
Joel Friedman's Math 340 Page
This page concerns Math 340, Section 101, for Winter 201415 Term 1
(i.e., Fall 2014). The dates of exams, once announced,
will not change; all other
dates, homeworks, etc. are subject to change.
Not all course materials are available at all times (especially solution
sets to homeworks).
Materials here are not necessarily free of errors; some corrections might only
be announced in class.
Final Exam 
Our final exam is on Tuesday, December 16, in LSK 201, at noon.
Here is a rough
course outline
describing what we have covered in this course, what you need to
know and be able to do, and pointers to the appropriate
sample exam problems (all of the sample exam problems
appear in other documents).
Here is a draft of the
note sheet for the final
exam.

Midterm 
The midterm was held on Wednesday, October 22, covering
material up to and including October 8:
the handout on game theory, Chapters 2 and 3, and the applications of
Chapters 2 and 3 to game theory (see the blog and the homework exercises).
Here is
the midterm with solutions;
the midterm was scaled by s(x), where x is your raw score out of 30,
given by: 5x if x <= 10,
2x+30 if 10 <= x <= 25, and 4x20 if x >= 25 (so 10 scales to 50,
15 to 60, 25 to 80, etc.)
Here is a draft of the
note sheet that will be
provided to you.
You should be able to do all the homework problems, exercises from the
handout, and all Sample Exam Problems (see below) from Topics 1 and 2.
Location will be our usual classroom; the exam will be 40 minutes long
(it will begin some 10 or so minutes after 2pm);
you will be seated in alphabetical order by last name (as it appears
on my class list).

Basic Materials 
Here is a general overview
of this course.
We will first follow
Matrix Games and Poker
(a supplemental article), which may be updated periodically;
we will also refer to
"TwoPerson ZeroSum Games," by Alan Washburn.
We then follow the textbook,
"Linear Programming" by Vanderbei, 4th edition;
it is available to anyone with a CWL account.
We will then revisit matrix games and poker.
Other applications will be covered as time permits.
We have another article on eta matrices, which includes notes
for class and (will include) sample exam problems for homework;
here is
an article
on Eta Matrices, the Assignment Problem, and other applications.

Blog 
Here is a general skeletal blog for this course.
This will show where we are in the text, and list some of the key
points, terminology, etc. It is skeletaljust a bare outlinesince
we will follow the supplemental article and textbook very closely.
Here are two slides from September 19:
maple_first_lp.txt, and
maple_first_game.txt,
illustrating
two applications of the simplex method.
A slide about a large feasibility question, discussed on September 26, is
your_task190.txt.

Homework 
Homework to be listed here.
Homework #1, due Sept 15: 9.1(1),(3),(5);
9.2(3),(6);9.3
from "Matrix Games and Poker."
Homework was graded out of 9;
solutions.
Homework #2, due Sept 22: 9.4, 9.7, 9.8, 9.12. One additional statement
was added to 9.8, to make things easier, as of September 15; make sure
you hit the "refresh" button to get the latest version.
Homework was graded out of 12;
solutions.
Homework #3, due Sept 29, is given
here.
Homework was graded out of 9;
solutions.
Homework #4, due Oct 6, is given
here.
It was graded out of 10; 3 points for the first two problems, and
4 points for the last problem.
Solutions.
Homework #5, due Oct 17, is given
here.
Solutions.
Homework #6, due November 14:
Problems 3.1, 3.2, 3.4 of the handout on eta matrices.
Solutions.
Homework #7, due November 24:
Problems 3.5, 3.6, 3.7, 3.9 of the handout on eta matrices.
Solutions.

Office Hours 
Office hours before the final exam, all in Mathematics Building room
210:
Thursday (December 11) 23pm;
Friday 23:30pm;
Monday 1:303pm.

Previous Exams 
Note that material and emphasis changes from year to year; look at
"Sample Exam Problems" below to see which problems on which exams
are relevant to our course.
Exams available (some with brief solutions):
 midterm 1997 (solutions) [Anstee's rule is explained
in Problem 1],

midterm 1999 (solutions),

midterm 2000 (solutions),

midterm 2001 (solutions),

midterm 2007 and solutions[The equilibrium strategry for each player is the same as the optimum "announce a mixed strategry"],

final 1997,

final 1999 (solutions),

final 2000 (solutions).

Midterm 2008 and solutions [Here "Announce" means "announces a pure strategry" and
"Scream" means "announces a mixed strategy"],

Final 2008,

Midterm 2009 and solutions
[Same remark as Midterm 08 regarding "Annouce" and "Scream"],

Final 2009, and

Midterm 2014 with solutions.

Old Exam Problems 
The follow list of old exam problems is OUTDATED in that some
of these areas we did not cover this year, and some areas covered do
not appear below. For the list of Sample Exam
Problems for the final exam 2014 you should consult:
the course outline.
Topic 1: Game theory and poker (covering "Matrix Games and Poker" and
selections from Washburn):
Mid 07: 4; Mid 08: 1,5; Fin 08: 1; Mid 09: 2,6; Fin 09: 3,7;
and all sample exam problems from "Matrix Games and Poker"
Topic 2: The simplex method and perturbation method to avoid cycling
(covering Vanderbei, Chap 13):
Mid 97: 1,3; Mid 99: 1,3; Mid 00: 1,2,4,5; Mid 01: 1,3;
Fin 97: 1; Fin 99: 2; Fin 00: 1; Mid 08: 2,4; Fin 08: 4; Mid 09: 1,3;
Fin 09: 4;
Topic 3: Duality theory (Vanderbei, Chap 5):
Mid 97, 2; Mid 99: 2; Mid 00: 3, Mid 01: 2, Mid 07: 1,2;
Fin 97: 2; Fin 99: 1; Mid 08: 3; Fin 08: 3; Mid 09: 4; Fin 09: 5;
Topic 4: Dual Simplex Method (Vanderbei 5.65.7) and
Revised Simplex Method (Vanderbei, Chap 6, 8.18.4):
Fin 97: 3; Fin 99: 3,4; Fin 00: 3 (first half), 5; Fin 08: 5,6;
Mid 09: 5; Fin 09: 1,6;
Topic 5: Sensitivity and Parametric Analysis (Vanderbei, Chap 7):
Mid 99: 4; Fin 97: 4; Fin 99: 5; Fin 00: 4; Fin 09: 2;
Topic 6: Game theory and poker revisited (Vanderbei, Chap 11,
"Matrix Games and Poker" and selections from Washburn):

