Jeffrey S. Case
Assistant Professor
The Pennsylvania State University, Department of Mathematics

Contents: Spring 2016
Math 311W: Concepts of Discrete Mathematics
MWF 1:25--2:15pm, 117 Sackett Building

Office: 221 McAllister Building
Office Hours: MW 3-4pm, or by appointment.
Office Hours for week of Jan. 18--22: TW 3-4pm, or by appointment (no class on Monday, January 18)
Office Hours for week of Feb. 22--26: W 3-4pm and Th 10:30-11:30am, or by appointment
Office Hours for week of May 2--6: M 10:30am--noon, or by appointment

Syllabus
For further information, please visit ANGEL.

Final Exam: Monday, May 2, 2016 from 6:50pm to 8:40pm in 111 CHAM

Homework Assignments (Do all problems; problems marked with an asterisk are eligible for extra credit presentations)

  1. (Due 1/20):
    Section 2.1: 1, 3, 4*, 7*, 8
    Section 2.2: 2, 6*, 8*, 10
    Solutions.
  2. (Due 1/27):
    Section 2.2: 5, 7
    Section 2.3: 1, 2*, 3*
    Extra Problem #1*: Suppose that A and B are finite sets. Show that |A × B| = |A| · |B|. (Note: You should do this by constructing a bijection between appropriate sets.)
    Extra Problem #2*: Prove that |A × B| = |B × A| for all sets A and B. (Caution: A and B are not assumed to be finite sets.)
    Solutions.
  3. (Due 2/3):
    Section 2.3: 7, 8*, 9
    Section 3.1: 3*, 4, 5*
    Extra Problem #1*: Suppose R is an equivalence relation and a partial ordering on a set A. Show that R is the identity relation IA on A; that is, R = {(x,x) : x ∈ A}.
    Extra Problem #2: Suppose that (A, ≤) is a partially ordered set and B ⊆ A. Define the relation B on B by B = ≤ ∩ (B × B). Show that (B, ≤B) is a partially ordered set.
    Solutions.
  4. (Due 2/10):
    See PDF.
    Solutions.
  5. (Due 2/17):
    Section 1.1: 2, 3*, 6*, 7
    Section 1.2: 1*, 2, 6*
    Solutions.
  6. (Due 3/2):
    Section 1.2: 3, 8*, 12
    Section 1.3: 5*, 6*, 8
    Section 1.4: 2, 7*
    Solutions.
  7. (Due 3/16):
    Section 1.4: 3, 5*, 6*
    Section 1.5: 1, 2, 3*, 5*
    Solutions.
  8. (Due 3/23):
    Section 1.6: 1, 2, 3*, 5, 7*, 8*, 10*
    Solutions.
  9. (Due 4/6):
    Section 4.1: 1, 4*, 5*, 6
    Section 4.3: 1*, 4*
    Solutions.
  10. (Due 4/13):
    Section 4.2: 1, 2*, 3*, 4*, 9, 12
    Section 4.3: 3*, 8
    Solutions.
  11. (Due 4/20):
    Section 5.1: 1*, 3, 4, 7*, 8*, 9*
    Section 5.2: 1, 3
    Solutions.
  12. (Due 4/27):
    Section 5.2: 2*, 5
    Section 5.3: 4, 5*, 7, 8, 9*
    Solutions.


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