Course Syllabus

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ECON 308: Mathematics for Economists — Fall 2025

Professor: Mahmoud El-Gamal

TAs: TBA

Class: MWF, 11:00—11:50 a.m., TBA

Lab: M, 4:00—4:50 p.m., TBA

Office hours: W, 12:30—1:30 p.m., KRF 429, or by appointment

Course Description: 

Mathematics is a language that allows us to communicate and think more clearly, often making it easier to solve problems. This is why modern economics uses the language of mathematics.

This course covers essential topics in mathematics used in intermediate and advanced economics and econometrics courses. This essential material can be learned in three or more mathematics courses, but those courses also cover numerous other topics that are of little use for economics.

Specifically, this course offers students concise coverage of three areas in mathematics and applied mathematics that we use extensively in mathematical and quantitative economics. The course content is split into three modules:

    • Linear algebra (weeks 1—5)
    • Calculus of several variables (weeks 6—10)
    • Optimization (weeks 11—15)

Assignments will include exercises in MATLAB (because there is little value today in doing much arithmetic or calculus by hand, and you have free access through the Rice site license), while exams will test basic understanding of the mathematical content.

      • I selected MATLAB due to its relative ease of use for students without coding experience. Students who are comfortable using other software platforms may do so.

AI-Assisted Learning (Optional):

  • I encourage you to use MATLAB Copilot (native to the MATLAB IDE) in homework assignments. 
      • If you are comfortable using other IDEs, you are also encouraged to use Github Copilot or other AI tools.

Textbook: 

  • Simon, Carl P., and Blume, Lawrence E. Mathematics for Economists. W.W. Norton, NY, 1994.

Financial Applications:

  • While the textbook covers a variety of economic applications, I will focus mostly on financial applications, both to add coherence and to enhance immediate practical relevance for students who have already learned the math in other courses. Thus, the linear algebra module will focus on asset pricing, while the calculus and optimization modules will focus on risk-return preferences and portfolio selection.

Tentative Syllabus: (Lecture slides posted before each class, under Files tab. These are live documents that will be updated frequently before and after class)

  • Week 01 -- Aug. 25, 27, 29: System of Linear Equations ( Chs. 6, 7)
  • Week 02 -- Sep. 03, 05: Matrix Algebra, Determinants,  Farkas's Lemma (Chs. 8, 9, parts of 26++)
  • Week 03 -- Sep. 8, 10, 12: Euclidean Spaces (Ch. 10)
  • Week 04 -- Sep. 15, 17, 19: Linear Independence, Projection, Bases, Decompositions, Generalized Inverse (Chs. 11, parts of 23, 27, 28++)
  • Week 05 -- Sep. 22, 24: Linear Programming (constrained optimization) 
    • Sep. 26: Exam 1 (chs. 6—11, parts of 26—28)
  • Week 06 -- Sep. 29, Oct. 01, 03: Sequences, Open and Closed Sets (Ch. 12)
  • Week 07 -- Oct. 06, 08, 10: Functions of Several Variables (Chs. 13, 30)
  • Week 08 -- Oct. 15, 17: Calculus of Several Variables I (Ch. 14)
  • Week 09 -- Oct. 20, 22, 24: Calculus of Several Variables II (Ch. 30)
  • Week 10 -- Oct. 27, 29: Implicit Functions and their Derivatives (Ch. 15)
    • Oct. 31: Exam 2 (chs. 12—15, 30)
  • Week 11 -- Nov. 03, 05, 07: Quadratic Forms, Unconstd. Optim. (Chs. 16, 17)
  • Week 12 -- Nov. 10, 12, 14: Constrained Optim. I: FOC (Ch. 18)
  • Week 13 -- Nov. 17, 19, 21: Constrained Optim. II: Envp. Thm., SOC (Ch. 19)
  • Week 14 -- Nov. 24: Homogeneous and Homothetic Functions (Ch. 20)
  • Week 15 -- Dec. 01, 03: Concave and Quasiconcave Functions (Ch. 21)
    • Dec. 5: Exam 3 (chs. 16—21)

Grading: 

  • Assignments: 40%
  • Three In-Class Exams: 60%

 

Course Summary:

Date Details Due