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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."
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.
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.
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 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.
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.
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