New PDF release: A Field Guide to Algebra (Undergraduate Texts in

By Antoine Chambert-Loir

This designated textbook specializes in the constitution of fields and is meant for a moment path in summary algebra. along with supplying proofs of the transcendence of pi and e, the publication contains fabric on differential Galois teams and an evidence of Hilbert's irreducibility theorem. The reader will listen 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 old improvement and leads the reader alongside many fascinating paths. moreover, there are theorems from research: as said sooner than, the transcendence of the numbers pi and e, the truth that the advanced numbers shape an algebraically closed box, and in addition Puiseux's theorem that exhibits 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 tricky. To make the ebook extra full of life, the writer has integrated photographs from the historical past of arithmetic, together with scans of mathematical stamps and images of mathematicians. Antoine Chambert-Loir taught this booklet while he was once Professor at École Polytechnique, Palaiseau, France. he's now Professor at Université de Rennes 1.

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A Field Guide to Algebra (Undergraduate Texts in Mathematics) by Antoine Chambert-Loir

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