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Unformatted text preview: MATH 373: Final Exam Monday, May 3, 2010 Answer all questions in the answer booklet. Please do these in order. You are expected to justify your answers in a manner that an average MATH 373 student should be able to follow. This includes sentences for clarification. Questions are on both sides of the page. This test is worth a total of 200 points. 1. Quickies - Provide a short justification (one sentence). [50 pts] (a) In Q [ x ] / x 2- x + 3 is it true that x 2- x- 3 + x 2- x + 3 =- 6 + x 2- x + 3 ? (b) T or F: x 10 + 12 x 9- 3 x 7 + 21 x 5- 6 x 3 + 300 x 2- 15 x + 12 is irreducible over Q . (c) The set of odd integers under addition is not a group. What is missing? (d) Suppose H S 5 with | H | = 10. How many cosets of H are in S 5 ? (e) T or F: If S n then o ( ) | n . (recall: o ( ) = order of ) (f) T or F: If G is a group with 15 elements then G is isomorphic to a subgroup of S 15 ....
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