Combinatorics 1 (조합론)

Class Info

Class Number: Math 736001
Dates: Sep 3, 2013 - Dec 5, 2013
Room: NS 313-3 (Tue) and NS 218 (Thu)
Meeting time:
Tuesday 15:00 - 16:15
Thursday 10:30 - 11:45

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 non-negative matrices and applications to random walks.
See also Codling et al. Random walk models in biology
Links
D. Textbook online version
Homework

Syllabus

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 4.4-5
15 Final Exam

Grading

We will have a mid-term test in late October and a final exam in mid-December.
The grades will be accorded the following weights.
Attendance 10%
Mid-term: 40%
Final: 50%

Homework

Assigned every Thursday and due to hand in on Thursday the week after.
Last modified: Tue Sep 10 16:30:19 KST 2013