A good problem book in undergraduate mathematics

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Does anyone know a good problem/exercise book in general undergraduate mathematics, the stuff covered by Arfken&Weber of Riley, Hobson and Bence: basically, vector algebra, analysis (real and complex),differential equations, algebra, vector analysis and maybe some geometry (analytical and differential) ?
 
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I would strongly recommend 'Engineering mathematics' and 'Advanced engineering mathematics' by K.A. Stroud. Pretty much everything I know about maths I've learned from those two books. They are not set out in the standard fashion, but are made up of carefully structured programmes which progress in a logical fashion...
 
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Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.

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