Course Syllabus

ECON 308: Mathematics for Economists — Fall 2026

Professor: Mahmoud El-Gamal

Class: MWF, 12:00—12:50 p.m., TBA

Lab: W, 5:00–5:50 p.m., TBA

Office hours: By appointment

TA: TBA

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

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

Specifically, this course offers students concise coverage of some elements in three areas of mathematics that we use extensively in economics. The course content is split into three modules, covering elements of:

• • Linear algebra (weeks 1—5; textbook chapters 6—11)
  • Calculus of several variables (weeks 6—10; textbook chapters 12—15)
  • Optimization (weeks 11—15; textbook chapters 16—21)

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 two short lecture sessions, each 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 during class, scanned to PDF, and uploaded to Canvas for grading and comments
  • 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
  • Exercise assignments will remain open on Canvas for a week after each class, in case students wish to resubmit answers to improve their grades
• 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
• Students will be allowed or required to use the MATLAB mobile app as an "evolved hand calculator" capable of doing linear algebra, calculus, mathematical programming, and symbolic math while working on class exercises and exam problems 

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 are not allowed to use any AI resources to assist with classwork or exams during class
• Students may use AI resources for tutoring purposes 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 "Math for Econ Virtual TA" (the Gem defaults to the "Fast" model, which is not good for math; always switch to "Pro" model before working with it) 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

Attendance Policy?

• I am not formally requiring in-person attendance, except on exam days
• Activity sheets will be posted on Canvas a few minutes before class. Work is completed on paper, scanned to PDF, and uploaded to Canvas within 10 minutes of the end of class. Students who choose not to attend may upload remotely on the same deadline
• The lowest three exercise-sheet grades are dropped, which absorbs occasional absences for illness or conflicts
• Slide decks will be shared after each lecture as reference material. The whiteboard mini-lectures, not the slides, are the first encounter with new material, so students who attend will be best prepared for the activity sheets
• Students who feel they can do the work on their own may skip class and use the textbook, AI tutors, or other resources to complete the activity sheets remotely. Be aware that exams are on paper, in class, with no external resources of any kind. Students who lean on AI for the activities are likely to stumble at the exams
• The only use of electronics in class and during exams should be the MATLAB mobile app, the PDF scanning app, and the Canvas app

Syllabus: 

• Week 01 -- Aug. 24, 26, 28: System of Linear Equations ( Chs. 6, 7)
• Week 02 -- Aug. 31, Sep. 2, 4: Matrix Algebra, Determinants,  Vectors, Farkas's Lemma (Chs. 8--10, parts of 26++)
• Week 03 -- Sep. 09, 11: Euclidean Spaces (Ch. 10), Supporting hyperplane (Vohra, Ch. 3)
• Week 04 -- Sep. 14, 16, 18: Linear Independence, Projection, Bases, Decompositions (Chs. 11, parts of 23, 27, 28++)
• Week 05 -- Sep. 21, 23: Linear Programming, duality, and Farkas's Lemma (Chs. 21 & 26, Vohra, Ch. 4, Dixit, Chs. 3--4)
  • September 25: Exam 1
• Week 06 -- Sep. 28, 30, Oct. 2: Sequences, Open and Closed Sets (Ch. 12)
• Week 07 -- Oct. 05, 07, 09: Functions of Several Variables (Chs. 13, 29)
• Week 08 -- Oct. 14, 16: Calculus of Several Variables I (Ch. 14)
• Week 09 -- Oct. 19, 21, 23: Calculus of Several Variables II (Ch. 30)
• Week 10 -- Oct. 26, 28: Implicit Functions and their Derivatives (Ch. 15)
  • October 30: Exam 2
• Week 11 -- Nov. 02, 04, 06: Quadratic Forms, Unconstrained Optim., Quadratic Programming (Chs. 16, 17)
• Week 12 -- Nov. 09, 11, 13: Constrained Optim. I: FOC (Ch. 18)
• Week 13 -- Nov. 16, 18, 20: Constrained Optim. II: Envp. Thm., SOC (Ch. 19, Dixit Chs. 5-6)
• Week 14 -- Nov. 23: Homogeneous and Homothetic Functions (Ch. 20)
• Week 15 -- Nov. 30, Dec. 02: Concave and Quasiconcave Functions (Ch. 21)
  • December 4: Exam 3

Course grading: 

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