Difference between revisions of "MAT4323"
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== Catalog entry == | == Catalog entry == | ||
| − | ''Prerequisite'': Algebra and Number Systems | + | ''Prerequisite'': Algebra and Number Systems [[MAT1313]], or Discrete Mathematical Structures (CS 2233/2231), or instructor consent. (3-0) 3 Credit Hours. |
''Contents'' | ''Contents'' | ||
| Line 47: | Line 47: | ||
|| Search trees, spanning trees, the Traveling Salesman Problem | || Search trees, spanning trees, the Traveling Salesman Problem | ||
|- | |- | ||
| − | | 10- | + | | 10-12 |
|| [[Network algorithms]] | || [[Network algorithms]] | ||
|| 4.1-4.5 | || 4.1-4.5 | ||
|| Shortest path , minimum spanning trees, matching algorithms, transportation problems. | || Shortest path , minimum spanning trees, matching algorithms, transportation problems. | ||
|- | |- | ||
| + | | 13-14 | ||
| + | || [[Finding order within chaos]] | ||
|| | || | ||
|| Ramsey's Theorem and Ramsey numbers | || Ramsey's Theorem and Ramsey numbers | ||
|} | |} | ||
Latest revision as of 15:53, 21 January 2025
Catalog entry
Prerequisite: Algebra and Number Systems MAT1313, or Discrete Mathematical Structures (CS 2233/2231), or instructor consent. (3-0) 3 Credit Hours.
Contents
Graph models (Isomorphisms, edge counting, planar graphs), Covering circuits and graph colorings (Euler circuits, Hamilton circuits, graph colorings), Network algorithms (Shortest path, minimum spanning trees, matching algorithms, transportation problems), Ramsey's Theorem and Ramsey numbers.
Sample textbooks
[1] Vladlen Koltun, Discrete Structures, Lecture Notes, Stanford University, 2008. Freely available online here
[2] Alan Tucker, Applied Combinatorics, Freely available online here
[3] Gary Chartrand and Ping Zhang, A First Course in Graph Theory, Dover Books on Mathematics, 2012.
Topics List
| Week | Topic | Sections from Tucker's book | Subtopics | Prerequisite |
|---|---|---|---|---|
| 1-3 | Graph models | 12.1-12.3 | Isomorphism, edge counting, planar graphs. | |
| 4-6 | Covering circuits | 2.1-2.4 | Euler circuits, Hamilton circuits, graph colorings, coloring theorems. | |
| 8-9 | Trees | 3.1-3.4 | Search trees, spanning trees, the Traveling Salesman Problem | |
| 10-12 | Network algorithms | 4.1-4.5 | Shortest path , minimum spanning trees, matching algorithms, transportation problems. | |
| 13-14 | Finding order within chaos | Ramsey's Theorem and Ramsey numbers |
