Download A Field Guide to Algebra (Undergraduate Texts in by Antoine Chambert-Loir PDF

By Antoine Chambert-Loir

This distinctive textbook makes a speciality of the constitution of fields and is meant for a moment path in summary algebra. along with offering proofs of the transcendence of pi and e, the e-book contains 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 strategies. In explaining those recommendations, the writer additionally offers reviews on their ancient improvement and leads the reader alongside many fascinating paths. furthermore, there are theorems from research: as acknowledged sooner than, 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 exhibits 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 publication extra energetic, the writer has integrated photographs from the historical past of arithmetic, together with scans of mathematical stamps and photographs of mathematicians. Antoine Chambert-Loir taught this booklet whilst he used to be Professor at École Polytechnique, Palaiseau, France. he's now Professor at Université de Rennes 1.

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