syllabus (Word)

I may choose from the above at random, but I will double the probability that 2.1, 2.2, 3.4, 3.6, 3.17, 5.6 are chosen.

Project info (preliminary version)

22M:151:002 Discrete Mathematical Models 3 s.h. Time & Location: 1:30P - 2:20P MWF 105 MLH Case history approach to discrete models from various fields (e.g., genetics, psychology, health care, scheduling); construction, interpretation, analysis, simulation, testing of models; development of discrete mathematics. This course provides an introduction to discrete mathematics. A case history approach is taken to discrete models from various fields (e.g., genetics, psychology, health care, scheduling). Construction, interpretation, analysis, simulation, testing of models, and development of discrete mathematics are covered. Grading is based on homework and exams. The course is taught by a faculty member. Prerequisites: 22M:027 Introduction to Linear Algebra or equivalent

HW #1 (due 1/30): p. 18 #4, determine the number of digraphs with n vertices.

HW #2 (due 2/6): 2.1: 1, 2, 4, 9, 11; 2.2: 1 - 7, 12, 14, 17, scheduling handout

HW #3 (due 2/13): 2.2: 21, Fragment Assembly of DNA handout, Eulerian handout and

1.) If G is a digraph, determine necessary and sufficient conditions for an Eulerian closed chain to
exist. Are the necessary conditions the same as the sufficient conditions?

2.) If G is a digraph, determine necessary and sufficient conditions for an Eulerian chain to
exist. Are the necessary conditions the same as the sufficient conditions?

HW#4 (due 2/20): 1.) Give a rough estimate of the computational complexity of the traveling
salesperson
problem

and 2.3: 1, 2, 3, 4, 6, 10, 11, 18

HW#5 (due 2/27): 2.4: 1, 2, 3, 4, 5, 7, 8, 12.

HW#6 (due 3/5): 2.4: 13, 14, 15. Define NP complete. List the types of graph theory problems we have covered to far. Briefly describe the type of problem. Note that TSP and Fragment Assembly of DNA basically belong to the same type of problem. Thus you would not want to list both problems, but instead would list

1.) Hamiltonian path problem. Description: Finding a path or chain which visits each vertex exactly once. In some applications, a closed path or chain is desired. In many applications, one looks for the path with maximum (or minumum) edge weights.

HW#7 (due 3/12) 3.1: 1, 2, 3, 4, 10, 14, 15; 3.2: 1, 2, 3, 4, 5, 6, 8, 9

HW#8 (due 3/26) 3.2: 11, 14, 19; 3.3: 1, 3, 5, 6, 8, 10, 11, 12; 3.4: 1, 7, 8, 9abcd, 11a

HW#9 (due 4/2) 3.6: 1-5, 7, 8, 10, 11, 13-21

HW#10 (due 4/9) Handout p. 119: 1abc, 2abc, 3, 5abd, 15; and 5.1: 2, 4; 5.2: 1, 2, 4, 9, 12, 15

HW#11 (due 4/16) 5.3 # 1b, 2b, 4ab

HW#12 (due 4/23) 5.4: 1, 2, 4, 5, 6, 8, 10; and 5.5: 1, 2, 4-8, 12, 14

HW#13 (due 4/30) 5.6: 1ab, 2ab, 3, 5, 6; and

HW#14 (due 5/7) 5.7: 5, 7c, give an indepth analysis of #7, 10

Project due dates:

Topic Due: March 31

Project Outline with References: April 7

Written Report: April 28

Proesentations: May 3-7

References

(1.) Applied Combinatorics by Fred Roberts, Prentice Hall; (February 28, 1984) ISBN: 0130393134

(2.) Introduction to Computational Molecular Biology by Joao Carlos Setubal, Joao Meidanis, Jooao Carlos Setubal, Brooks Cole; (January 16, 1997) ISBN: 0534952623

TENTATIVE CLASS SCHEDULE-ALL DATES SUBJECT TO CHANGE (click on date/section
for pdf file of corresponding class material):

Monday | Wednesday | Friday | |

Week 1 | 1/21: ch 1 | 1/23: counting rules | |

Week 2 | 1/26: 2.1 | 1/28: Ch 2(ps) | 1/30: p. 5 - 8 in (1) |

Week 3 | 2/2: p. 37 in (2), For fun Bacterial ID | 2/4: Fragment Assembly of DNA (Ch 4 in (2)) | 2/6: Eulerian chain |

Week 4 | 2/9: Eulerian chain | 2/11: | 2/13: |

Week 5 | 2/16: | 2/18: 2.3, 4 2.3, 4 | 2/20: |

Week 6 | 2/23: Midterm 1 | 2/25: 2.4, p. 38 - 41 in (2), p. in (1) | 2/27: tress |

Week 7 | 3/1: 3.1 | 3/3: | 3/5: 3.2 |

Week 8 | 3/8: | 3/10: 3.3 | 3/12: 3.4 |

Spring Break | |||

Week 9 | 3/22: 3.4 | 3/24: 3.6 | 3/26: 3.6 |

Week 10 | 3/29: chromatic polynomial, p. 111 - 121 in (1) | 3/31: | 4/2: 5.1 |

Week 11 | 4/5: 5.2 | 4/7: 5.3 | 4/9: review (tif) mht |

Week 12 | 4/12: Midterm 2 | 4/14: 5.4 | 4/16: 5.4, 5.5 |

Week 13 | 4/19: 5.5 | 4/21: 5.6 | 4/23: |

Week 14 | 4/26: | 4/28: | 4/30: |

Week 15 | 5/3: | 5/5: | 5/7: |