# Fall 2024 - ECON 831 G100

## Overview

• #### Course Times + Location:

Sep 4 – Dec 3, 2024: Mon, Tue, Wed, Thu, Fri, Sun, 9:00 a.m.–4:00 p.m.
Burnaby

Sep 4 – Dec 3, 2024: TBA, TBA
Burnaby

• #### Instructor:

David Freeman
dfa19@sfu.ca

ECON 331.

## Description

#### CALENDAR DESCRIPTION:

Introduction to mathematics required for PhD level coursework and research in economics. Topics may include real analysis, analysis on metric spaces, differential calculus, convexity, and optimization. Graded on a satisfactory/unsatisfactory basis.

#### COURSE DETAILS:

The goal of this course is to develop the fluency in mathematics required for PhD level coursework and research in economics.

The course content focuses on the basics of real analysis on metric spaces, building up to key theorems in optimization theory that are used in economics.  Course assessments require writing mathematical proofs.

Topics (subject to change):

1. Logic, proofs, sets and set operations.
2. Relations, functions, cardinality.
3. Metric spaces: distance, epsilon balls, Euclidean space.
4. Basic topology (open and closed sets), sequences, convergence.
5. Compactness, the Heine-Borel Theorem.
6. Continuity of functions, the Weierstrass Extreme Value Theorem.
7. Convex analysis: convexity, the Separating Hyperplane Theorem; Calculus: differentiation, optimization theorems.
8. Correspondences, Berge’s Maximum Theorem.
9. Contraction Mapping Theorem, Infinite Horizon Optimization via Dynamic Programming.

Prerequisites:  ECON 331 and graduate standing or instructor’s permission.

• Test + Quizzes 20%
• Final Exam 80%

## Materials

1. Lay, S. 2005. Analysis: With an Introduction to Proof. Pearson. (4th or 5th edition).
2. Sundaram, R. 1996. A First Course in Optimization Theory.  Cambridge.
3. Vohra, R. 2005. Advanced Mathematical Economics. Routledge.
4. de la Fuente, A. 2000. Mathematical Methods and Models for Economists. Cambridge University Press.

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.