Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements.
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.
Added by: alexa19 | Karma: 4030.48 | Black Hole | 29 March 2010
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How Solve Word Problems in Arithmetic
Nothing strikes fear into the hearts of math students more than word problems. In How to Solve Word Problems in Arithmetic, noted math teacher Phyllis Pullman defangs the dreaded word problem for 5th through 8th grade-level arithmetic students by emphasizing the mechanics and grammar of problem-solving, and focusing on problems involving arithmetic skills, area, percent, basic geometry, measurement, and statistics.
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Groups Acting on Hyperbolic Space: Harmonic Analysis and Number Theory
This book deals with a broad range of topics from the theory of automorphic functions on three-dimensional hyperbolic space and its arithmetic group theoretic and geometric ramifications. Starting off with several models of hyperbolic space and its group of motions the authors discuss the spectral theory of the Laplacian and Selberg's theory for cofinite groups. This culminates in explicit versions of the Selberg trace formula and the Selberg zeta-function.
This book will help children learn to add 3, 4, 5 and bigger single-digit numbers in a step-by-step manner, thereby solidifying their calculation skills. Building basic addition skills is vital to later understanding the decimal system, which is the foundation of higher-level arithmetic concepts and skills taught at school. The purpose of this book is to prepare children for school-level math.
