Math 181: A Mathematical World
Fall 2008
Instructor: Tom Cooney
Email: tcooney@math.uiuc.edu
Classroom: 143 Altgeld
Time: 9:00-9:50pm Monday, Wednesday, Friday
Office: 150 Altgeld
Office Hours: 2:00-2:50pm Wednesday, 2-2:50pm Friday, 3-3:50pm Thursday or by appointment.
Textbook: For All Practical Purposes: Mathematical Literacy in Today's World, Seventh Edition, W.H. Freeman and Company.
Course Description: Introduction to selected areas of mathematical sciences through
application to modeling and solution of problems involving networks, circuits, trees, linear
programming, random samples, regression, probability, inference, voting systems, game
theory, symmetry and tilings, geometric growth, comparison of algorithms, codes, and data
management.
Homework assignments, exam dates and other course details will be posted on
this website.
Here is the syllabus.
You can check your grades at the compass website.
This course adheres strictly to the University's Student Code Part 4 Policy on Academic Integrity. Cheating of any kind on the homeworks, exams, or the final will result in a letter being placed in your permanent school file and may result in an immediate F in the course.
Links This week's homework assignment
Solutions, review sheets to Hour Exams 1 and 2
Quiz 10: Friday, the 21st of November
Hour Exam 3: Friday, the 5th of December
List of topics for Hour Exam 3
Review sheet from Wednesday's class
Question 3 about weighted voting systems should ask about Banzhaf power index and not the Shapley-Shubik power index. Banzhaf is more straightforward than Shapley-Shubik for this particular example. Shapley-Shubik would be quite tedious to do carefully and correctly for this particular example.
Review sheet on fair division, question 5(a)
Solutions to Exam 3
Let me know if you have any questions.
Final Exam: Monday, 15th of December 1:30-4:30 pm in 143 Altgeld
Homework Assignments
Homework Assignment 1
Chapter 1: (p. 25) Problems 4, 8, 9, 21, 24, 26, 36, 37, 48, 53.
Due Date: Friday, the 5th of September.
Homework Assignment 2
Chapter 2: (p. 64) Problems 1, 11, 23, 27, 29a), 35, 36, 40a)b), 42.
Due Date: Friday, the 12th of September.
Homework Assignment 3
Chapter 2: (p. 72) Problems 49, 51a)b)c), 63 (and EXPLAIN your answers!), 68
Chapter 3: (p. 110) Problems 4, 5
Chapter 3: (p. 112) Problems 12, 19
Chapter 3: (Skill Check, p. 108) 2 (Explain) , 3 (Explain)
Due Date: Friday, the 19th of September.
Homework Assignment 4
Chapter 3: (p. 112) 15, 18a)b), 34, 36, 43, 46, 47
(and depending on how much we cover: 63)
Chapter 3: (Skills Check, p.108) 12
(and depending on how much we cover 18, 20)
Due Date: Friday, the 26th of September.
Comments on Homework 4 and Quiz 4
Homework Assignment 5
Chapter 3: (p.110) 45, 46, 63, 65.
Due Date: Friday, the 3rd of October.
Homework Assignment 6
Chapter 9: (p. 364)
Problems 2, 3, 5, 7, 9a)b), 10a)b), [but not 24a)]
Due Date: Friday, the 10th of October.
Homework Assignment 7
Chapter 9: (p. 364)
Problems 8, 10c)d), 13, 17, 20, 24, 27, 28, 33
Due Date: Friday, the 17th of October.
Homework Assignment 8
Chapter 10:
Problems 2, 4, 7, 8, 9, 12
Due Date: Friday, the 24th of October.
Homework Assignment 9
Chapter 11: See this pdf file for this week's homework assigment.
As announced in Wednesday's class, question 8 of the homework assignment will not be due until next week. The rest of the assignment is still due Friday but question 8 can wait until we have discussed that topic further.
My thanks to Melissa Dennison for problems on Homework Assignments 9 and 10.
Due Date: Friday, the 7th of November.
Homework Assignment 10
Chapter 11: See this pdf file for this week's homework assignment.
Problem 5 (Banzhaf power index with many voters) is postponed and will be due Friday, 21st instead of Friday, 14th. All other problems are still due Friday, 14th.
Due Date: Friday, the 14th of November.
Use combinations to compute the Banzhaf power index of the weighted voted
system
[7:3,2,2,2,2,2].
(This is the postponed problem from homework 10.)
Chapter 11: Problem 17, p.426 - a little more practice with combinations.
Chapter 13: Problems 2,3,7, p. 498
Due Date: Friday, 21st of November.
Homework Assignment 12
Chapter 13: p. 499,
Problems 19, 21, 22, 23, 4
Due Date: Friday, 5th of December.
Hour Exams 1 and 2
Hour Exam 2: Friday, the 31st of October
List of Topics for Exam 2
Review sheet from Wednesday's class
As noted, in the email I sent to the class, these two pdf files should also include Approval voting, which is definitely examinable material for Friday's exam. Good luck! Happy Halloween!
Solutions to Exam 2
Hour Exam 1: Friday, the 3rd of October
List of Topics for Exam 1
Review Sheet from Wednesday's class
Solutions to Exam 1
Probable Exam Dates
You will be given at least a week's notice of the actual exam dates.
The hour exams will be held (in class) near the following dates:
Hour Exam 1: Friday, 3rd of October.
Hour Exam 2: Friday, 31st of October.
Hour Exam 3: Friday, 5th of December.
The final will be held (in 143 Altgeld):
1:30-4:30 p.m. on Monday, 15th of December 2008. The final will cover the entire course.
Links
Tom Cooney's homepage
Solutions to and Comments on Quizzes and Homework Assignments
Check your grades at the compass website.
Wikipedia
A good source for interesting and often also true mathematical tidbits. Try
searching for
Euler, Konigsberg Bridge Problem, William Rowan Hamilton, Voting systems, Borda, Condorcet
The publisher of the textbook has computer applets online here, which you can use to get some more practice with the ideas in the course.
The very first graph theory problem ever, the bridges of Konigsberg
Lots of mathematical info from
Wolfram Research ,
one of the world leaders in mathematical computer software,
based right here in Urbana-Champaign.
The MacTutor
History of Mathematics archive : Mathematicians' biographies and more!
This is the webpage from the last time I taught this course. Approach with caution! Things will be different this semester.
