practice.html

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.

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

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

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.