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

By Antoine Chambert-Loir

This exact textbook specializes in the constitution of fields and is meant for a moment path in summary algebra. along with delivering proofs of the transcendence of pi and e, the e-book 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 in regards to the algebraic constitution in their recommendations. In explaining those ideas, the writer additionally offers reviews on their historic improvement and leads the reader alongside many attention-grabbing paths. moreover, there are theorems from research: as said earlier 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 workouts on the finish of every bankruptcy, various in measure from effortless to tricky. To make the publication extra energetic, the writer has integrated photos from the background 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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