Heights of Polynomials and Entropy in Algebraic Dynamics

2013-06-29
Heights of Polynomials and Entropy in Algebraic Dynamics
Author: Graham Everest
Publisher: Springer Science & Business Media
Total Pages: 217
Release: 2013-06-29
Genre: Mathematics
ISBN: 1447138988
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The main theme of this book is the theory of heights as they appear in various guises. This includes a large body of results on Mahlers measure of the height of a polynomial. The authors'approach is very down to earth as they cover the rationals, assuming no prior knowledge of elliptic curves. The chapters include examples and particular computations, with all special calculation included so as to be self-contained. The authors devote space to discussing Mahlers measure and to giving some convincing and original examples to explain this phenomenon. XXXXXXX NEUER TEXT The main theme of this book is the theory of heights as it appears in various guises. To this §End.txt.Int.:, it examines the results of Mahlers measure of the height of a polynomial, which have never before appeared in book form. The authors take a down-to-earth approach that includes convincing and original examples. The book uncovers new and interesting connections between number theory and dynamics and will be interesting to researchers in both number theory and nonlinear dynamics.

Geometric Methods in Algebra and Number Theory

2006-06-22
Geometric Methods in Algebra and Number Theory
Author: Fedor Bogomolov
Publisher: Springer Science & Business Media
Total Pages: 365
Release: 2006-06-22
Genre: Mathematics
ISBN: 0817644172
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* Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory * The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry * Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry

The Arithmetic of Dynamical Systems

2010-05-05
The Arithmetic of Dynamical Systems
Author: J.H. Silverman
Publisher: Springer Science & Business Media
Total Pages: 518
Release: 2010-05-05
Genre: Mathematics
ISBN: 038769904X
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This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function. A principal theme of arithmetic dynamics is that many of the fundamental problems in the theory of Diophantine equations have dynamical analogs.This graduate-level text provides an entry for students into an active field of research and serves as a standard reference for researchers.

From Analysis to Visualization

2020-03-16
From Analysis to Visualization
Author: David H. Bailey
Publisher: Springer Nature
Total Pages: 447
Release: 2020-03-16
Genre: Mathematics
ISBN: 3030365689
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Students and researchers from all fields of mathematics are invited to read and treasure this special Proceedings. A conference was held 25 –29 September 2017 at Noah’s On the Beach, Newcastle, Australia, to commemorate the life and work of Jonathan M. Borwein, a mathematician extraordinaire whose untimely passing in August 2016 was a sorry loss to mathematics and to so many members of its community, a loss that continues to be keenly felt. A polymath, Jonathan Borwein ranks among the most wide ranging and influential mathematicians of the last 50 years, making significant contributions to an exceptional diversity of areas and substantially expanding the use of the computer as a tool of the research mathematician. The contributions in this commemorative volume probe Dr. Borwein's ongoing legacy in areas where he did some of his most outstanding work: Applied Analysis, Optimization and Convex Functions; Mathematics Education; Financial Mathematics; plus Number Theory, Special Functions and Pi, all tinged by the double prisms of Experimental Mathematics and Visualization, methodologies he championed.

Noise, Oscillators and Algebraic Randomness

2008-01-11
Noise, Oscillators and Algebraic Randomness
Author: Michel Planat
Publisher: Springer
Total Pages: 417
Release: 2008-01-11
Genre: Science
ISBN: 3540454632
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Noise is ubiquitous in nature and in man-made systems. Noise in oscillators perturbs high-technology devices such as time standards or digital communication systems. The understanding of its algebraic structure is thus of vital importance. The book addresses both the measurement methods and the understanding of quantum, 1/f and phase noise in systems such as electronic amplifiers, oscillators and receivers, trapped ions, cosmic ray showers and in commercial applications. A strong link between 1/f noise and number theory is emphasized. The twenty papers in the book are comprehensive versions of talks presented at a school in Chapelle des Bois (Jura, France) held from April 6 to 10, 1999, by engineers, physisicts and mathematicians.

Number Theory and Polynomials

2008-05-08
Number Theory and Polynomials
Author: James Fraser McKee
Publisher: Cambridge University Press
Total Pages: 350
Release: 2008-05-08
Genre: Mathematics
ISBN: 0521714672
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Contributions by leading experts in the field provide a snapshot of current progress in polynomials and number theory.

Discourses on Algebra

2012-12-06
Discourses on Algebra
Author: Igor R. Shafarevich
Publisher: Springer Science & Business Media
Total Pages: 288
Release: 2012-12-06
Genre: Mathematics
ISBN: 3642563252
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Using various examples this monograph shows that algebra is one of the most beautiful forms of mathematics. In doing so, it explains the basics of algebra, number theory, set theory and probability. The text presupposes very limited knowledge of mathematics, making it an ideal read for anybody new to the subject. The author, I.R. Shafarevich, is well-known across the world as one of the most outstanding mathematicians of this century as well as one of the most respected mathematical writers.