Author: F. J. van der LindenPublisher:
ISBN:
Category :
Languages : en
Pages : 33
Book Description
Euclidean Rings in Imaginary Quadratic Fields with Two Infinite Primes
Author: F. J. van der LindenEuclidean Rings with Two Infinite Primes
Author: F. J. van der LindenPublisher:
ISBN:
Category : Algebraic fields
Languages : en
Pages : 222
Book Description
Finite and Infinite Primes for Rings and Fields
Author: David HarrisonPublisher: American Mathematical Soc.
ISBN: 0821812688
Category : Algebraic fields
Languages : en
Pages : 66
Book Description
On Euclidean Rings and Principal Ideal Domains
Author: Jacqueline Marcia BraunPublisher:
ISBN:
Category : Algebraic fields
Languages : en
Pages : 98
Book Description
Reviews in Number Theory, 1984-96
Author: Algebraic Number Theory
Author: J.S. ChahalPublisher: CRC Press
ISBN: 1000402185
Category : Mathematics
Languages : en
Pages : 166
Book Description
This book offers the basics of algebraic number theory for students and others who need an introduction and do not have the time to wade through the voluminous textbooks available. It is suitable for an independent study or as a textbook for a first course on the topic. The author presents the topic here by first offering a brief introduction to number theory and a review of the prerequisite material, then presents the basic theory of algebraic numbers. The treatment of the subject is classical but the newer approach discussed at the end provides a broader theory to include the arithmetic of algebraic curves over finite fields, and even suggests a theory for studying higher dimensional varieties over finite fields. It leads naturally to the Weil conjecture and some delicate questions in algebraic geometry. About the Author Dr. J. S. Chahal is a professor of mathematics at Brigham Young University. He received his Ph.D. from Johns Hopkins University and after spending a couple of years at the University of Wisconsin as a post doc, he joined Brigham Young University as an assistant professor and has been there ever since. He specializes and has published several papers in number theory. For hobbies, he likes to travel and hike. His book, Fundamentals of Linear Algebra, is also published by CRC Press.
CWI Newsletter
Author: Perfect Lattices in Euclidean Spaces
Author: Jacques MartinetPublisher: Springer Science & Business Media
ISBN: 9783540442363
Category : Mathematics
Languages : en
Pages : 556
Book Description
Lattices are discrete subgroups of maximal rank in a Euclidean space. To each such geometrical object, we can attach a canonical sphere packing which, assuming some regularity, has a density. The question of estimating the highest possible density of a sphere packing in a given dimension is a fascinating and difficult problem: the answer is known only up to dimension 3. This book thus discusses a beautiful and central problem in mathematics, which involves geometry, number theory, coding theory and group theory, centering on the study of extreme lattices, i.e. those on which the density attains a local maximum, and on the so-called perfection property. Written by a leader in the field, it is closely related to, though disjoint in content from, the classic book by J.H. Conway and N.J.A. Sloane, Sphere Packings, Lattices and Groups, published in the same series as vol. 290. Every chapter except the first and the last contains numerous exercises. For simplicity those chapters involving heavy computational methods contain only few exercises. It includes appendices on Semi-Simple Algebras and Quaternions and Strongly Perfect Lattices.
Certain Number-Theoretic Episodes In Algebra
Author: Sivaramakrishnan RPublisher: CRC Press
ISBN: 1420015060
Category : Mathematics
Languages : en
Pages : 660
Book Description
Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important aspects of interconnections between number theory and commutative algebra. Using a pedagogical approach, the author presents the conceptual foundations of commutati
Waves in Complex Media
Author: Luca Dal NegroPublisher:
ISBN: 1009178180
Category : Science
Languages : en
Pages : 714
Book Description
This book offers a clear and interdisciplinary introduction to the structural and scattering properties of complex photonic media, focusing on deterministic aperiodic structures and their conceptual roots in geometry and number theory. It integrates important results and recent developments into a coherent and physically consistent story, balanced between mathematical designs, scattering and optical theories, and engineering device applications. The book includes discussions of emerging device applications in metamaterials and nano-optics technology. Both academia and industry will find the book of interest as it develops the underlying physical and mathematical background in partnership with engineering applications, providing a perspective on both fundamental optical sciences and photonic device technology. Emphasizing the comprehension of physical concepts and their engineering implications over the more formal developments, this is an essential introduction to the stimulating and fast-growing field of aperiodic optics and complex photonics.