**
Mathematics 6
Spring 2001
Syllabus**

* Date
Topics
Homework*

3-28 | 5.1, 5.2 Sets and counting | 5.1: 2, 14, 16, 42, 44, 46, 48; 5.2: 2, 4, 10, 12 |

3-30 | 5.2, 5.3 Venn diagrams, counting | 5.2: 16, 30, 48; 5.3: 4, 16, 18, 20, 34, 36, 38 |

4-2 | 5.4, 5.5 Permutations, combinations | 5.4: 3, 4, 8, 18, 24, 40, 54, 56, 57; 5.5: 3, 8, 19, 24, 33 |

4-4 | 5.5, 5.6 More permutations, combinations | 5.5: 28, 29, 30, 44, 47, 48, 61, 66; 5.6: 1, 2, 4 |

4-6 | 5.6, 5.7 Finish counting, start probability theory | 5.6: 9, 10, 11, 13, 28; 5.7: 27, 29, 30, 32, 37, 38 |

4-9 | 6.1-6.3 Assigning probabilities | 6.2: 2, 6(b)(c), 10(a)(i)-(iv), 14; 6.3: 2, 3, 8, 10, 18; 6.4: 1 |

4-11 | 6.4 Calculating probabilities | 6.4: 4, 5, 8, 20, 25, 27, 28, 33, 38;
Optional problem: What is the probability
that, given a group of r people, exactly two of them have the same birthday? |

4-13 | 6.5 Conditional probability | 6.5: 1, 5, 6, 8, 12, 15, 16, 21, 40 |

4-16 | 6.6 Tree diagrams | 6.6: 4, 6, 7, 9, 16, 18, 19, 22; 6.7: 3, 14 |

4-18 | 6.7 Bayes' theorem, review | 6.7: 4, 11, 12, 13; Supplementary exercises, p. 314: 1, 2, 3, 4, 5 |

4-20 | review, 2.1 Systems of linear equations | Supplementary exercises, p.314: 6, 11, 12, 13, 18, 31; 2.1: 18, 20 |

The test on Wednesday the 25th in Bradley 101 at 7:00 covers up to here.

4-23 | 2.1, .2.2 More linear equations | 2.1: 23; 2.2: 9, 10, 13, 14, 15, 26 |

4-25 | 2.3 Algebra with matrices | 2.3: 10, 12, 22, 26, 28, 30, 38, 39, 41, 46 |

4-27 | 2.4, 2.5, 2.6 Inverses of matrices | 2.4: 2, 4, 8, 20, 26; 2.5: 4, 5, 7, 8, 9, 18 |

4-30 | 2.6 Input-output analysis, expected values | 2.6: 2, 7, 8, 10; 7.4: 9, 13 |

5-2 | 8.1 Markov processes | 8.1: 2, 4, 10(a)(b)(c), 12, 14, 15(a). Also, draw the transition diagrams in 10 and 12. |

5-4 | 8.2 Regular stochastic matrices | 8.2: 2, 6, 8, 12, 15, 18 |

5-7 | 8.3 Absorbing Markov chains | 8.3: 2, 4, 8, 10, 14, 15 |

5-9 | 9.1 Strictly determined games | 9.1: 2, 4, 6, 8, 10, 12.
8.3: 16. Also do: 16(c) For how many years can a person who
is just starting as a first-line
manager expect to be a top manager? |

5-11 | 9.2 Mixed strategies | 9.2: 2, 5, 6. p. 422, 12 |

The test on Wednesday the 16th in Bradley 101 at 7:00 covers the previous three weeks.

5-14 | 9.3 Optimal mixed strategies | 9.3: 1, 2, 4, 8, 10, 11 |

5-16 | 13.1 Graphs | 13.1: 2, 6 (Either draw the graph or explain why there is none.) 10, 18, 20, 24, 26 |

5-18 | 13.2 Paths and circuits | 13.2: 2, 6, 8, 9, 12, 14, 18 |

5-21 | 13.6 Trees and Euler characteristic | 13.6: 4 (Also, what is the Euler characteristic of each of the three graphs?), 10, 12, and these problems |

5-23 | Planar graphs, tournaments | these problems |

5-25 | Tournaments, cyclic triples (guest lecturer) | these problems due Monday, the 28th, by noon. |

5-30 | Review | no homework |

The final exam on Friday, the 1st, from 9:00 to 11:00
covers the entire course, but will emphasize material covered since the
scond exam.

The final is in Cook Auditorium.