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.

Click here for Quiz Solutions and Comments on Homeworks and Quizzes

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.

Homework Assignment 11

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.

  • Department of Mathematics
    College of Liberal Arts and Sciences
    University of Illinois at Urbana-Champaign
    273 Altgeld Hall, MC-382
    1409 W. Green Street, Urbana, IL 61801 USA
    Department Main Office Telephone: (217) 333-3350 Fax (217) 333-9576