The Nature of Mathematics, 12th Edition
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Section 8.2 Homework Hints

    Problems 1-3
    There questions are basically definitions and procedures.
    Read the book and then paraphrase each in your own words.
    Problems 4-11
    Review the definition of a tree and see Examples 1 and 2.
    Problems 12-19
    Review the definition of a spanning tree and remove edges as shown in Example 4.
    Problems 20-25
    It is generally difficult to find all of the spanning trees, but these trees are simple enough that you can proceed systematically to find them all.
    Problems 26-31
    Read the directions carefully to understand the transition from ball-and-stick model to bond-line drawing to tree diagram, as shown in Figure 8.33.
    Problems 32-41
    Use Kruskal's algorithm to find the minimum spanning tree, as shown in Example 6.
    Problems 42-43
    Use the number-of-vertices-and-edges-in-a-tree theorem to answer these questions.
    Problems 44-47
    Draw a tree and then use the number-of-vertices-and-edges-in-a-tree theorem to answer these questions.
    Problems 48-49
    Use the number-of-vertices-and-edges-in-a-tree theorem.
    Problems 50-54
    Use Krukal's algorithm as shown in Examples 6 and 7.

    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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