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math4250finalexam

math4250finalexam - Math 4250/6250 Final Exam This...

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Math 4250/6250 Final Exam This take-home exam covers material from the entire class. Please don’t be afraid to read over the notes and the sections in the book as you work on the problems– there is more in the notes than we were able to cover in the lectures, and some of those extra facts might be helpful to you as you work on the exam problems. As before, please pick 4 of the following problems. You must pick one from each of the four categories: Curve theory, The First Fundamental Form, The Second Fundamental Form, and Geodesics and Gauss-Bonnet. In each category there is an “easier” problem and a “harder” problem. If you are a graduate student, you must attempt two ”harder” problems. If you are an undergraduate, you will get some bonus credit for doing “harder” problems. You are permitted to use You are not permitted to use Maple (or Mathematica or MATLAB) The internet A calculator (or graphing calculator) DoCarmo Other books Your notes Other people’s notes Your brain Other people’s brains Class notes posted on the website The problems are organized by subject area (easier and harder): 1. (Curve theory, easier) Suppose we have a strictly convex curve
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