The Nature of Mathematics, 12th Edition
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Section 8.1 Homework Hints

    Problems 1-5
    There questions are basically defintions and procedures.
    Read the book and then paraphrase each in your own words.
    Problems 6-11
    Classify each vertex as even or odd to use Euler's circuit theorem. If an Euler circuit exists, then start at one of the even vertices to draw the circuit. See Example 3.
    Problems 12-17
    You can either use trial-and-error or the nearest-neighbor method to find a Hamiltonian cycle. See Example 5.
    Problems 18-23
    Classify each room as even or odd according to the number of doors in each room, and then use Euler's circuit theorem. If it is an Euler circuit, then begin in an even room to draw the circuit. See Example 4.
    Problems 24-27
    Classify each vertex as even or odd and use Euler's circuit theorem. If there is an Euler circuit, then start an an even vertex and draw the circuit. See Example 3.
    Problems 28-31
    Either use trial-and-error or the Nearest Neighbor method to find a Hamiltonian cycle. See Example 4.
    Problem 32
    See Example 2 and Table 8.1, and then apply Euler's circuit theorem.
    Problem 33
    See Example 5. One possible solution:
    1, 6, 7, 8, 9, 10, 11, 12, 13, 19, 18, 17, 16, 20, 15, 14, 5, 4, 3, 2, 1.
    Can you find another?
    Problems 34-40
    See Example 2 and Table 8.1, and then apply Euler's circuit theorem.

    Note: Homework Hints are given only for the Level 1 and Level 2 problems.

    However, as you go through the book be sure you look at all the examples in the text. If you need hints for the Level 3 problems, check some sources for help on the internet (see the LINKS for that particular section. As a last resort, you can call the author at (707) 829-0606.

    On the other hand, the problems designated "Problem Solving" generally require techniques that do not have textbook examples.

    There are many sources for homework help on the internet.

    Algebra.help
    Here is a site where technology meets mathematics. You can search a particular topic or choose lessons, calculators, worksheets for extra practice or other resources.
    http://www.algebrahelp.com/

    Ask Dr. Math
    Dr. Math is a registered trademark. This is an excellent site at which you can search to see if your question has been previously asked, or you can send your question directly to Dr. Math to receive an answer.
    http://mathforum.org/dr/math/
    Quick Math
    This site provides online graphing calculators. This is especially useful if you do not have your own calculator.
    http://www.quickmath.com/

    The Math Forum @ Drexel
    This site provides an internet mathematics library that can help if you need extra help. For additional homework help at this site, click one of the links in the right-hand column.
    http://mathforum.org/

    Mathematics Home Page
    Access the Clemens and Alcuins Library of CSB/SJU and find one of the world's best collections of mathematical internet sites.
    http://library.csbsju.edu/rqs.phtml?subject_id=32

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