Algebra Assignment 3

# Algebra Assignment 3 - Algebra I, Courant Institute, New...

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Algebra I , Courant Institute, New York University, Fall 2011 Always check the class bboard on the blackboard site from home.nyu.edu (click on academics, then on Derivative Securities) before doing any work on the assignment. Assignment 3, due September 29 Corrections: (None yet) Problems from page 34. 1. [5.1] 2. [5.2] 3. [5.3] 4. [5.4] The case of even and odd n may be diﬀerent. Give the matrices explicitly for n = 4 and n = 5. 5. [5.5] When a mathematician asks: “Is this an accident?”, what she or he means is: “Is there a theorem that shows that this kind of thing happens a lot?” In the present case, the cycle structure of a permutation is a list of the number of cycles of each length. For example, a p S 20 could have two 5-cycles, a 4-cycle, a transposition, and leave the remaining 4 elements unmoved. There are many diﬀerent permutations with the same cycle structure. There may be a theorem relating the cycle structures of pq and qp . To look for this theorem, suppose r S n and ask about the cycle structures of p and rpr - 1 . Can you ﬁnd a relationship of this kind between pq and qp ? Problems from page 70

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## This note was uploaded on 09/26/2011 for the course MATH 120508 taught by Professor Jdoug during the Fall '08 term at Drexel.

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Algebra Assignment 3 - Algebra I, Courant Institute, New...

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