Antoine Chambert-Loir's 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 distinctive 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 publication 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 in regards to the algebraic constitution in their suggestions. In explaining those strategies, the writer additionally offers reviews on their ancient improvement and leads the reader alongside many attention-grabbing paths. additionally, there are theorems from research: as said ahead of, the transcendence of the numbers pi and e, the truth that the complicated numbers shape an algebraically closed box, and in addition 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 publication extra full of life, the writer has included images from the heritage of arithmetic, together with scans of mathematical stamps and photographs 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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A Field Guide to Algebra (Undergraduate Texts in Mathematics) by Antoine Chambert-Loir

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