MATH-101/101A Mathematical Thinking   
Basic class information

  • The book we are using, Math in Society 2.5 by David Lippman, can be downloaded here.  Here's a local copy as well. 

Week 1.  January 26 - January 30.    
Day
 Class Covers
 Assignments, etc.
Tuesday
 Snow day.
 Snow day.
Thursday
 Syllabus, short introduction to topics we'll cover.  Read about voting theory (starts on page 35) up to and including at least the Borda count method.

Week 2.  February 2 - February 6.
Day
 Class Covers
 Assignments, etc.
Tuesday
 We'll start on voting theory--the preference schedule, the plurality method, and the majority criterion. Read about voting theory (starts on page 35) up to and including at least the Borda count method.
Thursday
 I have notes from an online version:
Introduction to voting theory.
Voting theory framework.
Voting theory framework part II.

 Exercises beginning on page 53: 1, 2, 3a-3c.

Homework #1 is on D2L.  (Found in the quiz section)

Week 3.  February 9 - February 13.    
Day
 Class Covers
 Assignments, etc.
Tuesday
  Insincere Voting, Plurality with Eliminations.

An outline.

 3e, 4e, 7, 17,
3d, 4d,  9, 14, 18.

Do homework #2 on D2L when you are ready..  (Found in the quiz section)
Thursday
 The Condorcet criterion, the monotonicity criterion, Borda count.

 3d, 4d,  9, 14, 18.

Homework #3 is on D2L and covers Borda count.


Week 4.  February 16 - February 20.
Day
 Class Covers
 Assignments, etc.
Tuesday
 Pairwise comparisons (Copeland's method).  Majority candidates are always Condorcet candidates.


 Exercises:  3, 4 (all parts).  13, 15, 16, 19, 20.
Thursday
 Independence of irrelevant alternatives criterion. 

Conclusions on voting theory.  Arrow's Impossibility theorem. Is IIA a fair criterion?

Weighted voting systems.  Starts on page 59. 		Homework #4 is on D2L and covers pairwise comparisons.

Quiz 1 is on D2L and covers all of voting theory.  Take it within a week.

Starting on page 70 in the book,  Anything in 1-8 is good.  19, 20.

Week 5.  February 23 - February 27.    
Day
 Class Covers
 Assignments, etc.
Tuesday
 Coalitions and counting coalitions.  Here's how I count coalitions.. The Banzhof power index. 9 - 14 are good problems.  You should be reading the chapter as we go along.

Do homework #5 covering the basics of weighted voting when you are ready.

Do homework #6 (Banzhof and coalitions) on D2L when you have tried the book problems.
Thursday
 Sequential coalitions.  A word about counting sequential coalitions.  The Shapley-Shubik power index. 15 - 18 are good, 21.

Do homework #7 (Shapley Shubik) on D2L when you have tried the book problems.

Quiz 2 will be ready soon.  It will cover weighted voting.

Week 6.  March 2 - March 6.
Day
 Class Covers
 Assignments, etc.
Tuesday
 Fair division concepts and terminology.  Divider-chooser.  Starts on page 93.

 
Starting on page 108, exercises 1 - 6.
Do homework #8 (basics of fair division) when you are ready.
Thursday
 The lone-divider method for 3 players and more.


Last diminisher.
 Exercises 7, 8, 17a and b,  18, 19.
Homework #9 covers lone divider.  Take it soon.

11-14 are good problems.  Be sure to try 15.
Homework #10 covers (mostly) last diminisher.

Week 7.  March 9 - March 13.    
Day
 Class Covers
 Assignments, etc.
Tuesday
 Finish last deminisher.

The method of sealed bids. 		11-14 are good problems.  Be sure to try 15.
Homework #10 covers (mostly) last diminisher.

Add 9, 10.
Homework #11 is about the method of sealed bids.

Take Quiz 3 on fair division before the test.
Thursday
 Review for test 1. 

Study!

Spring Holiday.  March 16 - March 20.    
Day
 Class Covers
 Assignments, etc.
Monday
 No Classes.
 No Classes.
Tuesday
 No Classes. No Classes.
Wednesday
 No Classes. No Classes.
Thursday
 No Classes. No Classes.
Friday
 No Classes. No Classes.

Week 8.  March 23 - March 27.
Day
 Class Covers
 Assignments, etc.
Tuesday
 Test 1.

 		Test 1.
Thursday
 Concepts of graph theory.  (Starts on 117 in the book.)

 		1 - 8 starting on page 146.
Do homework #12 (basics of graph theory) on D2L when you have tried the book problems.

Week 9.  March 30 - April 3.
Day
 Class Covers
 Assignments, etc.
Tuesday
 Notes on last class: beginning graph theory.
Euler's theorems, Euler circuits, Euler paths, and Fleury's algorithm. 		11, 12.
Do homework #13 (Euler's theorems) on D2L.
Thursday
 Eulerizations, optimal Eulerizations, Hamilton paths and circuits.  Complete graphs.

Why no algorithm?  Clay Millennium Prize Problems

 13 - 18.

Week 10.  April 6 - April 10.    
Day
 Class Covers
 Assignments, etc.
Tuesday
 Dijkstra's algorithm. 9, 10.  Quiz 4 is online!
Thursday
 Quiz 5 on Dijkstra's algorithm is in class!  There will not be make-ups.

Week 11.  April 13 - April 17.
Day
 Class Covers
 Assignments, etc.
Tuesday
 Complete graphs.  Number of HC on a complete graph.
The Traveling Salesperson Problem.  (TSP)  An example.  The nearest neighbor and repetitive nearest neighbor algorithm.

 19-22 just part a. for each.
27 (consider complete graphs up to n=10)  31.
Thursday
 The repetitive nearest neighbor algorithm.  The cheapest link algorithm.  An example. Another example.
 19-22
27 (consider complete graphs up to n=10)  31.
Do homework #14 (Nearest neighbor solutions to the TSP) on D2L.
Do homework #15 (cheapest link solutions to the TSP) on D2L.

Take Quiz 6 on the TSP when you are ready, before the next class.

Week 12.  April 20  - April 24.    
Day
 Class Covers
 Assignments, etc.
Tuesday
 Trees. Minimum network problems. Kruskal’s Algorithm

 23 - 25.
Take Quiz 7 on the minimum spanning tree when you are ready.
Thursday
 Recitation day.  Get caught up on homework and quizzes in D2L.

Week 13.  April 27 - May 1.
Day
 Class Covers
 Assignments, etc.
Tuesday
 Review of graph theory. An example.  The solutions.
Thursday
 Test 2.

Week 14.  May 4 - May 8.
Day
 Class Covers
 Assignments, etc.
Tuesday
 Go over test 2.  Finishing comments.
Thursday
 Review for the final.  Bring me questions.

Finals Week.  May 11 - May 15.  See the final exam schedule on the registrar's page.
Day
 Class and Final Exam Time
Monday
Tuesday
Wednesday
Thursday
Mathematical Thinking:  Thu, May 14, 2026 12:30 PM to 2:30 PM