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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.