# Discrete Mathematics

Providing the theoretical foundation for non-continuous mathematics and computer science, with applications to puzzles, patterns, games, and magic tricks

This is a curious mathematics course in that it has a theoretical flavor, meaning that abstract thinking is central to the course, and yet it is an application-oriented mathematics course, meaning that we will develop mathematical tools as needed to solve specific problems. The moral of this story is that it is often the abstract nature of mathematics that allows it to correctly model and solve real-world problems. One catch with this particular book is that often the first applications we will see are mathematical puzzles and games. After studying the mathematical ideas behind these "recreationalâ€ť problems, we will then apply them to more practical applications, many of which come from the field of computer science. The course covers typical topics from discrete mathematics including logic and proof, sets and functions, combinatorics and probability, and graph theory.

## Problems

Try the assigned problems from each section as it is covered, use any related online resources to relevant problems, and ask questions in class and during office hours. Keep solutions in a bound (spiral or theme-style) notebook, and you may use this resource while taking the weekly quizzes. Working on problems outside of class is the primary mechanism by which you will learn the course material.
• Section 1.2. Problems 1, 2, 4 - 8, 12, 13, 21, 22, 24. Online problems are similar to 1, 2, 4, 5, 6, 12, 21, 24
• Section 1.3. Problems 1, 3 - 9, 11 - 15, 17, 18, 21. Online problems are similar to 6 - 9, 11, 13
• Section 1.4. Problems 1, 3 - 6, 8 - 11, 14 - 16. Online problems are similar to 3, 4, 6
• Section 1.5. Problems 1, 3 - 5, 7, 10 - 14, 16, 17, 19, 21, 23, 25 - 28, 30. Online problems are similar to 4, 5, 6, 10, 11, 23, 25-27
• Section 2.1. Problems 1-3, 4(a-d), 5, 6, 8, 9, 12, 13, 14(a,c). Online problems are similar to 4, 6, 8, 12, 13
• Section 2.2. Problems 1-6, 7(a-c), 13, 14, 29. Online problems are similar to 1-6
• Section 2.3. Problems 1, 2, 3(a-e), 4(a-c), 5, 6, 8(a-d), 10. Online problems are similar to 3 and 8.
• Section 2.5. Problems 1, 2, 3, 4, 5, 7, 22, 23, 24, 32. Online problems are similar to 1, 4, 7, 22, 23, 32
• Section 2.6. Problems 1, 2, 3, 4, 5, 9, 11, 13, 14, 15, 16, 21. Online problems are similar to 1-5, 14, -16
• Section 3.1. Problems 1-3, 5-7, 9-11, 15(a-d), 16(a-d), 17(b-e), 18, 26, 28, 29. Online problems are similar to
• Section 3.2. Problems 1-6, 12-17. Online problems are similar to
• Section 3.3. Problems 4, 5, 12, 14, 15, 16, 18, 19. Online problems are similar to
• Section 5.1. Problem 1-10, 12-14, 18, 20. Online problems are similar to
• Section 5.2. Problems 1-3, 6, 7, 9, 11, 12, 14, 15, 20, 21, 24-27, 29, 30, 36-39. Online problems are similar to
• Section 5.3. Problems 1, 3, 6, 9-15, 18, 20, 21, 23, 25, 29, 31-33. Online problems are similar to
• Section 5.4. Problems 1-5, 10, 12, 15-22. Online problems are similar to
• Section 5.6. Problems 1-4, 6-10. Online problems are similar to
• Section 6.1. Problems 1-9, 13-16, 18, 19.
• Section 6.2.* Problems 1-8, 13, 15-17, 24-26.
• Section 6.3.* Problems 1-10, 15, 18.
• Section 4.1. Problems 1-5, 8-11, 14, 15, 17, 18, 21, 22, 25-28.
• Section 4.2. Problems 3-7, 10, 14-17, 19
• Section 4.3. Problems 1-6, 11, 14, 15, 17
• Section 4.6. Problems 1, 2, 4-8, 12-15, 18-21
• Section 7.1. Problems 1-4, 6-11, 13-16
• Section 7.3. Problems 1-5
• Section 7.4. Problems 1-7, 15

## Contact Doug Ensley

Douglas Ensley, Ph.D.
Professor of Mathematics
Shippensburg University
Shippensburg, PA 17257
Phone: 717.477.1406

deensley@ship.edu