Applied Mathematics Descriptive Theory

Applied Mathematics Descriptive Theory
topic  :Applied Mathematics Descriptive Theory
This project looks at the thickness of nonplanar graphs. Thickness is a difficult topic due to the lack of theoretical results. However, an investigation into the thickness of nonplanar graphs offers excellent insight into planar graphs. Below are the specific requirements for Project 2.
Use Theorem 4.11 on page 90 to help with the requirements.
– Select and discuss a graph, G, with thickness 2
— Show the graph and provide all of the descriptive information
— Show the planar graphs that can be superimposed to form G
– Select and discuss a graph, H, with thickness 3
— Show the graph and provide all of the descriptive information
— Show the planar graphs that can be superimposed to form H
– Select and discuss a maximal planar graph with 8 vertices
— Show the graph and provide all of the descriptive information
— Discuss how the addition of a single edge creates a graph of thickness 2
— Show the planar graphs that can be superimposed to form the graph with its additional edge
– Discuss some generalizations about graphs of thickness 2
— Let us know what you learned during this project
— Provide additional graphs as required
A few notes about format: use MS PowerPoint for your presentation; develop a presentation that is 10-20 slides in length; incorporate audio files into your presentation in order to explain your work; use Equation Editor for all mathematical symbols, e.g. x ∈ X or Cl(A) ⋂ Cl(X-A); and select fonts, backgrounds, etc. to make your presentation look professional.


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Rubric for Applied Mathematics Descriptive Theory

A (4) B (3) C (2) D/F (1/0)
Focus: Purpose Purpose is clear Shows awareness of purpose Shows limited awareness of purpose No awareness
Main idea Clearly presents a There is a main idea Vague sense of a No main idea
main idea and supported throughout main idea, weakly
supports it most of the paper. supported
throughout the throughout the
paper. paper.
Organization: Well-planned and Good overall There is a sense of No sense of
Overall well-thought out. organization, includes organization, organization
Includes title, the main although some of the
introduction, organizational tools. organizational tools
statement of main are used weakly or
idea, transitions and missing
Organization: All paragraphs have Most paragraphs have Some paragraphs Para. lack clear ideas
Paragraphs clear ideas, are clear ideas, are have clear ideas,
supported with supported with some support from
examples and have examples and have examples may be
smooth transitions. transitions. missing and
transitions are weak.
Content Exceptionally well- Well-presented and Content is sound and Content is not sound
presented and argued; ideas are solid; ideas are
argued; ideas are detailed, developed present but not
detailed, well- and supported with particularly
developed, evidence and details, developed or
supported with mostly specific. supported; some
specific evidence & evidence, but
facts, as well as usually of a
examples and generalized nature.
specific details.
Research (if Sources are Sources are well Sources support The paper does not
assignment exceptionally well- integrated and some claims made in use adequate
includes a integrated and they support the paper’s the paper, but might research or if it does,
research support claims claims. There may be not be integrated the sources are not
component) argued in the paper occasional errors, but well within the integrated well.
very effectively. the sources and paper’s argument. They are not cited
Quotations and Works Cited conform There may be a few correctly according
Works Cited to MLA style sheet. errors in MLA to MLA style, nor
conform to MLA style.. listed correctly on
style sheet. the Works Cited
Style: Sentence Sentences are clear Sentences are clear Sentences are Sentences aren’t
structure and varied in but may lack generally clear but clear
pattern, from simple variation; a few may may have awkward
to complex, with be awkward and there structure or unclear
excellent use of may be a few content; there may
punctuation. punctuation errors. be patterns of


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