Read e-book online A Field Guide to Algebra (Undergraduate Texts in PDF

By Antoine Chambert-Loir

ISBN-10: 0387214283

ISBN-13: 9780387214283

ISBN-10: 1441919473

ISBN-13: 9781441919472

This precise textbook makes a speciality of the constitution of fields and is meant for a moment direction in summary algebra. along with supplying proofs of the transcendence of pi and e, the ebook comprises 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 techniques, the writer additionally presents reviews on their historic improvement and leads the reader alongside many attention-grabbing paths. furthermore, 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 change. There are routines on the finish of every bankruptcy, various in measure from effortless to tough. To make the ebook extra full of life, the writer has integrated photos from the historical past of arithmetic, together with scans of mathematical stamps and photographs 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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