'17 Fall: Analysis and Optimization (UN2500)

What's new

Section 01: MW 11:40am-12:55pm in 207 Mathematics Building Kent 413
Section 02: MW 2:40pm-3:55pm in 203 Mathematics Building

Instructor: Shotaro Makisumi (623 Mathematics, makisumi@math.columbia.edu)
Please contact me by email. I cannot promise to read any messages/comments sent through Canvas.

Topics: Quadratic forms, Hessian, implicit functions. Convex sets, convex functions. Optimization, constrained optimization, Kuhn-Tucker conditions. Linear programming, calculus of variations. For details, see the syllabus.

Prerequisites: Calculus III and Linear Algebra. We will review some of the relevant background, but at a pace and level that assumes prior exposure. Please speak with me if you are not sure if you have the background.

The official text

should be available from the bookstore. We will also use a chapter (freely available online, to be linked from the syllabus) from


There will be two 75-minute in-class midterms and a final.

Make-up midterms will be given only under exceptional circumstances, and you will need a note from a doctor or a dean. The final must be taken at the scheduled time. If you have two final examinations scheduled at the same time, it is the responsibility of the other department to provide an alternate exam. Examinations will not be rescheduled because of travel arrangements. It is your responsibility to schedule travel appropriately.

The use of electronic devices during exams is not allowed and will automatically result in a zero for the exam. In addition, anyone found to have cheated on an exam will receive a failing grade for the course and be subject to administrative discipline.


Problem sets (available under Files on Canvas) every 7-10 days, due in the homework box on the fourth floor of the Mathematics building. Collaboration and discussion with your classmates is encouraged, but I encourage you to attempt the problems on your own before you discuss them with friends. You must write up assignments individually. I will drop the lowest two homework grades from your average. Late homework will not be accepted.



Students requiring special accommodation should contact the Office of Disability Services (ODS) promptly. You can find more information here.