rev1 - Z n , , . 12. Modular matrix addition and...

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Math 3124 Thursday, September 22 First Test Review The test will cover as far as (and including) Section 14. Topics will include 1. Operations, associative and commutative law. 2. One-to-one and onto mappings. A mapping is invertible if and only if it is one-to-one and onto. 3. Composition of mappings. 4. Writing a permutation as a product of disjoint cycles; e.g. (1 5 3) - 1 (1 4 6 5 2) = (1 4 6)(2 3 5) 5. Subgroups 6. G T and G ( T ) . 7. Cayley tables. 8. Symmetry groups. 9. S n and A n 10. Equivalence relations. 11. Modular arithmetic:
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Unformatted text preview: Z n , , . 12. Modular matrix addition and multiplication. 13. The order of an element 14. The order of a permutation which is the product of disjoint cycles of lengths a 1 , . . . , a n is [ a 1 , . . . , a n ] (least common multiple). 15. The order of ( g , h ) in G H is [ o ( g ) , o ( h )] . 16. 15 puzzle and ISBN numbers wont be tested. Test on Tuesday, September 27. Review session at 4:50 p.m. in McBryde 126 on Sunday September 25....
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