The Nature of Mathematics, 12th Edition
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Chapter1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
Chapter 18
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Reference Topics

An historical reference, along with a solution and interesting links for the Konigsberg bridge problem is found at this site:
http://mathforum.org/isaac/problems/bridgesol1.html

This site gives an overview of graph theory, including the bridges of Konigsburg and the four-color problem (Section 8.3). It also includes a link to some games on graphs.
http://www-leibniz.imag.fr/GRAPH/english/overview.html

This site gives an nice overview of graph theory (beginning link)and overlaps the material in the next section of the text (advanced link).
http://www.cs.usask.ca/resources/tutorials/csconcepts/1999_8/tutorial/index.html

This site from Math 103 at the University of Alabama provides a nice overview of Euler circuits and Hamilton cycles.  Click on the topic in the left column.
http://www.ctl.ua.edu/math103/

This site provides a thorough overview of the Traveling Salesperson Problem (TSP):
http://www.nist.gov/dads/HTML/travelingSalesman.html

This site provides a TSP problem solver:
http://home.hiwaay.net/~kdunn/problems/tsp.shtml

This site, by Chris Caldwell provides Graph Theory tutorials:
http://www.utm.edu/departments/math/graph/

This site intends to be a comprehensive listing of papers, source code, preprints, and technical reports about the TSP problem:
http://www.ing.unlp.edu.ar/cetad/mos/TSPBIB_home.html

An interesting site about Mobius strips is found at this site:
http://mathforum.org/sum95/math_and/moebius/moebius.html