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Pages: [<<] 1 2 3 4 [>>] | - Page 635 - Section 9.5
Leonhard Euler (1707-1783) -- The material about Euler from A Short Account of the History of Mathematics, 4th edition, 1908) by W.W. Rouse Ball, can be found here.
http://www.maths.tcd.ie/pub/HistMath/People/Euler/RouseBall/RB_Euler.html
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- Page 638 - Section 9.5
Graph Theory Lessons -- Graph theory lessons, based on a software system called Petersen are available at the website of Christopher Mawata at the University of Tennessee, Chattanooga who developed this system. The software can draw, edit and manipulate simple graphs, as well as examine properties of graphs, and demonstrate them using computer animation, Among topics addressed are the handshaking theorem, isomorphism of graphs, complete graphs, subgraphs, regular graphs, platonic graphs, adjacency matrices, graph coloring, bipartite graphs, simple circuits, Euler and Hamilton circuits, trees, unions and sums of graphs, complements of graphs, line graphs, spanning trees, plane graphs, shortest paths, and minimal spanning trees. To find these lessons, go here.
http://www.utc.edu/~cpmawata/petersen/
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- Page 638 - Section 9.5
1.4.7 Eulerian Cycle/Chinese Postman -- You can find source code for algorithms that find Euler circuits at the Stony Brook Algorithm Repository, run by Steven Skiena (note the terminology used at this site).
http://www.cs.sunysb.edu/~algorith/files/eulerian-cycle.shtml
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- Page 638 - Section 9.5
The Hamiltonian Page -- You can find links for a vast array of resources on Hamiltonian paths and circuits, including reports, books, and research papers, as well as source code, here.
http://www.densis.fee.unicamp.br/~moscato/Hamilton.html
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- Page 638 - Section 9.5
Chinese Postman WWW Page
-- You can download source code for solving the Chinese postman problem here.
http://www.cs.sunysb.edu/~algorith/implement/chinese-postman/implement.shtml
(Added: Fri Jul 28 2006)
- Page 638 - Section 9.5
The Hamiltonian Page -- A comprehensive list of Web resources relating to Hamilton circuit and paths, including articles, technical reports and source code can be found here.
http://www.ing.unlp.edu.ar/cetad/mos/Hamilton.html
(Added: Fri Jul 28 2006)
- Page 638 - Section 9.5
1.5.5 Hamiltonian Cycle -- Source code for algorithms for finding Hamilton circuits can be found at the Stony Brook Algorithm Repository, run by Steven Skiena.
http://www.cs.sunysb.edu/~algorith/files/hamiltonian-cycle.shtml
(Added: Fri Jul 28 2006)
- Page 640 - Section 9.5
Sir William Rowan Hamilton -- A biography and a photograph of Hamilton can be found at the MacTutor History of Mathematics Archive at the University of St. Andrews, Scotland.
http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Hamilton.html
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- Page 641 - Section 9.5
Gray codes -- Consult a site developed by David Joyner and Jim McShea of the Mathematics Department of the United States Naval Academy to learn more about applications of Gray codes and to obtain software for algorithms that generate these codes.
http://web.usna.navy.mil/~wdj/gray.htm
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- Page 643 - Section 9.5
Gray Code -- You can find more out about Gray codes at Eric Weisstein's World of Mathematics site here.
http://mathworld.wolfram.com/GrayCode.html
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- Page 646 - Section 9.5 Exercises
Julius Peter Christian Petersen -- A biography and a photograph of Julius Petersen can be found at the MacTutor History of Mathematics Archive at the University of St. Andrews, Scotland.
http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Petersen.html
(Added: Fri Jul 28 2006)
- Page 646 - Section 9.5 Exercises
If a graph has an Euler circuit, how do we find it? -- A description of Fleury’s algorithm and an example of its use can be found here.
http://www.ctl.ua.edu/math103/euler/ifagraph.htm
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- Page 647 - Section 9.5 Exercises
Knight’s Tour -- To find out more about knight’s tours and try to construct your own knight’s tours, go here.
http://web.telia.com/~u85905224/knight/eknight.htm
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- Page 647 - Section 9.5 Exercises
The Knight’s Tour -- You can find an applet that lets you try to manually construct a knight’s tour here.
http://www.borderschess.org/KnightTour.htm
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- Page 647 - Section 9.5 Exercises
Closed (Re-entrant) Knight Tours -- An interesting discussion of re-entrant knight tours can be found here.
http://www.borderschess.org/KTclosed.htm
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- Page 649 - Section 9.6
1.4.4 Shortest Path -- Source code for finding the shortest path between two vertices in a graph can be found at the Stony Brook Algorithm Repository, run by Steven Skiena.
http://www.cs.sunysb.edu/~algorith/files/shortest-path.shtml
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- Page 649 - Section 9.6
Dijkstra’s Algorithm -- A description of Dijkstra’s algorithm and an animation showing how it works can be found here.
http://www.cs.auckland.ac.nz/software/AlgAnim/dijkstra.html
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- Page 649 - Section 9.6
Dijkstra’s Algorithm -- You can find a description of Dijkstra’s algorithm and an applet demonstrating it here.
http://www.cs.mcgill.ca/~cs251/OldCourses/1997/topic29/
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- Page 650 - Section 9.6
Edsger Wybe Dijkstra -- An obituary of Edsger Dijkstra can be found here.
http://www.cs.utexas.edu/users/EWD/obituary.html
(Added: Fri Jul 28 2006)
- Page 653 - Section 9.6
TSPBIB Home Page -- A comprehensive list of Web resources relating to the Traveling Salesman Problem (TSP) and related problems, including articles, technical reports, and source code implementing various algorithms for solving the traveling salesman problem can be found here.
http://www.ing.unlp.edu.ar/cetad/mos/TSPBIB_home.html
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- Page 653 - Section 9.6
1.5.4 Traveling Salesman Problem -- Source code for solving the traveling salesman problem can also be found at the Stony Brook Algorithm Repository, run by Steven Skiena.
http://www.cs.sunysb.edu/~algorith/files/traveling-salesman.shtml
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- Page 656 - Section 9.6 Exercises
All pairs Minimum Routes problem -- You can find a description of Floyd’s algorithm, as well as an applet implementing it, here.
http://students.ceid.upatras.gr/~papagel/project/kef5_7_2.htm
(Added: Fri Jul 28 2006)
- Page 657 - Section 9.7
Graph Theory Lessons -- Graph theory lessons, based on a software system called Petersen are available at the website of Christopher Mawata at the University of Tennessee, Chattanooga who developed this system. The software can draw, edit and manipulate simple graphs, as well as examine properties of graphs, and demonstrate them using computer animation, Among topics addressed are the handshaking theorem, isomorphism of graphs, complete graphs, subgraphs, regular graphs, platonic graphs, adjacency matrices, graph coloring, bipartite graphs, simple circuits, Euler and Hamilton circuits, trees, unions and sums of graphs, complements of graphs, line graphs, spanning trees, plane graphs, shortest paths, and minimal spanning trees. To find these lessons, go here.
http://www.utc.edu/~cpmawata/petersen/
(Added: Fri Jul 28 2006)
- Page 657 - Section 9.7
1.4.12 Planarity Detection and Embedding -- Source code for algorithms that determine whether a graph is planar and that produce a drawing of the graph in the plane without edges crossing can be found at the Stony Brook Algorithm Repository, run by Steven Skiena.
http://www.cs.sunysb.edu/~algorith/files/planar-drawing.shtml
(Added: Fri Jul 28 2006)
- Page 660 - Section 9.7
Nineteen Proofs of Euler's Formula: V-E+F=2 -- You can find an amazing collection of 19 different proofs of Euler’s formula on the Geometry Junkyard site here.
http://www1.ics.uci.edu/%7Eeppstein/junkyard/euler/
(Added: Fri Jul 28 2006)
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