Course Syllabus

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ECON 308: Mathematics for Economists — Fall 2026

Professor: Mahmoud El-Gamal

Class: MWF, 12:00—12:50 p.m., BKH 102

Lab: W, 5:00–5:50 p.m., KRF 110

Office hours: By appointment

TA: Jorge Zazueta

Course Description: 

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

Almost every problem in economic theory is a constrained optimization problem: e.g., a consumer maximizing utility subject to a budget, a firm minimizing cost subject to an output target, or a society maximizing welfare subject to scarce resources

This course covers essential topics in mathematics used in intermediate 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. The course content is split into three modules, covering elements of:

    • Linear algebra (weeks 1—5; textbook chapters 6—11) -- the tools for solving systems of equations for optimality conditions + the geometry of constraints: vectors, hyperplanes, and projection
    • Linear programming and calculus of several variables (weeks 6—10; Vohra Chs. 2, 4; textbook chapters 14—15, 30) -- LP duality, shadow prices, and no-arbitrage pricing, then gradients, Hessians, Taylor's theorem, and the implicit function theorem, bridging linear programming to KKT
    • Optimization (weeks 11—15; textbook chapters 16—21) --  constrained optimization (Lagrange and KKT), the workhorse method of economic theory

Textbook: 

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

Supplemental material from:

  • Vohra, Rakesh. Advanced Mathematical Economics, Routledge, NY, 2005.
  • Dixit, Avinash. Optimization in Economic Theory, 2nd ed. Oxford University Press, 1990.

Classwork and grading:

  • The legendary late Math professor Paul Halmos wrote that "For a student of mathematics to hear someone talk about mathematics does hardly any more good than for a student of swimming to hear someone talk about swimming." In this course, you will learn to do mathematics by doing mathematics in class
  • Every class will include short lecture sessions, followed by student work on an exercise problem sheet
    • Students may discuss exercise problems with their neighbors, but must write their own answers
    • All exercise problems will be done on paper (see the update below)
    • Exercise problems will be graded lightly: 8/10 for any meaningful work, 9/10 for only partial but correct work, and 10/10 for perfect or nearly perfect work
  • Update (October 2, 2026): Activity sheets may be started in class or completed outside class and are due on Canvas 24 hours after class ends. Answer keys are posted when the upload window closes. No electronic assistance (calculators or AI) before submission; all work is under the honor code.
  • Lab sessions will be ideal times to get feedback and rework assignment problems, and to prepare for exams
  • There will be three exams, one for each module. Exam problems will be graded for correctness and must be completed during the allotted class time

Special Needs:

  • Any students who need special accommodations should inform the professor as soon as possible so that we may make special arrangements to accommodate them

AI Policy and Gemini Virtual TA:

  • Students may not use any AI resources or calculators on exercise sheets before submitting them, or on exams. The classroom is device-free.
  • Students may use AI resources for tutoring purposes after submission if they wish (e.g., to understand textbook or lecture material, work through additional problems, or get feedback on their exercise and exam solutions)
  • Toward the latter end, I have created a Google Gem "Virtual TA for Econ 308" that knows the problems we studied in class, and that exam problems will be similar. This Gem is also instructed to teach you using the Socratic method, instead of giving you answers too quickly

Syllabus: 

  • Week 01 -- Aug. 24, 26, 28: Systems of Linear Equations ( Chs. 6, 7)
  • Week 02 -- Aug. 31, Sep. 2, 4: Matrix Algebra, Determinants (Chs. 8--9, parts of 26++)
  • Week 03 -- Sep. 09, 11: Vectors, Euclidean Spaces (Ch. 10)
  • Week 04 -- Sep. 14, 16, 18: Linear Independence, Bases, Subspaces, Projection, Decompositions (Chs. 11, parts of 27, 28)
  • Week 05 -- Sep. 21, 23: Exam 1 review (Test 1 self-checks); introduction to linear programming
    • September 25: Exam 1 (covering material from weeks 1-4 only)
  • Week 06 -- Sep. 28, 30, Oct. 2: Linear Programming and Duality (Vohra Ch. 4; Dixit Chs. 3–4)
  • Week 07 -- Oct. 05, 07, 09: Farkas's Lemma and No Arbitrage; Farkas for Linear Programs; Complementary Slackness and Shadow Prices (Vohra Chs. 2, 4; Dixit Chs. 3–4)
  • Week 08 -- Oct. 14, 16: Calculus of Several Variables I: partial derivatives, gradients, the chain rule and the Jacobian; an investor's marginal utility and the state prices her choice implies (Ch. 14, §§14.1–14.7)
  • Week 09 -- Oct. 19, 21, 23: Calculus of Several Variables II: existence of an optimum (Weierstrass), Taylor approximation, second derivatives and the Hessian (Ch. 30, §§30.1–30.3; §14.8; Vohra §1.3)
  • Week 10 -- Oct. 26, 28: Exam 2 review; self-assessment on Weeks 6–9, no new material
    • October 30: Exam 2 (covering material from weeks 6-9 only)
  • Week 11 -- Nov. 02, 04, 06: Quadratic Forms and Definiteness; Unconstrained Optimization; Constrained Quadratic Forms (Chs. 16–17)
  • Week 12 -- Nov. 09, 11, 13: Constrained Optim. I: Lagrange Multipliers, Inequality Constraints (KKT), Mixed Constraints and Minimization (Ch. 18)
  • Week 13 -- Nov. 16, 18, 20: Constrained Optim. II: Envelope Theorem and Roy's Identity, Second-Order Conditions (Ch. 19.1–19.3; Dixit Chs. 5–6)
  • Week 14 -- Nov. 23: Euler's Theorem and Risk Contributions (Ch. 20, brief; bonus, not on Exam 3)
  • Week 15 -- Nov. 30, Dec. 02: Test 3 Self-Checks
    • December 4: Exam 3 (covering material from weeks 11-13 only)

Course grading: 

  • Exercise problem sheets: 50% (the lowest three exercise-sheet grades will be dropped)
  • Exams: 50% 

 

Course Summary:

Course Summary
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