Math 375
Discrete Mathematics

Instructor

Ernest Boyd, Wissink 273, 389-1452
Office Hours:

Textbook

Discrete Mathematics, Sixth Edition, by Richard Johnsonbaugh

Course Content

Discrete mathematics is more a way of thinking and organizing one's ideas, rather than a complete theory. Consequently, we will be approaching the subject as a set of individual problems to explore somewhat like little puzzles to be solved. We will concentrate on problems from combinatorics and graph theory in chapters four through ten. We will briefly review logic notation and set notation in chapters one and two, which we will use throughout the course.

Schedule

12:00 - 12:50 pm, MTRF, Wissink 288A
No classes on Sep. 4, Oct. 27, and Nov. 23-24

Tests

Thursday, Sep. 28, Thursday, Oct. 26, and Tuesday, Nov. 28.

Final exam

Tuesday, Dec. 12, 10:15 am - 12:15 pm.

Grading Policy

Each test will be graded on its own scale normalized to 100%. The final will also be graded on a scale normalized to 100%. All of the homework and quizzes collected will be totaled and graded as one test. At the end of the semester the five grades will be averaged and compared to the average of the scales. Grading will reflect the mathematical correctness of the answer and the quality of the presentation in terms of completeness and organization. Active participation in the class discussions will also be factored into the evaluations. Make-up tests will be given only in special cases, when an excused absence has been prearranged. Incompletes will follow the university's policy as expressed in the student bulletins and the faculty handbook. No incomplete will be given to repeat the entire course.

MSU provides students with disabilities reasonable accommodation to participate in educational programs, activities or services. Students with disabilities requiring accommodation to participate in class activities or meet course requirements should first register with the Office of Disability Services, located in 0132 Memorial Library, telephone 389-2825, TDD 711 and then contact me as soon as possible.



Homework Assignments

  1. Review pages 76-79 and pages 53-60.
  2. Page 168 #5, 7, 11, 18-23, 25, 32,34, 44-50. Hand in #23, 47, 50 on Friday, Sep. 8.
  3. Read Section 5.1.
  4. Page 213 #8, 16, 17, 21, 38.
  5. Page 179 #27. Hand in this problem on Tuesday, Sep. 19.
  6. Page 217 #12-16.
  7. Review
  8. Page 226 #20, 23-26, 34-41, 48, 55, 57, 59, 60, 62, 67.
  9. Page 237 #7, 11, 14, 20, 32, 33, 58-60, 65, 70. Hand in #20, 33, 65 on Friday, Oct. 6.
  10. Page 265 #15, 17, 20, 22, 26, 33, 35, 36, 40. Hand in #17, 26, 40 on Tuesday, Oct. 10.
  11. Hand in the following two problems on Monday, Oct. 16.
    1. We have seven distinct boxes containing identical balls. From the first box you can pick at most three balls, but there is no limit on the other boxes. How many ways can we pick ten balls?
    2. We have fifty identical jobs to distribute to three distinct processors. How many ways can we do it if each processor must get at least ten jobs, but no more than twenty jobs?
  12. Page 273 #5, 11-15. Hand in #5 on Friday, Oct. 20.
  13. Page 287 #9-12, 18-20, 31-32.
  14. Page 300 #17, 22, 35, 43. Also solve an = 6an-1 - 13an-2 with a0 = 1 and a1 = 3.
  15. Review
  16. For what values of C will an = an-1 - Can-2 have an tend to zero as n increases for all choices of initial values on a0 and a1? Hand in this problem along with #5 on the Review sheet on Friday, Nov. 3.
  17. Page 327 #11, 14, 15, 17, 18, 24, 25, 46 - 49.
  18. Page 337 #10, 13, 16, 19, 22, 23, 29, 30, 35, 36, 72, 75, 76. Hand in #35, 36, 72 on Tuesday, Nov. 14.
  19. Page 346 #9, 10, 11, 14, 15. Hand in these problems on Friday, Nov. 17.
  20. Page 351 #10.
  21. Page 355 #5, 6, 11, 12, 14, 21, 22, 25, 26.
  22. Page 361 #3, 22, 23.
  23. Page 386 #30, 32.
  24. Page 390 #22-25.
  25. Page 397 #1, 4.
  26. Page 402 #2, 20-22.
  27. Review
  28. Read pages 444-460 for the Max Flow Min Cut Theorem.
  29. Review


Mathematica Supplements

  1. Truth Table
  2. Euclidean Algorithm
  3. RSA Encryption
  4. ISBN Check Digit
  5. Fibonacci Sequence
  6. Combinatorics
  7. Generating Function
  8. Function Iteration
  9. Nonlinear Finite Difference Equation
  10. Linear Second Order Finite Difference Equation
  11. Weighted Graph for Example of Dijkstra's Algorithm, Prim's Algorithm and Kruskal's Algorithm
  12. Colored Digraph for Minty Cycle or Cocycle in Out-of-Kilter Algorithm
  13. Weighted Digraph for Example of Max Flow Min Cut Theorem


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