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8 Nov 2022: a) Let H 6 Cn. Identify the quotient Cn/H. (b) Show that N = {e, (12)(34), (13)(24), (14)(23)} is a normal subgroup of S4.

25 Jan 2022: 163 (2014), no. 2, 369–431. [24] Raphaël, P.; Schweyer, R., Stable blow up dynamics for the 1-corotational energy critical harmonic heat flow,Comm. ... Vlasov-Poisson system, Ann. Inst. H. Poincaré Anal. Non Lind́eaire 24 (2007), no.

27 Oct 2022: g]| 1 21 42 56 24 24α 14 2 0 1 0 0β 15 1 1 0 1 1γ 16 0 0 2 2 2.

22 Nov 2022: 1. (i) What are the transitive subgroups of S4? Find a monic polynomial over Z of degree 4 whoseGalois group is V = {e, (12)(34), (13)(24), (14)(23)}.(ii) Let

24 Oct 2022: 24) Consider Σ = {0, 1, ε, (, ), , , , }. Define a context-free grammar G over Σ such that L(G) is theset of regular expressions over the alphabet {0, 1}.

17 Feb 2022: 5) Determine which of the following polynomials are irreducible in Q[X]:X4 2X 2, X4 18X2 24, X3 9, X3 X2 X 1, X4 1, X4 4.

12 Dec 2022: 2 =. 11. 1 dx =nj=1. Aj. 24. (iii) We have 11f(x) dx.

12 Dec 2022: as n. 24. 10 Distance and compact sets. This section could come almost anywhere in the notes, but provides somehelpful background to the section on Runge’s theorem.

7 Oct 2022: 24. and hecne X|fn(x)|pdµ(x). (sup. ‖g‖Lp′1. Xf(x)g(x)dµ(x). )p. If the rhs is finite, the monotone convergence Theorem applied to the