Math 181 D2 - A Mathematical World - Spring 2012
140 Henry Building, MWF 11:00 a.m.-11:50 a.m.
Welcome to the course webpage for Math 181 section D2. Please check this page frequently for important announcements and information pertaining to this course.
Office Hours: Mondays from 9:50 to 10:50 a.m., Wednesdays from 12:00 to 1:00 p.m., and by appointment
Course Overview: I think that it is important for a course to have a storyline. A storyline not only insures the course remains interesting for the duration of the semester, but it also provides students with a framework to organize the information and details he or she has learned from the course. This way, students may view the course material as a family of related concepts as opposed to a disconnected collection of random facts and trivia. Motivated by the set-up of the course and textbook, I plan to deliver two storylines this semester. The first will be titled Structure and Symmetry and the second will be titled Social and Societal Mathematics. As we progress through each storyline, I anticipate that these titles will take on more and more meaning for students.
Lecture Notes and Topics: I will post an overview and some notes from each lecture along with the topics covered in the lecture. The file for each lecture will be available for download the evening of that lecture. At the end of each document, I will suggest reading and homework problems to help master the material covered. The purpose of these notes is to make studying easier and more accessible for students, however, they are not meant to be a substitute for class attendance. Please inform me of any typos via email.
| Date | Topics | Sections |
|---|---|---|
| 01/18/2012 | Graphs, Circuits, and the Bridges of Konigsberg | 1.1, 1.2 |
| 01/20/2012 | Proofs, Euler Circuits, and the Postman Problem | 1.2 |
| 01/23/2012 | Problem Session | 1.1, 1.2 |
| 01/25/2012 | More on the Postman Problem and Euler Circuits | 1.2 |
| 01/27/2012 | Eulerizations, Rectangular Networks, and Garbage Collection | 1.3, 1.4 |
| 01/30/2012 | Complete Graphs, Hamilton Circuits, and the Traveling Salesman | 2.1, 2.2, 2.3 |
| 02/01/2012 | Problem Session | 1.3, 1.4 |
| 02/03/2012 | Dirac's Theorem (for Hamilton Circuits), Spanning Trees, and Power Lines | 2.4 |
| 02/06/2012 | Spanning Trees and Order-Requirement Directed Graphs | 2.5 |
| 02/08/2012 | Problem Session | All Ch. 2 |
| 02/10/2012 | Permutations, Symmetries of Graphs, and Card Shuffling | N/A |
| 02/13/2012 | Sets, Functions, and Graph Automorphisms | N/A |
| 02/15/2012 | Problem Session (followed by Quiz) | N/A |
| 02/17/2012 | Cycles, Transpositions, and Trading in Pro Sports | N/A |
| 02/20/2012 | Finished discussing 2/17 lecture | N/A |
| 02/22/2012 | Review for Exam 1 | N/A |
| 02/24/2012 | Exam 1 | N/A |
| 02/27/2012 | Properties of Distance and Isometries | 19.2 |
| 02/29/2012 | Mirrors and Isometries of the Euclidean Plane | 19.2 |
| 03/02/2012 | Problem Session | 19.2 |
| 03/05/2012 | Groups and the "Big Picture" of Symmetry, Part 1 | 19.4 |
| 03/07/2012 | Groups and the "Big Picture" of Symmetry, Part 2 | 19.4, 17.3 |
| 03/09/2012 | Review and Completion of 03/05 and 03/07 Lectures | 19.4, 17.3 |
| 03/12/2012 | Groups and the "Big Picture" of Symmetry, Part 3 | 19.4, 17.3 |
| 03/14/2012 | Finished 03/12/2012 lecture | 19.4, 17.3 |
| 03/16/2012 | Began Game Theory | |
| 03/26/2012 | Game Theory Terminology and the Location Game | Intro to 15, 15.1 |
| 03/28/2012 | Review for Exam 2 | |
| 03/30/2012 | Exam 2 | |
| 04/02/2012 | Pure Strategies for Two-Person Total Conflict Games | 15.1 |
| 04/04/2012 | Mixed Strategies for Two-Person Total Conflict Games | 15.2 |
| 04/06/2012 | Mixed Strategies for Two-Person Total Conflict Games Continued | 15.2 |
| 04/09/2012 | Partial Conflict Games and Nash Equilibria | 15.3 |
| 04/11/2012 | Work in Groups | N/A |
| 04/13/2012 | Work in Groups | N/A |
| 04/20/2012 | Social Choice and Voting, Part 1 | 9.1, 9.2 |
| 04/23/2012 | Social Choice and Voting, Part 2 | 9.3 |
| 04/25/2012 | Review for Exam 3 | N/A |
| 04/27/2012 | Exam 3 | N/A |
Quiz Schedule: Each quiz scheduled will be posted here along with the relevant material that the quiz will cover. All quizzes will be scored out of 20 points.
| Date | Lectures | Sections | Median | Mean | Std Dev | |
|---|---|---|---|---|---|---|
| Quiz 1 | 01/25/2012 | 01/18 and 01/20 | 1.1, 1.2 | 16 | 80.2% | 17.1% |
| Quiz 2 | 02/01/2012 | 01/25 and 01/27 | 1.3, 1.4 | 16 | 74.9% | 20.0% |
| Quiz 3 | 02/10/2012 | 01/30, 02/01, 02/03, 02/06 | 2.1, 2.2, 2.3, 2.4, 2.5 | 17 | 84.5% | 14.4% |
| Quiz 4 | 02/15/2012 | 02/10 and 02/13 (except graph automorphisms) | N/A | 18 | 87.0% | 12.0% |
| Quiz 5 | 02/20/2012 | Cumulative Practice for Exam 1 - All Previous Material | All Ch. 1 and Ch. 2 | 13 | 65.2% | 18.0% |
| Quiz 6 | 03/07/2012 | 02/27 and 02/29 | 19.2 | 9.5 | 44.8% | 21.9% |
| Quiz 7 | 03/14/2012 | 03/05 through 03/12 | 19.4, some of 17.3 | 15 | 74.6% | 17.7% |
| Quiz 8 | 04/04/2012 | 03/26 and 04/02 | 15 Intro, 15.1 | 20 | 95.2% | 9.3% |
| Quiz 9 | 04/11/2012 | 04/04, 04/06 | 15.1, 15.2 | 14 | 76.7% | 9.8% |
| Quiz 10 | 04/18/2012 | 04/09 | 15.3 | 20 | 92.9% | 14.2% |
Midterm Exam Schedule:
| Date | Lectures | Sections | Median | Mean | Std Dev | |
|---|---|---|---|---|---|---|
| Exam 1 #2 | 02/24/2012 | 01/18-02/20 Inclusive | Ch. 1 and Ch. 2 and Pre-Ch.19 material | 80 | 79.6% | 14.2% |
| Exam 2 | 03/30/2012 | 02/27-03/14 Inclusive, Practice | 19.2,19.4, 17.3 | 63 | 68.3% | 15.3% |
| Exam 3 | 04/27/2012 | 03/26-04/23 Inclusive | 15 Intro, 15.1-15.3, 9 Intro, 9.1-9.3 | 81.5 | 77.9% | 16.6% |