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GROUP THEORY (MATH 33300)
8. Isomorphism Theorems 26 9. Direct products 29 10. Group actions 34 11. Sylow’s Theorems 38 12. Applications of Sylow’s Theorems 43 13. Finitely generated abelian groups 46 14. The symmetric group 49 15. The Jordan-Holder Theorem 58¨ 16. Soluble groups 62 17. Solutions to exercises 67 Recommended text to complement these notes: J.F ...
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Martingale Theory Problem set 3, with solutions …
people.maths.bris.ac.uk3.6HW We place N balls in K urns (in whatever way) and perform the following discrete time process. At each time unit we choose one of the balls uniformly at random (that is : each ball is chosen with probability 1=N) and place it in one of the urns also uniformly chosen at random (that is: each urn is chosen with probability 1=K). Denote by X ...
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