Well posted the third TMA for M337 Complex Variables and just like the fifth TMA for M208 there were bits in the last question which had me stumped. Anyway a brief resume

1) Questions on Calculus of residues to solve Integrals and series

Relatively straightforward and a joy to do

2) Questions on zero's, maxima of functions and Inverse Taylor series

Again tricky but quite straightforward

3) a) A question showing that two series are direct analytic continuations of each other

What you have to do is show that if the two series have a common region and they take the same values on the region then the series with the larger region can be seen as a diect analytic continuation of each other. However whilst I could see that they had a common region pages and pages of scribbling failed to convince me that the two series were equal on this region.

b) A straightforward application of the residue theorem to solve an Integral

c) The use of Wierstrass's theorem to show that a series is convergent

Again the method is to a) show that the series is bounded by a sequence of positive terms

b) show that the sequence of positive terms is convergent

a) was straightforward but I couldn't show that the series of positive terms was convergent it failed as far as

I could see the ratio test and the comparison test.

d) Some straightforward questions on the Gamma function

So should be close to getting full marks for 1 and 2 and about half the avaiable marks for question 3. As there are only three questions I should just scrape a grade two pass.

So I'll give myself a week off to concentrate on

a) Cambridge Computing projects

b) The variational method in General relativity and it's application to the Robertson

Walker metric

c) Cubics, quartics and quintics

I;ve found (yet another) book on Galois theory which takes a nice historical perspective and doesn't get to bogged down in formal detail until the end

http://www.galois-theorie.de/galois-theory.htm

I would probably reccomend this book as the best starting point.

Finally so far have got 8 recruits to the shared activity forum on the Cambridge Computing projects forum

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