Get 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 specific textbook makes a speciality of the constitution of fields and is meant for a moment path in summary algebra. in addition to 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 listen approximately equations, either polynomial and differential, and concerning the algebraic constitution in their suggestions. In explaining those options, the writer additionally offers reviews on their old 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 photographs from the heritage of arithmetic, together with scans of mathematical stamps and photographs of mathematicians. Antoine Chambert-Loir taught this booklet 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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