Time | Mon, Wed 8:40–9:55am, 10:10–11:25am |
Place | Math 312 |
Instructor | Anand Deopurkar (anandrd at math ) |
TAs | Sebastian (spm2152 ), Max (mk3675 ), Nawaz (njs2155 ), Peiran (pf2317 ), Peter (pwl2107 ), Yih-Jen (yak2110 ) |
Office hours |
Monday 12:30pm–2pm, Tuesday 6pm–7pm During reading week: Wednesday to Sunday 6pm–7pm |
This is a tentative plan of the course. It will be in flux, with some restructuring as we go along.
Date | Topic | Reading | Homework |
---|---|---|---|
Jan 20 | Overview and review of optimization in one variable | Your favorite Calculus book | |
Jan 25 | Linear inequalities and optimization in 2 variables | LEF 9.1 9.2 | |
Jan 27 | Review of linear algebra: matrices, linear dependence, rank | SHSS 1.1–1.4 | Homework 1 (solutions). |
Feb 1 | Open, closed, compact sets, maximum theorem | SHSS 13.1, 13.2, 13.3 | |
Feb 3 | Convex sets | SHSS 2.2, 13.5 | Homework 2 (solutions). |
Feb 8 | The simplex method | LEF 9.3 | |
Feb 10 | Duality | LEF 9.4 | |
Feb 15 | Simplex/duality continued | LEF 9.4, Chapter 2 from Tom Fergusson's notes, Lecture 25 from Pinkham. | Homework 3(solutions) |
Feb 17 | Midterm 1 | ||
Feb 22 | Gradients and stationary points | SHSS 2.1, 3.1 | |
Feb 24 | Taylor's theorem | SHSS 2.6 | Homework 4(solutions) |
Feb 29 | Quadratic forms, eigenvalues, spectral theorem | SHSS 1.7 | |
Mar 2 | Hessians, second order conditions, local min/max | SHSS 3.2 | Homework 5(solutions). |
Mar 7 | Convex optimization | SHSS 2.2–2.4 | |
Mar 9 | Convex optimization continued | SHSS 2.2–2.4 | Homework 6(solutions). |
Mar 14 | Spring break! | ||
Mar 16 | Spring break! | ||
Mar 21 | Implicit function theorem | SHSS 2.7 | |
Mar 23 | Constrained optimization: Lagrange multipliers | SHSS 3.3 | |
Mar 28 | Constrained optimization: Second order conditions | SHSS 3.4 | |
Mar 30 | Midterm 2 | ||
April 4 | Constrained optimization: Second order conditions continued | SHSS 3.4 | |
April 6 | Inequality constraints: Kuhn-Tucker conditions | SHSS 3.5 | Homework 7(solutions) |
April 11 | Convex optimization: Sufficient conditions | SHSS 3.6 | |
April 13 | Mixed constraints, envelope theorems | SHSS 3.8, 3.3 | Homework 8(solutions) |
April 18 | Calculus of variations | SHSS 8.1 | |
April 20 | The Euler-Lagrange equation | SHSS 8.2–8.3 | Homework 9(solutions) |
April 25 | Solving the EL equation | TBD | |
April 27 | Constrained variational problems | TBD |
Our primary text will be
We will complement it with the following:
The first book is available online for free. The chapters we will use from the second book are also available online for free. I have provided the links to the chapters in the course plan below.
Many times in economics, science, and social science, we need to optimize a function under given constraints. That is, we must find the values of the inputs that make the function attain the maximum or the minimum value. The course will cover foundational topics from linear algebra, multivariable calculus, and mathematical analysis that are applicable to these questions. The techniques we will learn include:
Calculus III and Linear Algebra are required. While we will spend some time refreshing ideas from these courses, it will not be a substitute for learning them for the first time.
There will be weekly homework posted on this website. It will be usually due on Wednesday before 5pm in the homework boxes. Late homework will not be graded. To compensate for the inflexible late homework policy, I will drop the lowest 2 homework scores, so that you won't be penalized for not turning in homework in those really bad weeks.
There will be 2 in-class midterms and a final. The dates for the exams are as follows.
Your final grade will be determined by your performance on the the homework, the midterms, and the final. They will contribute in the following ratio:
It is fine to work with your friends on homework but do spend time thinking about the problems on your own before you start discussing. Also, you must write up the solutions by yourself. Do not, under any circumstance, pass of someone else's work as your own! As a matter of academic honesty, write the names of your collaborators on top of your submission. This will not affect your grade.