Download A Field Guide to Algebra (Undergraduate Texts in by Antoine Chambert-Loir PDF

By Antoine Chambert-Loir

This specific textbook specializes in the constitution of fields and is meant for a moment path in summary algebra. in addition to delivering proofs of the transcendence of pi and e, the ebook comprises fabric on differential Galois teams and an evidence 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 suggestions, the writer additionally presents reviews on their old improvement and leads the reader alongside many fascinating paths. furthermore, there are theorems from research: as said earlier than, the transcendence of the numbers pi and e, the truth that the advanced 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 change. There are workouts on the finish of every bankruptcy, various in measure from effortless to tough. To make the e-book extra full of life, the writer has included photos from the background of arithmetic, together with scans of mathematical stamps and images of mathematicians. Antoine Chambert-Loir taught this publication while he was once Professor at École Polytechnique, Palaiseau, France. he's now Professor at Université de Rennes 1.

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