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."

An Introduction to Number Theory provides an introduction to the main streams of number theory. Starting with the unique factorization property of the integers, the theme of factorization is revisited several times throughout the book to illustrate how the ideas handed down from Euclid continue to reverberate through the subject.

In particular, the book shows how the Fundamental Theorem of Arithmetic, handed down from antiquity, informs much of the teaching of modern number theory. The result is that number theory will be understood, not as a collection of tricks and isolated results, but as a coherent and interconnected theory.

A number of different approaches to number theory are presented, and the different streams in the book are brought together in a chapter that describes the class number formula for quadratic fields and the famous conjectures of Birch and Swinnerton-Dyer. The final chapter introduces some of the main ideas behind modern computational number theory and its applications in cryptography.

Written for graduate and advanced undergraduate students of mathematics, this text will also appeal to students in cognate subjects who wish to learn some of the big ideas in number theory.

South Carolina, one of the oldest states in the Union has a very haunting history. Here find 30 ghostly stories from the coastal, central, and Piedmont areas. Find out about the famous "Gray Man" who wanders the beaches of Pawleys Island, warning residents of oncoming danger. Hear the ruckus raised by the ghost of legendary pirate Stede Bonnet, who is still seen and heard at night near the spot of his demise. Hear the sounds of battle on the calmest of evenings in Charleston, smell the smoke and gunpowder, and feel the strong sadness where soldiers fell at Fort Sumter. Visit the Cool Springs Plantation where some ghostly parties never end. From a monster at college to ghost lights in modern buildings, and more, South Carolina is home to spirits, spooks, and all manner of unearthly beings from eras long past.

While there are differences between cultures in different places and times, colonial representations of indigenous peoples generally suggest they are not capable of literature nor are they worthy of being represented as nations. Colonial representations of indigenous people continue on into the independence era and can still be detected in our time. The thesis of this book is that there are various ways to decolonize the representation of Amerindian peoples. Each chapter has its own decolonial thesis which it then resolves. Chapter 1 proves that there is coloniality in contemporary scholarship and argues that word choices can be improved to decolonize the way we describe the first Americans. Chapter 2 argues that literature in Latin American begins before 1492 and shows the long arc of Mayan expression, taking the Popol Wuj as a case study. Chapter 3 demonstrates how colonialist discourse is reinforced by a dualist rhetorical ploy of ignorance and arrogance in a Renaissance historical chronicle, Agustin de Zarate's Historia del descubrimiento y conquista del Peru. Chapter 4 shows how by inverting the Renaissance dualist configuration of civilization and barbarian, the Nahua (Aztecs) who were formerly considered barbarian can be "civilized" within Spanish norms. This is done by modeling the categories of civilization discussed at length by the Friar Bartolome de las Casas as a template that can serve to evaluate Nahua civil society as encapsulated by the historiography of Fernando de Alva Ixtlilxochitl, a possibility that would have been available to Spaniards during that time. Chapter 5 maintains that the colonialities of the pre-Independence era survive, but that Criollo-indigenous dialogue is capable of excavating their roots to extirpate them. By comparing the discussions of the hacienda system by the Peruvian essayist Manuel Gonzalez Prada and by the Mayan-Quiche eye-witness to history Rigoberta Menchu, this books shows that there is common ground between their viewpoints despite the different genres in which their work appears and despite the different countries and the eight decades that separated them, suggesting a universality to the problem of the hacienda which can be dissected. This book models five different decolonizing methods to extricate from the continuities of coloniality both indigenous writing and the representation of indigenous peoples by learned elites.

While there are differences between cultures in different places and times, colonial representations of indigenous peoples generally suggest they are not capable of literature nor are they worthy of being represented as nations. Colonial representations of indigenous people continue on into the independence era and can still be detected in our time. The thesis of this book is that there are various ways to decolonize the representation of Amerindian peoples. Each chapter has its own decolonial thesis which it then resolves. Chapter 1 proves that there is coloniality in contemporary scholarship and argues that word choices can be improved to decolonize the way we describe the first Americans. Chapter 2 argues that literature in Latin American begins before 1492 and shows the long arc of Mayan expression, taking the Popol Wuj as a case study. Chapter 3 demonstrates how colonialist discourse is reinforced by a dualist rhetorical ploy of ignorance and arrogance in a Renaissance historical chronicle, Agustin de Zarate's Historia del descubrimiento y conquista del Peru. Chapter 4 shows how by inverting the Renaissance dualist configuration of civilization and barbarian, the Nahua (Aztecs) who were formerly considered barbarian can be "civilized" within Spanish norms. This is done by modeling the categories of civilization discussed at length by the Friar Bartolome de las Casas as a template that can serve to evaluate Nahua civil society as encapsulated by the historiography of Fernando de Alva Ixtlilxochitl, a possibility that would have been available to Spaniards during that time. Chapter 5 maintains that the colonialities of the pre-Independence era survive, but that Criollo-indigenous dialogue is capable of excavating their roots to extirpate them. By comparing the discussions of the hacienda system by the Peruvian essayist Manuel Gonzalez Prada and by the Mayan-Quiche eye-witness to history Rigoberta Menchu, this books shows that there is common ground between their viewpoints despite the different genres in which their work appears and despite the different countries and the eight decades that separated them, suggesting a universality to the problem of the hacienda which can be dissected. This book models five different decolonizing methods to extricate from the continuities of coloniality both indigenous writing and the representation of indigenous peoples by learned elites.

Do ghosts exist? Is it possible that certain events can leave a mark on a location and repeat themselves over and over again? In North Carolina the answer is a definite yes! In the mountain town of Asheville, former, long-dead residents of the Smith-McDowell house still linger in the halls, reminding staff and visitors of their presence with ghostly voices. The long-dead crew of the WWII Battleship North Carolina in the Port City of Wilmington comes to life at nightthough they lost their lives in battle, they continue to go about their duties. They've been seen walking down corridors in full uniform only to vanish as they pass by witnesses! Don't miss the glowing fog at Cape Hatteras that takes on the shape of a featureless human walking towards the shore at night, and the Devil's Tramping Ground where deadly steps kill all the plant life in the Piedmont. Read 34 haunting tales and ghostly encounters from some of the most fascinating haunted locations that North Carolina has to offer!

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."

Includes up-to-date material on recent developments and topics of significant interest, such as elliptic functions and the new primality test

Selects material from both the algebraic and analytic disciplines, presenting several different proofs of a single result to illustrate the differing viewpoints and give good insight

This book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory. The journey starts with the basic idea that new number systems arise from solving different equations, leading to (abstract) algebra. Along this journey, the reader will be exposed to important ideas of mathematics, and will learn a little about how mathematics is really done.Starting at an elementary level, the book gradually eases the reader into the complexities of higher mathematics; in particular, the formal structure of mathematical writing (definitions, theorems and proofs) is introduced in simple terms. The book covers a range of topics, from the very foundations (numbers, set theory) to basic abstract algebra (groups, rings, fields), driven throughout by the need to understand concrete equations and problems, such as determining which numbers are sums of squares. Some topics usually reserved for a more advanced audience, such as Eisenstein integers or quadratic reciprocity, are lucidly presented in an accessible way. The book also introduces the reader to open source software for computations, to enhance understanding of the material and nurture basic programming skills. For the more adventurous, a number of Outlooks included in the text offer a glimpse of possible mathematical excursions. This book supports readers in transition from high school to university mathematics, and will also benefit university students keen to explore the beginnings of algebraic number theory. It can be read either on its own or as a supporting text for first courses in algebra or number theory, and can also be used for a topics course on Diophantine equations.

This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence.

Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits.

"Ergodic Theory with a view towards Number Theory" will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.

This memoir chronicles the journey of an academic, tracing a path from primary school in Zambia to a career in higher education as a mathematician and educational leader. Set against the backdrop of the 20th century, the book explores how early influences and historical events shape an individual's life and professional trajectory. The author shares childhood experiences across three parts of Africa, providing an original perspective as a witness to the post-colonial period. Through personal reflections, the memoir delves into the emergence of ideas and collaborations in mathematics and how these shape career choices. It also offers candid observations on the major changes in British higher education since the 1980s. Intended for a general audience, this book provides a compelling read for anyone interested in the experience of becoming a mathematician, and higher education in general.