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) (Due 1/20): Section 2.1: 1, 3, 4*, 7*, 8 Section 2.2: 2, 6*, 8*, 10 Solutions. (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. (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. (Due 2/10): See PDF. Solutions. (Due 2/17): Section 1.1: 2, 3*, 6*, 7 Section 1.2: 1*, 2, 6* Solutions. (Due 3/2): Section 1.2: 3, 8*, 12 Section 1.3: 5*, 6*, 8 Section 1.4: 2, 7* Solutions. (Due 3/16): Section 1.4: 3, 5*, 6* Section 1.5: 1, 2, 3*, 5* Solutions. (Due 3/23): Section 1.6: 1, 2, 3*, 5, 7*, 8*, 10* Solutions. (Due 4/6): Section 4.1: 1, 4*, 5*, 6 Section 4.3: 1*, 4* Solutions. (Due 4/13): Section 4.2: 1, 2*, 3*, 4*, 9, 12 Section 4.3: 3*, 8 Solutions. (Due 4/20): Section 5.1: 1*, 3, 4, 7*, 8*, 9* Section 5.2: 1, 3 Solutions. (Due 4/27): Section 5.2: 2*, 5 Section 5.3: 4, 5*, 7, 8, 9* Solutions. Previous Courses: Previous Courses at Princeton University: