MATH:4060: Discrete Mathematical Models

MATH:4060:0001 Discrete Mathematical Models

Spring 2019 11:30A - 12:20P MWF 205 MLH

Instructor:  Dr. Isabel K. Darcy,    Department of Mathematics, AMCS, and Informatics,    University of Iowa

Office: 25J MLH               Phone: 319-335-0770         Email: isabel-darcy AT uiowa.edu           
Office hours: MF 10:45 - 11:15am, W 9:45 - 11:15am, and by appointment.

Text: Graph Theory and Complex Networks by Maarten van Steen
Recommended Texts:
         Reinhard Diestel, Graph Theory, Springer GTM 173
         Graph Theory with Applications J.A. Bondy and U.S.R. Murty

Syllabus

TENTATIVE CLASS SCHEDULE-ALL DATES SUBJECT TO CHANGE (click on date/section for pdf file of corresponding class material):
 

Monday Wednesday FridayHW/Announcements
Week 1 1/14:   Intro , Proofs, notes 1/16:  2.1 1/18:   2.1 HW 1 (due Friday 1/18): Worksheet
Week 2 MLK day 1/23: Thm 2.2, notes 1/25:  Thm 2.2, notes , 2.4
quiz 1 over ch 1 and 2 (see Exercises)
HW 2,      Answers
Week 3 1/28:  Slides (pdf), (ppt) 1/30:  2/1:  Slides (pdf), (ppt)
quiz 2, Answers
Practice problems for Friday's quiz
Week 4 2/4:  2/6:  connected(pdf), notes
HW 3 and 4 due
2/8:  planar graphs(pptx), (pdf), Vertex cut, notes,
HW 5 due
HW 3 and 4 due Wednesday 2/6

HW 4

HW 3: Create slide(s) for your 1 minute presentation on a graph theory application. Make sure your slide(s) include
(1) Define the problem
(2) What do the vertices represent
(3) What do the edges represent
(4) What can graph theory say about your real-life problem? Can you formally state the graph theory problem(s)?

Use large font (best minimum = 24 point, 18 OK) Figures are helpful. INCLUDE YOUR NAME and affiliation.

HW 5 (due Friday). Does thm 2.4 hold for all graphs or should the definition of κ(G) be modified for a special case. How does this special case affect the proof of κ(G) ≤ λ(G)? I.e., can you find a case for which the proof of κ(G) ≤ λ(G) needs modification? Check the assumptions in the proof (this should help you find the special case). Can you prove that κ(G) ≤ λ(G)? Explore.

Week 5 2/11:  notes 2/13:  Mini exam 1: 12% 2/15: 
Week 6 2/18:  2/20:  HW 6 due 2/22:  HW 6 (due Wed 2/20): Final draft of slide(s) for your 1 minute presentation on a graph theory application.
Week 7 2/25:  2/27: Quiz 3 3/1: Mini-presentations??
Wee k 8 3/4:  3/6:  3/8:  Midterm: 22%
Week 9 3/11:  3/13:  3/15: 
*****Spring Break****
Week 10 3/25:  3/27:  3/29: 
Week 11 4/1:  4/3: Quiz 4 4/5: 
Week 12 4/8:  4/10:  4/12:  Mini exam 1: 12%
Week 13 4/15:  4/17:  4/19: 
Week 14 4/22:  4/24: Quiz 5 4/26: 
Week 15 4/29:  5/1:  5/3: 
Final's Week