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27 Nov 2009: 1. The square matrices A and B over the field F are congruent if B = P T AP for some invertible matrixP over F. ... Which, if any, over Q?) Try to get away with the minimum calculation.(.

13 Nov 2009: 13. Let V be a vector space of finite dimension over a field F. ... Verify that (DS) = SD and (SD) = DS. 16. For A an n m and B an m n matrix over the field F , let τA(B) denote trAB.Show that, for

21 Jan 2009: Since in this case B is a polynomial algebra andsince V is a finite set, X is contained in the union of finitely many rational (thatis, defined over Fp) linear subspaces ... Lond. Math. Soc. 36(3) (1978), 385–447.[14] H. Strade, Simple Lie algebras

4 Aug 2009: bounded, and thus it converges to a point. Proof. First consider it over R. ... Since | zz0 | 1,| zz0 |. n converges over the reals (as it is a geometric progression)(note, we say nothing about C), so by the comparison test.

12 Aug 2009: as P runs over a set of coset representatives for E(K)/nE(K). ... So over k the singular locus of the reductionis either a point or a line.