CSCI/MATH 2427
Discrete Mathematical Structures
Spring 2013

Last modified 4/29/13

Announcements

In class we discussed an algorithm to find the connected components of a graph. A student asked me to write that algorithm as a program the way I would write it. Here it is.

See here for tutoring availability in Austin 209.

Yuan He is a graduate student who can tutor students in this course. If you feel it will help, please contact him at hey12@students.ecu.edu to arrange a time for tutoring.


Syllabus

This is a course in discrete mathematics suitable for the study of computer science. See the syllabus for details.


Office hours

MW 2:00–3:00 and TTh 1:30–2:30 or by appointment.


Notes

Notes on proofs


Homework exercises

  1. (Due Wed. Jan. 23) Rosen, p. 13–14, questions 14(a–f), 16(a–d), 18(a–d).

  2. (Due Mon. Jan. 28) Rosen, p. 34-35, questions 4(a,b), 10(a,b), 12(a,b), 18 (but do it by a sequence of equivalence-preserving steps), and the following.

  3. (Due Fri. Feb. 1) Rosen, pages 53..., exercises 10, 12, 13 and 16, and pages 65... exercises 12, 26, all parts of each.

  4. (Due Mon. Feb. 18) Rosen, page 91, exercises 2, 4, 10, 14, 22, page 108 exercises 14, 16, 22.

  5. (Due Mon. Feb. 25) Rosen, page 108 exercises 30, 34 and page 125 exercises 5, 6, 10, 19, 20.

  6. (Due Mon. Mar. 4) Rosen, page 126, exercise 26, 27 and page 136 exercises 4, 12, 16(a,b). For exercises 12 and 16, use propositional reasoning, not Venn diagrams. To show that two sets are equal, prove that their membership requirements are equivalent. To show that A is a subset of B, show that the membership requirement for A implies the membership requirement for B.

  7. (Due Mon. March 25) Rosen, page 329, exercise 4, 7. (For problem 4, just do a proof by induction using the style that we have used in class. Do not break it down into steps (a-f). For problem 7, do not use induction. Just use algebra and summation formulas.) Also:

    1. Find closed form for the sum for k ε {1,...,n} of (4k−2), for n a positive integer.
    2. Find closed form for the sum for k ε {0,...,n} of (4k−2), for n a nonnegative integer.

  8. (Due Monday, April 1) Rosen, pages 330, 331 exercises 14, 54; page 396 exercises 4, 10, 14, 18, 36; page 413, 414 exercised 4, 26.

  9. (Due Monday, April 22) Rosen, page 665, 666 exercises 4, 6, 18, 34.


Articles

Students think they can multitask. Here's proof they can't.