# Michelle Delcourt

## MATH 181: A Mathematical World, Section F1, Fall 2016

### Instructor: Michelle Delcourt Class Location: 343 Altgeld Hall Class Time: 2-2:50pm Monday, Wednesday, Friday Office Location: 169 Altgeld Hall Office Hours: 1-1:50pm Wednesday, 2-2:50pm Thursday Email: delcour2 (at) illinois (dot) edu In this course we will explore the foundations of graph theory, coding theory, voting theory, game theory, and geometry with a focus on real-world applications and hands-on activities.

#### Syllabus

• The syllabus is available here.
• Emergency Procedures
• #### Optional Homework

Here are some suggested practice problems from the book (edition 10) to help to study for quizzes and exams.

To Prepare for Exam 1

Chapter 1 (Week 1, Sections 1.1, 1.2, 1.3)
Exercises 2, 3, 18, 19, 21, 40, 59, 60

Chapter 2 (Week 2, Sections 2.1, 2.2, 2.3, 2.4)
Exercises 1, 2, 3, 39, 46, 55, 57

Chapter 3 (Week 3, Section 3.5)
Exercises 77, 78 (71, 72 edition 9)

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To Prepare for Exam 2

Chapter 17 (Weeks 4, 5, & 6, Sections 17.1, 17.2, 17.3, 17.4)
Exercises 1, 2, 6, 10, 16, 17, 18, 19, 24, 25, 28, 30, 31, 32, 36, 38, 39, 40

Chapter 9 (Week 6, Sections 9.1, 9.2, 9.3, 9.4)
9, 10, 11, 17 a b c

Chapter 10 (Week 7, Sections 10.1, 10.2, 10.3, 10.5)
7, 9, 12, 16, 17

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To Prepare for Exam 3

Chapter 12 (Week 8, Sections 12.1, 12.3)
SKILLS CHECK 1, 3

Chapter 13 (Weeks 9 & 10, Sections 13.1, 13.2, 13.5, 13.6)
SKILLS CHECK 10, 14, 17, 19, 21
EXERCISES 2, 3, 10, 11, 13, 26

Chapter 15 (Week 11, Sections 15.2, 15.3)
SKILLS CHECK 20, 21, 22

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To Prepare for the Final [Review]

Review Material for Exams 1-3

Chapter 20 (Weeks 12, 13, 15, & 16, Sections 20.1, 20.3, 20.5)
EXCERCISES 1, 2, 15, 17, 18, 19, 23, 24, 25, 26, 27, 36

#### Class Log

Week 1 (Graph Theory, Chapter 1)
Monday, August 22 (Intro to Graphs, Section 1.1) [Worksheet]
Wednesday, August 24 (Euler Circuits, Sections 1.2, 1.3) [Worksheet]
Friday, August 26 (Activity: Magic Trick Using Euler Circuits) [Worksheet]

Week 2 (Graph Theory, Chapter 2)
Monday, August 29 (Hamiltonian Circuits, Sections 2.1, 2.2) [Worksheet]
Wednesday, August 31 (Minimum Cost Spanning Trees, Sections 2.3, 2.4) [Worksheet]
Friday, September 2 (Activity: Traveling Sales Person and Pokémon Go) [Worksheet]

Week 3 (Graph Theory, Chapter 3)
Monday, September 5 No Class (Labor Day)
Wednesday, September 7 (Scheduling and Coloring, Section 3.5) [Worksheet]
Friday, September 9 (Activity: Four Color Theorem) [Worksheet]

Week 4 (Coding Theory, Chapter 17)
Monday, September 12 (Binary Codes, Section 17.1) [Worksheet]
Wednesday, September 14 (Parity-Check Sums, Section 17.2) [Worksheet]
Friday, September 16 Exam 1

Week 5 (Coding Theory, Chapter 17)
Monday, September 19 (Data Compression, Section 17.3) [Worksheet]
Wednesday, September 21 (Cryptography, Section 17.4) [Worksheet]
Friday, September 23 (Activity: Ciphers) [Worksheet]

Week 6 (Coding/Voting Theory, Chapter 17/Chapter 9)
Monday, September 26 (Cryptography Continued, Section 17.4) [Worksheet] [Vigenère Square]
Wednesday, September 28 (Intro to Voting Theory, Sections 9.1-9.4) [Worksheet]
Friday, September 30 (Activity: Non-transitive Dice) [Worksheet]

Week 7 (Voting Theory, Chapter 10/Chapter 11)
Monday, October 3 (Manipulating Voting Systems, 10.1-10.3) [Worksheet]
Wednesday, October 5 (The Chair's Paradox, 10.5, 11.1) [Worksheet][C-Span]
Friday, October 7 (Activity: Caucusing) [Worksheet] Project Proposals Due

Week 8 (Voting Theory, Chapter 12)
Monday, October 10 (Electing the President, 12.1) [Worksheet]
Wednesday, October 12 (Electing the President, 12.3) [Worksheet][C-Span]
Friday, October 14 Exam 2 (Drop Day)

Week 9 (Game Theory, Chapter 13)
Monday, October 17 (Adjusted Winner Procedure, 13.1) [Worksheet]
Wednesday, October 19 (Fair Division, 13.2) [Worksheet]
Friday, October 21 (Activity: Monty Hall Problem) [Worksheet]

Week 10 (Game Theory, Chapter 13)
Monday, October 24 (Divide and Choose, 13.2, 13.5) [Worksheet]
Wednesday, October 26 (Cake Division, 13.6) [Worksheet]
Friday, October 28 (Activity: Cake and Fair Division) [Worksheet]

Week 11 (Game Theory, Chapter 15)
Monday, October 31 (Total-Conflict Games, 15.2) [Worksheet]
Wednesday, November 2 (Partial-Conflict Games, 15.3) [Worksheet]
Friday, November 4 (Activity: Prisoners' Dilemma and Newcomb's Paradox) [Worksheet]

Week 12 (Geometry, Chapter 20)
Monday, November 7 (Regular Tilings, 20.1) [Worksheet]
Wednesday, November 9 (Penrose Tilings, 20.5) [Worksheet]
Friday, November 11 Exam 3

Week 13 (Geometry, Chapter 20)
Monday, November 14 (Guest Lecturer: Melinda Lanius)
Wednesday, November 16 (Escher Tilings, 20.3) [Worksheet]
Friday, November 18 (Activity: Tilings) [Worksheet]

Week 14
Monday, November 21 No Class (Thanksgiving Break)
Wednesday, November 23 No Class (Thanksgiving Break)
Friday, November 25 No Class (Thanksgiving Break)

Week 15 (Geometry)
Monday, November 28 (Tetris and Pentominos, 20.3) [Worksheet]
Wednesday, November 30 (Activity: Symmetry and Snow) [Worksheet][Slides]
Friday, December 2 (Activity: Platonic Solids) [Worksheet]

Week 16 (Geometry)
Monday, December 5 (Activity: Archimedean Solids) [Worksheet]
Wednesday, December 7 Review [Review]
Friday, December 9 No Class (Finals)

Tuesday, December 13 Final Exam 8:00am-11:00am in our classroom

#### Quizzes

Quiz 1, Friday, August 26 [Quiz]
Quiz 2, Friday, September 2 [Quiz]
Quiz 3, Friday, September 9 [Quiz]
Quiz 4, Friday, September 23 [Quiz]
Quiz 5, Friday, September 30 [Quiz]
Quiz 6, Friday, October 7 [Quiz]
Quiz 7, Friday, October 21 [Quiz]
Quiz 8, Friday, October 28 [Quiz]
Quiz 9, Friday, November 4 [Quiz]
Quiz 10, Friday, November 18 [Quiz]
Quiz 11, Friday, December 2 [Quiz]

#### Project

Students will complete a project analyzing a topic of interest to them (and of some relation to mathematics).
Project proposal, due Friday, October 7. [Form]
Final project, due Wednesday, November 30. [Project Guidelines]

#### Exams

Exams are given during class, in the usual classroom, so no conflict exams will be given. Please refer to the syllabus for the policy on missed exams or quizzes.

Exam 1, Friday, September 16 [Exam]
Exam 2, Friday, October 14 [Exam]
Exam 3, Friday, November 11 [Exam]
Final Exam, Tuesday, December 13 8:00am-11:00am in our classroom (Altgeld 343) [Review]

Extra Help
Need help? If you can't attend the office hours above, there are other options here.
OMSA (Office of Minority Students) offers free tutoring services on campus. For their schedule refer to OMSA.