Graph Theory Mini-projects are designed to critically stretch your thinking, let you explore the concept, or make you look at a specific situation or related problem. By nature, they are more...

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Graph Theory Mini-projects are designed to critically stretch your thinking, let you explore the concept, or make you look at a specific situation or related problem.  By nature, they are more difficult than the regular exercises. Weights are assigned to the edges of graphs to show connection. The smaller the weight, the closer the relationship. A spell checker in a word processing program makes suggestions when it finds a word not in the dictionary.  To determine what words to suggest, it tries to find similar words.  One measure of word similarity is the Levenshtein distance, which measures the number of substitutions, additions, or deletions that are required to change one word into another.   For example, the words spit and spot are a distance of 1 apart; changing spit to spot requires one substitution (i for o).   Likewise, spit is distance 1 from pit since the change requires one deletion (the s).  The word spite is also distance 1 from spit since it requires one addition (the e). The word soot is distance 2 from spit since two substitutions would be required. Part 1:   Pick a four letter misspelled word (example “moke” –you cannot use this one it is just an example) as the center word , and try to find at least ten dictionary words which are a Levenshtein distance of 1 from the original misspelled word.  (so for the misspelled word "moke" you could have words such as make, mike, mole,smoke, toke, etc.) Now draw a graph - put your misspelled word in the center and then surround this word with the 10 dictionary words you found.  Circle all words. Then draw a line from the misspelled word to each of the dictionary words, like spokes on a wheel. Since each word is a Levenstein distance of 1 from the center word we label each spoke "1" to represent the distance. Part 2: Use the same graph as you made for part 1 BUT take the distance measurement off.  We all know that when we misspell a word not every word Levenshtein distance one is equally likely to happen.  Decide on a method (one you make up but not Levenshtein) to decide the probability to of how connectted the words to the misspelled word would be.  For example if the misspelled word is moke- make might be more likely than mike.  But you MUST decide on the method you are using and then use that method to assign the weights. Describe the method.  This graph will have all the same words as graph for part a, just with different weights on the edges (spokes).  You can base the weights on any reasonable approach:  proximity of keys on a keyboard, common language errors, etc.  How might a “spell checker” use these values? Turn in the two graphs - labeled part 1 and part 2 and a description of the method you used to assign weights for part 2.   Turn in by attachment by the due date in the class schedule. Finance Mini-projects are designed to critically stretch your thinking, let you explore the concept, or make you look at a specific situation or related problem.  By nature, they are more difficult than the regular exercises. Assume you will purchase a new car. The dealer is currently offering a special promotion: you can choose A) a $1500 rebate up front with 6% financing OR B) 0% financing for the first 36 months and 6% financing for the last 2 years.  Both loans are 5 years. Find the car you want to purchase and its cost and where you can purchase it from.(Do this from online or at a dealership) For promotion A · Compute the cost of the car after the rebate · Compute your monthly payment at the 6% interest. · Compute the final amount you paid (including interest) · Subtract the price of the car from the amount you paid to get the amount of the interest you paid. For promotion B · Since 3 years is 3/5 of the loan, take 3/5 the price and compute the monthly payment (this amount divided by 36 since there is no interest).  · Take the remaining 2/5 of the loan and compute the monthly payment at the 6% interest for the remaining 2 years.  Multiply the monthly payment by 24 to get the total amount spent · Add the 36 monthly payments from years 1-3 to the 24 monthly payments from years 4-5 · Compute the final amount you paid (including interest) · Subtract the price of the car from the total amount you paid to get the amount of the interest you paid. Conclusion · Compare the final amount  you paid from promotion A and from promotion B and which was the better buy.  Show clear calculations I can follow for your turned in work. · Report out (typed when possible) the calculations with your conclusions. Turn in your work by attachment by the due date in the class schedule.