Kategoria BISAC: Mathematics >> Number Theory

In Single Digits, Marc Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas of mathematics, including number theory, geometry, chaos theory, numerical analysis, and mathematical physics. For instance, why do eight perfect card shuffles leave a standard deck of cards unchanged? And, are there really "six degrees of separation" between all pairs of people? Chamberland explores these questions and covers vast numerical territory, such as illustrating the ways that the number...

This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters. Studying zeros of Selberg zeta functions for character deformations allows us to access the discrete spectra and resonances of hyperbolic Laplacians under both singular and non-singular perturbations. Areas in which the theory has not yet been sufficiently developed, such as the spectral theory of transfer operators or the singular perturbation theory of hyperbolic Laplacians, will profit from the numerical experiments discussed...

Now in its third decade, the Colorado Mathematical Olympiad (CMO), founded by the author, has become an annual state-wide competition, hosting many hundreds of middle and high school contestants each year. This book presents a year-by-year history of the CMO from 2004-2013 with all the problems from the competitions and their solutions. Additionally, the book includes 10 further explorations, bridges from solved Olympiad problems to 'real' mathematics, bringing young readers to the forefront of various fields of mathematics. This book contains more than just problems,...

This unique book explores the world of q, known technically as basic hypergeometric

series, and represents the author's personal and life-long study--inspired by Ramanujan--of

aspects of this broad topic. While the level of mathematical sophistication is

graduated, the book is designed to appeal to advanced undergraduates as well as

researchers in the field. The principal aims are to demonstrate the power of the methods

and the beauty of the results. The book contains novel proofs of many results in the

theory of partitions and the theory of...

Important results surrounding the proof of Goldbach's ternary conjecture are presented in this book. Beginning with an historical perspective along with an overview of essential lemmas and theorems, this monograph moves on to a detailed proof of Vinogradov's theorem. The principles of the Hardy-Littlewood circle method are outlined and applied to Goldbach's ternary conjecture. New results due to H. Maier and the author on Vinogradov's theorem are proved under the assumption of the Riemann hypothesis. The final chapter discusses an approach to Goldbach's conjecture through...

Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects.

The book focuses on both old and new results towards the solution of long-standing problems as well as it features some key historical remarks. The purpose of this volume is to present in a unified way...

Prime numbers have intrigued, inspired and infuriated mathematicians for millennia. Every school student studies prime numbers and can...

Essential number tracing practice for preschool and kindergarten.This fun book is a great way for children ages 3 and up to learn their numbers (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9) while practicing fine motor skills.

• Uppercase and lowercase letters
• Tracing sentences
• Quickly improve your child's handwriting
• Positive text helps to boost your chil's happiness and slft-esteem
• Best and most complete handwriting workbook
• Instant access to free online...