1.

Record Nr.

UNINA9910376035403321

Titolo

VMIL '17 : proceedings of the 9th ACM SIGPLAN International Workshop on Virtual Machines and Intermediate Languages : October 24, 2017, Vancouver, BC, Canada / / edited by Steve Blackburn [and seven others] ; sponsored by ACM SIGPLAN

Pubbl/distr/stampa

New York : , : ACM, , 2017

Descrizione fisica

1 online resource (27 pages)

Disciplina

006.605

Soggetti

Virtual computer systems

Programming languages (Electronic computers)

Computer software - Development

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Includes index.



2.

Record Nr.

UNINA9910983306603321

Autore

Tuset Lars

Titolo

Abstract Algebra via Numbers / / by Lars Tuset

Pubbl/distr/stampa

Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2025

ISBN

9783031746239

3031746236

Edizione

[1st ed. 2025.]

Descrizione fisica

1 online resource (462 pages)

Disciplina

512

Soggetti

Algebra

Number theory

Number Theory

Àlgebra

Teoria de nombres

Llibres electrònics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

Chapter 1. Number theory -- Chapter 2. Construction of numbers -- Chapter 3. Linear algebra -- Chapter 4. Groups -- Chapter 5. Representations of finite groups -- Chapter 6. Rings -- Chapter 7. Field extensions -- Chapter 8. Galois theory -- Chapter 9. Modules -- Chapter 10. Appendix.

Sommario/riassunto

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.