# Math 181: A Mathematical World (X1)

### Bert Guillou

**email:**bertg ♠ illinois ♦ edu

**Phone:**(217) 244-0286

**Office:**330 Illini Hall

**Office Hours:**Wednesday, 4-5PM.

Course Info

The initial plan is to cover chapters 1, 2, 9, 13, and 14 of the text.

Math 181 is an 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.

**Links:**

- Leonhard Euler
- The Seven Bridges of Königsberg
- Looking to make a quick million? Just solve one of the Clay Math Millenium Prizes
- Sir William Rowan Hamilton
- An article from the American Math Society on Bin Packing
- The Four Color Theorem (and here and here).
- Apportionment in America
- What is Game Theory? (An economist's perspective)
- Game Theory in
*The Dark Knight* - Illinois Driver's License Numbers

**Review materials for the Final Exam:**

- Review sheet 1
- Review sheet 2
- Review sheet 3
- Chapter 9 review sheet
- Rules for fractions: here and here.

### Schedule

Assignment | Date |
---|---|

Homework 1: Ch. 1: 14, 18, 21, 22
| Due Wed. Jan. 28 |

Quiz 1: Ch. 1 | Jan. 30, in class |

Homework 2: Ch. 1: 26, 28, 32, 34, 36, Ch. 2: 2(a), (b), (d)
| Due Wed. Feb. 4 |

Quiz 2: Ch. 2 | Feb. 6, in class |

Homework 3: Ch. 2: 44, 68, 70,
Ch. 3: 4, 16(a)-(c), 18(a),(b), 44
| Due Fri. Feb. 13 |

Quiz 3: Ch. 3 | Feb. 13, in class |

Exam 1 (Review sheet) | Feb. 20, in class |

Quiz 4: Ch. 8 | Feb. 27, in class |

Homework 4: Ch. 8: 10, 12; Handout: 2, 9, 16
| Due Fri. Feb. 27 |

Quiz 5: Ch. 8 (Conditional Probability, Bayes' Rule) | Mar. 6, in class |

Homework 5: Handout: 41, 43, 44, 46, 47
| Due Fri. Mar. 6 |

Quiz 6: Ch. 13 | Mar. 13, in class |

Homework 6: Ch. 13: 2, 4, 8, 12
| Due Fri. Mar. 13 |

Exam 2 (Review sheet) | Mar. 20, in class |

Quiz 6: Ch. 14 (Hamilton and Jefferson's Methods) | Apr. 3, in class |

Homework 7: Ch. 14: 2, 6(a,b), 10(a,b)
| Due Fri. Apr. 3 |

Quiz 7: Ch. 14 (Webster and Hill-Huntington Methods) | Apr. 10, in class |

Homework 8: Ch. 14: 12, 20, 28
| Due Fri. Apr. 10 |

Quiz 8: Ch. 15 (2 person games) | Apr. 17, in class |

Homework 9: Ch. 15: 2, 6, 8, 10
| Due Fri. Apr. 17 |

Exam 3 (Review sheet) | Apr. 24, in class |

Quiz 9: Ch. 9 | May 1, in class |

Homework 10: Ch. 9: 8, 12. Also, in these problems determine if there is a Condorcet winner.
| Due Fri. Apr. 17 |

FINAL EXAM!! | May 13, 7:00-10:00 PM |

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 |