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  1. Bog
  2. Matematik
  3. Algebra

Abstract Algebra via Numbers

Af: Lars Tuset Engelsk Hardback

Abstract Algebra via Numbers

Af: Lars Tuset Engelsk Hardback
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This book is a concise, self-contained treatise on abstract algebra with an introduction to number theory, where students normally encounter rigorous mathematics for the first time. The authors build up things slowly, by explaining the importance of proofs. Number theory with its focus on prime numbers is then bridged via complex numbers and linear algebra, to the standard concepts of a course in abstract algebra, namely groups, representations, rings, and modules.

The interplay between these notions becomes evident in the various topics studied. Galois theory connects field extensions with automorphism groups. The group algebra ties group representations with modules over rings, also at the level of induced representations. Quadratic reciprocity occurs in the study of Fourier analysis over finite fields. Jordan decomposition of matrices is obtained by decomposition of modules over PID’s of complex polynomials. This latter example is just one of many stunning generalizations of the fundamental theorem of arithmetic, which in its various guises penetrates abstract algebra and figures multiple times in the extensive final chapter on modules.

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This book is a concise, self-contained treatise on abstract algebra with an introduction to number theory, where students normally encounter rigorous mathematics for the first time. The authors build up things slowly, by explaining the importance of proofs. Number theory with its focus on prime numbers is then bridged via complex numbers and linear algebra, to the standard concepts of a course in abstract algebra, namely groups, representations, rings, and modules.

The interplay between these notions becomes evident in the various topics studied. Galois theory connects field extensions with automorphism groups. The group algebra ties group representations with modules over rings, also at the level of induced representations. Quadratic reciprocity occurs in the study of Fourier analysis over finite fields. Jordan decomposition of matrices is obtained by decomposition of modules over PID’s of complex polynomials. This latter example is just one of many stunning generalizations of the fundamental theorem of arithmetic, which in its various guises penetrates abstract algebra and figures multiple times in the extensive final chapter on modules.

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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 452
ISBN-13: 9783031746222
Indbinding: Hardback
Udgave:
ISBN-10: 3031746228
Kategori: Algebra
Udg. Dato: 3 dec 2024
Længde: 34mm
Bredde: 162mm
Højde: 242mm
Forlag: Springer International Publishing AG
Oplagsdato: 3 dec 2024
Forfatter(e): Lars Tuset
Forfatter(e) Lars Tuset

Kategori Algebra

ISBN-13 9783031746222

Sprog Engelsk

Indbinding Hardback

Sider 452

Udgave

Længde 34mm

Bredde 162mm

Højde 242mm

Udg. Dato 3 dec 2024

Oplagsdato 3 dec 2024

Forlag Springer International Publishing AG

Kategori sammenhænge