4203f10-mid1

# 4203f10-mid1 - exams have been returned in lecture. SIGN...

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NAME : MAD 4203 — Fall 2010 September 24, 2010 Midterm 1 Instructions: This is a closed book exam and no notes are allowed. You are not to provide or receive help from any outside source during the exam except that you may ask the instructor for clariFcation of a problem. You have 50 minutes and you should attempt all problems. Print your name in the space provided. Sign the ±ERPA release on the next page only if you wish your exam returned in lecture. Calculators or other computing devices are not allowed. You must show all work and give a reason (or reasons) for your answer. A correct answer with incorrect work will be considered wrong.

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FERPA RELEASE: Because of privacy concerns, I am not allowed to return your graded exams in lecture without your permission. If you want me to return yourexaminlecture ,p

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Unformatted text preview: exams have been returned in lecture. SIGN HERE: . Problem Points Score 1 35 2 35 3 30 Total 100 1. (35) Suppose that m, n 5. How many northeastern lattice paths are there from the point (0 , 0) to the point ( m, n ) which begin by going up, go through the point (4 , 2), and do not go through the point (4 , 5)? 1 2. (35) This problem has two parts. a. Prove that n k + n k + 1 = n + 1 k + 1 for all nonnegative integers n and k . b. Prove that n k =0 k n k = n 2 n-1 for all nonnegative integers n . 2 3. (30) A student has 37 days to write her thesis and she knows that it will take exactly 60 hours of work. Each day she works for a positive integer number of hours. a. How many diFerent possible schedules are there? b. Prove that no matter what schedule she chooses, there will be a succession of days during which she will have worked exactly 13 hours. 3 4...
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## This note was uploaded on 12/10/2011 for the course MAD 4203 taught by Professor Vetter during the Fall '10 term at University of Florida.

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4203f10-mid1 - exams have been returned in lecture. SIGN...

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