1. With your host… Alan Quebec

2. Group theory Orbits and counting Coding theoryPotpourri $100 $200 $300 $400 $500

3. The four group axioms

4. Bac k Closure Associativity Identity Inverses

5. A group with 11 elements is this kind of group

6. Bac k Cyclic

7. The easiest way to tell if a subset of G is a subgroup

8. Bac k Check that if x, y are elements of H, then so is xy -1

9. Why S 5 cannot have a subgroup of order 7

10. Bac k Lagrange’s Theorem

11. There are this many elements of order 13 in C 13

12. Bac k 12 (1 has order 1)

13. The difference between Gx and G x (Not just the names of the terms, but their meanings)

14. Bac k Gx is the orbit containing x; G x is the stabilizer of x

15. The size of an orbit if G = S 4

16. Bac k 4

17. The number of ways to color the edges of a pentagon red, green, and blue

18. Bac k

19. The number of ways to place colored pie slices into a Trivial Pursuit game piece like the one below, if only the orange and yellow pieces can be used

20. Bac k

21. The number of ways to color the edges of a pentagon red, green, and blue where 2 edges are green and 2 edges are blue

22. Bac k Bac k Coefficient of rb 2 g 2 is

23. The number of errors that this code can correct for: 00000, 01100, 00111, 11001

24. Bac k 0 (minimum distance is 2)

25. The length of a codeword in the linear code given by the associated matrix

26. Bac k 7

27. The maximum number of codewords in a code of length 7 that can correct for one error

28. Bac k 16, since

29. The number of codewords in the linear code given by the associated matrix

30. Bac k 2 4 = 16

31. This is the smallest linear code that contains the codewords 001, 110

32. Bac k 000, 100, 011, 111 (code must be a group)

33. These three sets are all rings

34. Bac k

35. A ring that is not a field has this distinguishing characteristic

36. Bac k Not all nonzero elements have multiplicative inverses

37. This is an example of an invertible power series where all coefficients are nonzero and the coefficient of is 10

38. Bac k Any matching power series that has a invertible constant term

39. The parity (even or odd) of the permutation (12345)

40. Bac k Even; decomposition into transpositions is (12)(23)(34)(45)

41. The order of the permutation (12)(345)

42. Bac k lcm(2, 3) = 6