Class InfoClass Number: Math 736001Dates: Sep 3, 2013  Dec 5, 2013 Room: NS 3133 (Tue) and NS 218 (Thu) Meeting time:
Purpose: Introduction to the Combinatorics of Surface Embeddings and the Probabilistic Method Texts: (D.) Reinhard Diestel, Graph Theory, Springer 2010 (M&T) Bojan Mohar and Carsten Thomassen, Graphs on Surfaces, Johns Hopkins University Press 2001. Jiří Matoušek Jan Vondrák, The Probabilistic Method Laszlo Lovász, Random Walks on Graphs: A Survey More detailed notes on nonnegative matrices and applications to random walks. See also Codling et al. Random walk models in biology 

Week  Topics  Chapters 
1  Graphs and Topology  D. 4.1 
2  Plane Graphs  D. 4.2 
3  Drawings  D. 4.3 
4  Kuratowski's Theorem  D. 4.4 
5  Plane Duality  D. 4.6 
6  Coloring Maps and Graphs  D. 5.1 
7  Midterm  
8  Classification of Surfaces  M&T 3.1 
9  Rotation Systems  M&T 3.2 
10  Embedding Schemes  M&T 3.3 
11  Genus of a Graph  M&T 3.4 
12  Combinatorial Embeddings  M&T 4.1 
13  Cycles  M&T 4.2 
14  The Genus Problem  M&T 4.45 
15  Final Exam 
Attendance  10% 
Midterm:  40% 
Final:  50% 