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Exercises

Exercises for Teaching Discrete Mathematics

Welcome to the SIGCSE Committee on the Implementation of a Discrete Mathematics Course's collection of representative exercises. The Committee's task was to develop and disseminate models for a one-semester course for Computing Curriculum 2001's Discrete Structures area. Part of this effort included identifying exercises and examples that instructors can use in such courses.

The Committee has identified the following set of exercises from the 5th edition of Kenneth Rosen's text Discrete Mathematics and Its Applications. These problems were chosen because they can be characterized as moderate to hard. Some of them are challenging enough to be assigned as group projects or take-home questions. Exercises similar to these can be found in any of the textbooks cited in the three models in the Committee's main report. (Rosen's text was chosen because it is the one most familiar to one of the co-facilitators, Bill Marion, who has used various editions over time.)

The Committee is seeking copyright clearance to post the full text of the exercises here. In the mean time, we list exercise numbers and page numbers. Note that page numbers indicate the first page in each set of exercises. Exercises are organized according to the Computing Curriculum 2001 units within discrete structures, namely...

  • DS1. Functions, Relations, and Sets
  • DS2. Basic Logic
  • DS3. Proof Techniques
  • DS4. Basics of Counting
  • DS5. Graphs and Trees
  • DS6. Discrete Probability

DS1. Functions, Relations, and Sets

  • Page 85, Exercise 30
  • Page 94, Exercise 29
  • Page 108, Exercises 12, 13, 17, 27, 45, 69
  • Page 479, Exercises 6, 8, 13, 20
  • Page 513, Exercises 3, 7, 8, 31, 46

DS2. Basic Logic

  • Page 16, Exercises 8, 15, 30, 42, 48, 59
  • Page 26, Exercises 8, 10, 29, 51
  • Page 40, Exercises 8, 10, 22, 41, 42, 48, 55
  • Page 51, Exercises 5, 8, 13, 18, 21, 28, 37, 44

DS3. Proof Techniques

  • Page 74, Exercises 10, 20, 35, 46, 58
  • Page 223, Exercises 11, 13, 19, 27, 32, 38, 44, 49, 51
  • Page 253, Exercises 11, 25, 34, 50, 60
  • Page 270, Exercises 14, 26, 33, 38, 43, 44, 47, 58
  • Page 283, Exercises 16, 18, 28

DS4. Basics of Counting

  • Page 310, Exercises 33, 37, 41, 51, 52
  • Page 319, Exercises 10, 16, 17, 20, 36
  • Page 324, Exercises 23, 35, 37
  • Page 409, Exercises 8, 17, 22, 23, 37, 42
  • Page 422, Exercises 7, 13, 14, 17, 26, 31, 45, 53
  • Page 433, Exercises 10, 11, 14, 15, 16

DS5. Graphs and Trees

  • Page 543, Exercises 20, 22
  • Page 554, Exercises 18, 25, 31, 35
  • Page 563, Exercises 28, 32, 33
  • Page 575, Exercises 15, 21
  • Page 588, Exercises 26, 28, 44, 45, 49
  • Page 601, Exercises 16, 18
  • Page 641, Exercises 11, 16, 24, 25
  • Page 656, Exercises 9, 14
  • Page 672, Exercises 18, 22, 26, 28
  • Page 685, Exercises 11, 17, 18, 21, 30, 41, 43
  • Page 693, Exercises 9, 18

DS6. Discrete Probability

  • Page 360, Exercises 15, 28
  • Page 376, Exercises 16, 22, 25, 26, 29, 30
  • Page 392, Exercises 7, 12, 32
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