Download e-book for kindle: A Field Guide to Algebra (Undergraduate Texts in by Antoine Chambert-Loir

By Antoine Chambert-Loir

ISBN-10: 0387214283

ISBN-13: 9780387214283

ISBN-10: 1441919473

ISBN-13: 9781441919472

This detailed textbook makes a speciality of 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 ebook comprises 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 recommendations. In explaining those strategies, the writer additionally presents reviews on their ancient 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 in addition Puiseux's theorem that exhibits 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 tricky. 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 ebook 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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