the Academic Support and Access Center (ASAC) for individual academic skills, counseling, workshops, tutoring and writing assistance, as well as Supplemental Instruction. All services are free. The services include the Writing Center (first floor of Bender Library), which assists students with academic writing and assignments. The Math/Stat Lab (Myers Building, 202-885-3154) which provides mathematics and statistics tutoring. Additional content tutoring is also available in the ASAC’s Tutoring Lab.

Academic Integrity

Standards of academic conduct are set forth in the University’s Academic Integrity Code. By registering for this course, you have acknowledged your awareness of the Academic Integrity Code and your obligation to become familiar with your rights and responsibilities as defined by the code. Violations of the Academic Integrity Code will not be treated lightly, and disciplinary actions will be taken should violations occur. The standard sanction for violations is failure of the course.

Emergency Preparedness

In the event of a declared pandemic (influenza or other communicable disease), American University will implement a plan for meeting the needs of all members of the university community. Should the university be required to close for a period of time, we are committed to ensuring that all aspects of our educational programs will be delivered to our students. These may include altering and extending the duration of the traditional term schedule to complete essential instruction in the traditional format and/or use of distance instructional methods. Specific strategies will vary from class to class, depending on the format of the course and the timing of the emergency. Faculty will communicate class-specific information to students via AU e-mail and Blackboard. Students are responsible for checking their AU e-mail regularly and keeping themselves informed of emergencies. In the event of a declared pandemic or other emergency, students should refer to the AU Web site (american.edu/emergency) and the AU information line at (202) 885-1100 for general university-wide information, as well as contact their faculty and/or respective dean’s office for course and school/college-specific information.

Sharing of Course Content

Students are not permitted to make visual or audio recordings, including live streaming, of classroom lectures or any class related content, using any type of recording devices (e.g., smart phone, computer, digital recorder, etc.) unless prior permission from the instructor is obtained, and there are no objections from any of the students in the class. If permission is granted, personal use and sharing of recordings and any electronic copies of course materials (e.g., PowerPoints, formulas, lecture notes and any classroom discussions online or otherwise) is limited to the personal use of students registered in the course and for educational purposes only, even after the end of the course.

Exceptions will be made for students who present a signed Letter of Accommodation from the Academic Support and Access Center. See: How Do I Request Accommodations?

http://www.american.edu/ocl/asac/Accommodations.cfm

To supplement the classroom experience, lectures may be audio or video recorded by faculty and made available to students registered for this class. Faculty may record classroom lectures or discussions for pedagogical use, future student reference, or to meet the accommodation needs of students with a documented disability. These recordings are limited to personal use and may not be distributed (fileshare), sold, or posted on social media outlets without the written permission of faculty.

Unauthorized downloading, file sharing, distribution of any part of a recorded lecture or course materials, or using information for purposes other than the student’s own learning may be deemed a violation of American University’s Student Conduct Code and subject to disciplinary action (see Student Conduct Code VI. Prohibited Conduct).