MATH 345 Final: MATH 345 Amherst F10M31Final

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Your solutions are due by 5 pm on wednesday, december 22nd. Exams turned in after that will not be accepted and will receive a grade of 0. Nishing on time, come speak to me well before then. I expect your solutions to be a polished, revised, reasonably concise nal draft. If you get stuck on one part of a multi-part problem, you can still work on the later parts. If you do this, you can use any results asserted the earlier parts as if they have been proved. (you may not use a later part to prove an earlier part. ) On problems involving homotopy or winding numbers, don"t worry about showing rigorously that a winding number is such-and-such, or that one contour is homotopic to another; drawing a reasonable picture and/or common sense is su cient. Assume that all numbers are in c and that all functions have domain and range in c, unless i specify otherwise.