Number Theory

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 distinctive textbook makes a speciality of the constitution of fields and is meant for a moment path in summary algebra. in addition to offering proofs of the transcendence of pi and e, the booklet contains 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 in regards to the algebraic constitution in their suggestions. In explaining those options, the writer additionally offers reviews on their ancient improvement and leads the reader alongside many fascinating paths. moreover, there are theorems from research: as acknowledged ahead of, 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 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 vigorous, the writer has included photographs from the historical past of arithmetic, together with scans of mathematical stamps and photographs of mathematicians. Antoine Chambert-Loir taught this publication while he used to be 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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