MATH 354-04, Spring 2006

PREREQUISITE: Math 250.

MEETING TIMES: Tues, Thurs 5:00-6:20 in SERC 220

INSTRUCTOR: Richard Lyons, lyons@math.rutgers.edu, 732-445-5090 or 732-445-2390
OFFICE HOURS: Tuesday 1:00-3:00 in Hill 236

SYLLABUS


ANNOUNCEMENTS:
Credit is not given for both 640:354 and 711:453.
To apply to enter a closed section of any Mathematics course, go to the online Mathematics Department special permission page.
A copy of the textbook is now on reserve in the study lounge in SERC.
In problem 16, 1.2, you should assume that r>=0 and s>=0.
The first midterm will take place in the regular class time on Feb. 28. Some review problems can be found in "Supplementary materials" below.
REVIEW SESSION FEB. 27 will meet at 5:45 in SERC 206, and WILL MOVE to SERC 217 at 6:30

Midterm #2 will be given in class on Tuesday, April 11. It will cover sections 3.2, 3.3, 3.4, 3.6, 4.1, 4.2, 4.3. In addition it will cover the primal-dual method (see notes below) as well as the relationship between primal and dual tableaux (see notes below).
REVIEW SESSION FOR MIDTERM #2 will take place in Hill 423, 5:30-7:30 p.m., Monday, April 10.

FINAL EXAM will take place WEDNESDAY, MAY 10, from 4:00-7:00 in SERC 220, our regular classroom.

FINAL REVIEW SESSION: Tuesday, May 9, from 4:00-7:00 p.m., in SERC 220, our regular classroom.


ALL ASSIGNMENTS MAY BE PICKED UP OUTSIDE MY OFFICE, HILL 236


ASSIGNMENTS:
Jan. 190.1: 14
0.5: 1, 5, 16, 18, 19
Read Chapter 1
Due Jan. 261.1: 1,4,8,11
1.2: 8,13,14,16
1.5: 1(i),(iii),(iv), 6,8
Due Feb. 22.1: 1,3,5 (don't hand these three in)
2.1: 8, 20, 22, 23
2.1: 19 BUT change "max" to "min" and make the first constraint x_1+2x_2+x_3<=6
2.2: 2, 3, 8
2.3: 2a), 3a)
Due Feb.92.3: 6,7,8,9,10,12,18,20,21,22
Due Feb.161.3: 18,20,22,24,30,34,36.
1.4: 16
Add'l A. Show that the function f(x)=-log(x_1)-log(x_2)-...-log(x_n) is a convex function.
Add'l B. Show that if f is any convex function and b any real number, then the solution set of the inequality f(x)<=b is a convex set.
(The definition of "convex function" is given in #35 of Section 1.3.)

Here x=[x_1 x_2 ... x_n]^T is a column vector in R^n, as usual.
due Feb.23
(hand in even #'s)
3.1: 2, 3, 5, 6
3.4: 2, 4, 5, 8
Due March 10 by 3 p.m.3.2: 1, 2, 3,4, 5, 6, 8
3.6: 1, 2, 3
Due 3/304.1: 5, 6
4.2: 3, 5, 6, 8, 9, 10
Solve the following LPP's using primal-dual: Exercise 3 in Sec 2.3
Minimize 2x-y subject to x+y >=3, -3x+2y<=6, x>=0, y>=0
Due April 64.3: 6, 8, 11
Due April 205.1: 9, 10, 11, 12
5.2: 1, 2, Project 1
Due Monday May 1
(at Hill 236)
5.2: 4, 5, 6, 7
5.4: 4, 5, 6, 7


SUPPLEMENTARY MATERIALS:

Supplementary notes on tableaux (5 pp.)   (2 pages on 1)
Examples of simplex method
Pages of blank tableaux: small medium large
Examples of 2-phase method
New supplementary notes on extreme points (Feb. 7) (10 pages) 2 pages on 1
Some solutions to problems due 2/16 (2 pages on 1)
Review problems for Exam 1 and some answers
(answer to last question in #1 corrected 2/27)
Notes on duality  2 pages on 1
Primal-Dual Simplex Method  2 pages on 1
Review problems for Exam 2  (on one page)   


QUIZZES AND EXAMS: 1/26
2/7 2/21 2/28 (Exam 1) 3/9 4/4 4/11 (Exam 2)


Maintained by lyons@math.rutgers.edu and last changed Mon May 8 14:18:37 2006