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21 May 2005: BA. B. B. B. A A D. A. DCC. AA A A. ... 3. (b) Now show that γ is an epimorphism (i.e., is surjective).

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26 Sep 2005: Let us compute the commutator of twosuch vector fields F(A,a) and F(B,b). ... Thus. [F(A,a),F(B,b). ]= F(C,c), where (C, c) = (AB BA,Ab Ba).

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21 May 2005: 8. Part (b) is incorrect: In the figure, the segments labelled A are supposed to beidentified and the segments labelled B are supposed to be identified, but theresulting segments A and ... a},{1, 2, 5}, {1, 2, 6}, {1, 3, 4}, {1, 5, 6},{2, 3, 5}, {2, 4, 6}

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9 Aug 2005: 6). µc =b P(c|b)b. b P(c|b)(7). σc =b P(c|b)(b µc)(b µc). ... al,. which would produce a P(w|B) as. P(w|B) b. P(w|c)P(c|B). (13).

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23 Nov 2005: 3. The symmetric difference of sets A and B is A 4 B = (A B) (B A). ... 8. Define a relation R on N by setting aRb if a divides b or b divides a.

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21 May 2005: 4. Which of the following subsets of R2 are (a) open, (b) closed? ... 1. 2 ANALYSIS II EXAMPLES 2. 7. If A and B are subsets of Rn, we write A B for the set {a b : a A,b B}.

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4 Nov 2005: 4. Which of the following subsets of R2 are (a) open, (b) closed? ... 1. 2 ANALYSIS II EXAMPLES 2. 7. If A and B are subsets of Rn, we write A B for the set {a b : a A,b B}.

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21 May 2005: Every continuous function on a compact interval [a,b] can be uniformly approximated bypolynomials (Weierstrass’ theorem). ... 12. Let B = B(0, 1) denote the open unit disc, C = C(0, 1) the unit circle and D the set{z C | |z| > 1}.

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9 Aug 2005: B B. B. B. B. B. 3. 3 B. 2, JK?;'JTLJK;A+= <-G=@243J ,/<K,/G ,/?S23Ml8 =@?; = 4, ;,/?812,/;PHN =? ; 4,/M3R+, 2JKL0,/<KN02', 4JK.)S2 =@?;CMJK;,8$, A+=@23JT81? ... B. B B B. B. B. B. B. , 234 =? M 814GQ=@MH ,/,/? ;,Q4JKL0,/; O804 2, E= M, 8=CM3JK?0<K,

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