1.

Record Nr.

UNINA9910208821003321

Autore

Cox David A.

Titolo

Primes of the form = x² + ny² : Fermat, class field theory, and complex multiplication / / David A. Cox

Pubbl/distr/stampa

Hoboken, New Jersey : , : Wiley, , 2013

©2013

ISBN

1-118-40072-0

1-118-40075-5

1-118-40074-7

Edizione

[Second edition.]

Descrizione fisica

1 online resource (419 pages) : illustrations, tables

Collana

Pure and Applied Mathematics

Disciplina

512.7/23

Soggetti

Numbers, Prime

Mathematics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

"Originally published: Primes of the form x² + ny², 1989"--Title page verso.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

From Fermat to Gauss -- Class field theory -- Complex multiplication -- Additional topics.

Sommario/riassunto

An exciting approach to the history and mathematics of number theory ". . . the author's style is totally lucid and very easy to read . . .the result is indeed a wonderful story." – Mathematical Reviews Written in a unique and accessible style for readers of varied mathematical backgrounds, the Second Edition of Primes of the Form p = x 2 + ny 2 details the history behind how Pierre de Fermat's work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. The book also illustrates how results of Euler and Gauss can be fully understood only in the context of class field theory, and in addition, explores a selection of the magnificent formulas of complex multiplication. Primes of the Form p = x 2 + ny 2 , Second Edition focuses on addressing the question of when a prime p is of the form x 2 + ny 2 , which serves as the basis for further discussion of various mathematical topics. This updated edition has several new notable features, including: A well-motivated introduction to the classical formulation of class field theory Illustrations of explicit numerical



examples to demonstrate the power of basic theorems in various situations An elementary treatment of quadratic forms and genus theory Simultaneous treatment of elementary and advanced aspects of number theory New coverage of the Shimura reciprocity law and a selection of recent work in an updated bibliography Primes of the Form p = x 2 + ny 2 , Second Edition is both a useful reference for number theory theorists and an excellent text for undergraduate and graduate-level courses in number and Galois theory.

2.

Record Nr.

UNINA9910865243403321

Autore

Stefanucci Gianluca

Titolo

Quantum Mechanics for Material Science : An Introduction / / by Gianluca Stefanucci

Pubbl/distr/stampa

Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2024

ISBN

9783031601712

9783031601705

Edizione

[1st ed. 2024.]

Descrizione fisica

1 online resource (241 pages)

Disciplina

530.1202462011

Soggetti

Quantum theory

Materials science

Atoms

Molecules

Quantum Physics

Materials Science

Atoms and molecules in external fields

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

Chapter 1. The fundamental concepts of quantum mechanics -- Chapter 2. Quantum systems in finite-dimensional Hilbert spaces 35 -- Chapter 3. A particle in one dimension -- Chapter 4. A particle in three dimensions -- Chapter 5. Spin and angular momentum composition -- Chapter 6. Approximation methods -- Appendix A: Dirac delta: definition and properties -- Appendix B: Levi-Civita tensor: definition



and properties -- Appendix C: Euler range: definition and properties.

Sommario/riassunto

This book is based on the course "Elements of Theoretical Physics," which the author has been teaching at the University of Rome Tor Vergata since 2017. It serves as an introduction to quantum mechanics, providing students with essential concepts and tools for future lessons, while still maintaining a comprehensive approach without relying heavily on the level of abstraction and mathematical rigor typically found in Physics programs. Understanding this book only requires knowledge of the mathematical concepts taught in the first two years of basic courses. The bachelor's degree program in Materials Science aims to train students with an interdisciplinary background in physics, chemistry, and engineering. While the study of quantum mechanics is essential, the same level of depth, abstraction, and mathematical rigor as in a Physics degree program is not a requirement. Unfortunately, most textbooks on Quantum Mechanics are geared toward Physics students, making it difficult to find suitable resources for Materials Science students. To make learning easier, the author has chosen not to refer students to various textbooks for different topics. Instead, he has created handouts that have evolved into a condensed textbook on quantum mechanics specifically tailored to the needs of the Materials Science program.