APMA 1210 Syllabus
Pre-requisites:Calculus and linear algebra. Prior knowledge of numerical linear algebra or scientific computing is definitely a plus.
Programming Language:MATLAB
Class times and locations: Tuesday and Thursday 9 - 10:20 am, B & H 157(I do not know the exact address!)
Instructor:Xingjie Li:
Office Hour: Tuesday and Thursday: 10:40 am – 11: 40 aminat Room 101,37 Manning St, or by appointment
TA: Lisa Eklund:
Recitation Hour: Thursday 5:30 – 6:30 pm in Room 102A, 180 George St.
Office Hour: Monday 7:00 – 9:00 pm in Room 102A, 180 George St.
Please note: 180 George St. closes at 5:00 pm on Thursday. Please arrange access to the building with Lisa via email if you will be late to recitation.
Please Do Not approach Professor Sandstede for any class-related issues!
Grade and Credit:
Course grades will be given based on homework, quizzes, two midterms and final exam scores. Homework is worth 5%, the quizzes are worth 205% the one two midtermsare is worth 230[lje1] % each, and the final exam is worth 3450% of your course grade.
Homework is due every Wednesday by 5 pm in the assigned box in the lobby of 182 George St. Late homework will not be accepted or graded. The 15 minutes in-class quiz will beis given every Thursday. It will havehas one problem based on homework assigned one or two weeks ago.
Your lowest quiz score will be dropped.
The midterm examsis will be given on Thursdays, Oct 18thth and Nov 2215ndth, Thursday. TheyItareis in class and closed book. The final exam will be at 2:00 pm on Tuesday, December 18th[lje2].is given in middle of December. It is closed book with one1A4 8.5in x 11in page cheat sheet[lje3]. Time and location of the final will be notified later.
Make sure that you can be present for each of the midterm and final exams. There will be NO makeup exams, except in exceptional circumstances and at the discretion of the instructor[lje4].
Collaboration Policy:
Students are encouraged to collaborate on homework assignments. If working in a group, each student should attempt the problems individually first and any work submitted should be written up independently. Brown’s Academic Code should be reviewed and strictly followed. It can be found at
Course Goals:
Following this course, students will be familiar with the basic terminology, notions and main results appearing in the literature. Students will understand the interplay between the two key aspects of Operations Research (OR): the modeling of a real-life problem v.s. the mathematical analysis of a model. We will not attempt to cover the full breadth of OR (even the following content list) during this semester[lje5](12 week, 24 classes) long course. However, we will cover the basics and fundamentals of the field of Linear Programming, and give a survey of the vastly varying topics in Nonlinear Programming. We will try to present an equal treatment of the mathematical analysis and the applications of OR.
Textbooks:
The recommended (and official text) is
- [HL] Hillier and Lieberman, Introduction to Operations Research, 9th edition.
We will occasionally draw material from other good books, such as
- [BV] S. Boyd and L. Vandenberghe, Convex Optimization
- [D1] G. B. Dantzig, Linear Programming 1. (available from Brown library as online resource)
- [D2] G. B. Dantzig, Linear Programming 2.
Course Content:(12 weeks, 24 classes):
1. Linear Programming and the Simplex Method.
Learn the mathematical basis of the liner programming (LP) and dual LP problem. Learn the fundamental concepts of the simplex method, and understand its uses and limitations. Topics:
(1) Introduction and formulation of the linear programming (LP) problem;
(2) The graphical and simplex methods for solving the LP problem;
(3)Variant of simplex method: M-method, two-phase method;
(4)Duality and sensitivity analysis.
2. Nonlinear Programming.
Understand the mathematical theory of characterizing the optimal solutions. Learn the design mechanism of well-known numerical algorithms. Learn to solve nonlinear optimizations from practical problems with computer aid.
(1) Global/local optimum, necessary condition, sufficient condition;
(2)Lagrange multiplier, KKT conditions;
(3) Unconstrained optimization algorithm: steepest descent / Newton method/
Conjugate gradient method.
(4) Constrained optimization algorithm: penalty / barrier / augmented Lagrangian
method
(5) Dual theory
(6) Quadratic programming algorithms.
3. Dynamic Programming.
Learn the technique of dynamic programming and how to identify when it is applicable.
4. Game theory.
[lje1]I thought you mentioned giving two midterms? Did you decide on one? You could do something like 20% quizzes, 20% midterm 1, 20% midterm 2, 35% final, 5% homework. The way you have listed it is fine with me too.
[lje2]This is determined by the registrar based on the course time and can be found in banner (selfservice.brown.edu)
[lje3]Double sided or single? A4 is primarily the European size paper and many students won’t know what that is.
[lje4]Typically students need permission from a Dean to reschedule a final. You can be more lenient than the Dean’s if you wish, but you can just say “except with permission from an Academic Dean”
[lje5]I wouldn’t mention exactly how long it is because there is a Thanksgiving holiday and reading period that make it ambiguous. We can talk about that if you want. Most math classes have class (even if it is a review session) during reading period which is Dec 8 through 12 this semester (