By Antoine Chambert-Loir

This particular textbook makes a speciality of the constitution of fields and is meant for a moment direction in summary algebra. along with delivering proofs of the transcendence of pi and e, the e-book contains fabric on differential Galois teams and an explanation of Hilbert's irreducibility theorem. The reader will pay attention approximately equations, either polynomial and differential, and concerning the algebraic constitution in their suggestions. In explaining those options, the writer additionally presents reviews on their historic improvement and leads the reader alongside many fascinating paths. additionally, there are theorems from research: as acknowledged ahead of, the transcendence of the numbers pi and e, the truth that the complicated numbers shape an algebraically closed box, and likewise Puiseux's theorem that indicates how you can parametrize the roots of polynomial equations, the coefficients of that are allowed to alter. There are workouts on the finish of every bankruptcy, various in measure from effortless to tough. To make the publication extra full of life, the writer has included images from the historical past of arithmetic, together with scans of mathematical stamps and photographs of mathematicians. Antoine Chambert-Loir taught this e-book whilst he was once Professor at École Polytechnique, Palaiseau, France. he's now Professor at Université de Rennes 1.

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