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Given the rapid pace of development in economics and finance, a
concise and up-to-date introduction to mathematical methods has
become a prerequisite for all graduate students, even those not
specializing in quantitative finance. This book offers an
introductory text on mathematical methods for graduate students of
economics and finance-and leading to the more advanced subject of
quantum mathematics. The content is divided into five major
sections: mathematical methods are covered in the first four
sections, and can be taught in one semester. The book begins by
focusing on the core subjects of linear algebra and calculus,
before moving on to the more advanced topics of probability theory
and stochastic calculus. Detailed derivations of the Black-Scholes
and Merton equations are provided - in order to clarify the
mathematical underpinnings of stochastic calculus. Each chapter of
the first four sections includes a problem set, chiefly drawn from
economics and finance. In turn, section five addresses quantum
mathematics. The mathematical topics covered in the first four
sections are sufficient for the study of quantum mathematics;
Black-Scholes option theory and Merton's theory of corporate debt
are among topics analyzed using quantum mathematics.
This book presents various theories and algorithms to create a
quantum computer. The concept of the classical and quantum
computers, and the concept of circuits and gates are reviewed. The
example of the Deutsch and the Deutsch-Josca algorithm is discussed
to illustrate some key features of quantum computing. The Grover
algorithm, considered to be of major milestone of the subject, is
discussed in detail to exemplify the techniques used in computer
algorithms. The role of quantum superposition (also called quantum
parallelism) and of quantum entanglement is discussed in order to
understand the key advantages of a quantum over a classical
computer.
Given the rapid pace of development in economics and finance, a
concise and up-to-date introduction to mathematical methods has
become a prerequisite for all graduate students, even those not
specializing in quantitative finance. This book offers an
introductory text on mathematical methods for graduate students of
economics and finance-and leading to the more advanced subject of
quantum mathematics. The content is divided into five major
sections: mathematical methods are covered in the first four
sections, and can be taught in one semester. The book begins by
focusing on the core subjects of linear algebra and calculus,
before moving on to the more advanced topics of probability theory
and stochastic calculus. Detailed derivations of the Black-Scholes
and Merton equations are provided - in order to clarify the
mathematical underpinnings of stochastic calculus. Each chapter of
the first four sections includes a problem set, chiefly drawn from
economics and finance. In turn, section five addresses quantum
mathematics. The mathematical topics covered in the first four
sections are sufficient for the study of quantum mathematics;
Black-Scholes option theory and Merton's theory of corporate debt
are among topics analyzed using quantum mathematics.
The primary aim of this book to understand, from an unbiased point
of view, the ground-breaking paradigms and policies that have
powered China's remarkable rise: from an agricultural society to an
industrial powerhouse and a leading nation in a span of merely
forty years from 1979 to 2019. The book covers the rise of China up
to 2019 and is divided into five parts. The first part takes a
strategic view of China's rise, the second part provides a
quantitative assessment of China's rise using macroeconomic
indicators; the third part provides a historical background of
modern China, starting from the unification of China in 221 BC to
the rise to power of the Communist Party of China, leading to the
establishment of the People's Republic of China in 1949. The fourth
part analyses China's governance as well as its economic system and
lastly, part five summarizes China's rise and the paradigms that
powered this rise.
The Conference on Quantum Mechanics, Elementary Particles, Quantum
Cosmology and Complexity was held in honour of Professor Murray
Gell-Mann's 80th birthday in Singapore on 24-26 February 2010. The
conference paid tribute to Professor Gell-Mann's great achievements
in the elementary particle physics.This notable birthday volume
contains the presentations made at the conference by many eminent
scientists, including Nobel laureates C N Yang, G 't Hooft and K
Wilson. Other invited speakers include G Zweig, N Samios, M
Karliner, G Karl, M Shifman, J Ellis, S Adler and A Zichichi.About
Murray Gell-MannMurray Gell-Mann, born September 15, 1929, won the
1969 Nobel Prize in physics for his work on the theory of
elementary particles.His contributions span the entire history of
particle physics, from the early days of the particle zoo to the
modern day QCD. Along the way, even as he proposed new quantum
numbers to bring order into the zoo, he had fun in naming them. And
thus was born Strangeness, Flavor, Hadrons, Baryons, Leptons, the
Eightfold Way, Color, Quarks, Gluons and, with Harald Fritzsch, the
standard field theory of strong interactions, Quantum
Chromodynamics (QCD).He also proposed with Richard Feynman the V-A
theory of beta decay. Gell-Mann discovered the Current Algebra,
proposed (with Levy) the sigma model of pions and the see-saw
mechanism for the neutrino masses.
Quantum Chromodynamics is the theory of strong interactions: a
quantum field theory of colored gluons (Yang-Mills gauge fields)
coupled to quarks (Dirac fermion fields). Lattice gauge theory is
defined by discretizing spacetime into a four-dimensional lattice -
and entails defining gauge fields and Dirac fermions on a lattice.
The applications of lattice gauge theory are vast, from the study
of high-energy theory and phenomenology to the numerical studies of
quantum fields.Lattice Quantum Field Theory of the Dirac and Gauge
Fields: Selected Topics examines the mathematical foundations of
lattice gauge theory from first principles. It is indispensable for
the study of Dirac and lattice gauge fields and lays the foundation
for more advanced and specialized studies.
An introduction to how the mathematical tools from quantum field
theory can be applied to economics and finance, providing a wide
range of quantum mathematical techniques for designing financial
instruments. The ideas of Lagrangians, Hamiltonians, state spaces,
operators and Feynman path integrals are demonstrated to be the
mathematical underpinning of quantum field theory, and which are
employed to formulate a comprehensive mathematical theory of asset
pricing as well as of interest rates, which are validated by
empirical evidence. Numerical algorithms and simulations are
applied to the study of asset pricing models as well as of
nonlinear interest rates. A range of economic and financial topics
are shown to have quantum mechanical formulations, including
options, coupon bonds, nonlinear interest rates, risky bonds and
the microeconomic action functional. This is an invaluable resource
for experts in quantitative finance and in mathematics who have no
specialist knowledge of quantum field theory.
'Kenneth Wilson was a brilliant and creative contributor to the
work on renormalization groups and phase transitions. He applied
his multifaceted genius to condensed matter physics as well as
nuclear and elementary particle physics.'by Murray Gell-MannThe
purpose of bringing out this volume is to commemorate the memory of
Ken Wilson and to preserve the legacy of his ground-breaking
advances. This volume brings together a collection of articles
written by colleagues of Ken Wilson as well as fellow physicists
and scholars - some of who knew him personally and others who are
knowledgeable about his sterling contributions to the foundations
of theoretical physics.To commemorate the memory of Ken Wilson,
many leading and illustrious physicists have contributed to this
volume - Ian Affleck, Belal E Baaquie, Ken Bowler, Edouard Brezin,
Tohru Eguchi, Michael E Fisher, Paul Ginsparg, Domenico Giuliano,
Stanislaw Glazek, Bailin Hao, Kerson Huang, Roman Jackiw, Richard
Kenway, H R Krishnamurthy, N D Mermin, Stuart Pawley, Michael
Peskin, Alexander Polyakov, John Schwarz, R Shankar, Akira Ukawa,
David Wallace, Franz Wegner, Steven Weinberg, and Anthony Zee.
'Kenneth Wilson was a brilliant and creative contributor to the
work on renormalization groups and phase transitions. He applied
his multifaceted genius to condensed matter physics as well as
nuclear and elementary particle physics.'by Murray Gell-MannThe
purpose of bringing out this volume is to commemorate the memory of
Ken Wilson and to preserve the legacy of his ground-breaking
advances. This volume brings together a collection of articles
written by colleagues of Ken Wilson as well as fellow physicists
and scholars - some of who knew him personally and others who are
knowledgeable about his sterling contributions to the foundations
of theoretical physics.To commemorate the memory of Ken Wilson,
many leading and illustrious physicists have contributed to this
volume - Ian Affleck, Belal E Baaquie, Ken Bowler, Edouard Brezin,
Tohru Eguchi, Michael E Fisher, Paul Ginsparg, Domenico Giuliano,
Stanislaw Glazek, Bailin Hao, Kerson Huang, Roman Jackiw, Richard
Kenway, H R Krishnamurthy, N D Mermin, Stuart Pawley, Michael
Peskin, Alexander Polyakov, John Schwarz, R Shankar, Akira Ukawa,
David Wallace, Franz Wegner, Steven Weinberg, and Anthony Zee.
'Why'? Why is the world, the Universe the way it is? Is space
infinitely large? How small is small? What happens when one
continues to divide matter into ever smaller pieces? Indeed, what
is matter? Is there anything else besides what can be seen?
Pursuing the questions employing the leading notions of physics,
one soon finds that the tangible and visible world dissolves -
rather unexpectedly - into invisible things and domains that are
beyond direct perception. A remarkable feature of our Universe is
that most of its constituents turn out to be invisible, and this
fact is brought out with great force by this book.Exploring the
Invisible Universe covers the gamut of topics in advanced modern
physics and provides extensive and well substantiated answers to
these questions and many more. Discussed in a non-technical, yet
also non-trivial manner, are topics dominated by invisible things -
such as Black Holes and Superstrings as well as Fields,
Gravitation, the Standard Model, Cosmology, Relativity, the Origin
of Elements, Stars and Planetary Evolution, and more. Just giving
the answer, as so many books do, is really not telling anything at
all. To truly answer the 'why' questions of nature, one needs to
follow the chain of reasoning that scientists have used to come to
the conclusions they have. This book does not shy away from
difficult-to-explain topics by reducing them to one-line answers
and power phrases suitable for a popular talk show. The
explanations are rigorous and straight to the point. This book is
rarely mathematical without being afraid, however, to use
elementary mathematics when called for. In order to achieve this, a
large number of detailed figures, specially developed for this book
and found nowhere else, convey insights that otherwise might either
be inaccessible or need lengthy and difficult-to-follow
explanations.After Exploring the Invisible Universe, a reader will
have a deeper insight into our current understanding of the
foundations of Nature and be able to answer all the questions above
and then some. To understand Nature and the cutting edge ideas of
contemporary physics, this is the book to have.
'Why'? Why is the world, the Universe the way it is? Is space
infinitely large? How small is small? What happens when one
continues to divide matter into ever smaller pieces? Indeed, what
is matter? Is there anything else besides what can be seen?
Pursuing the questions employing the leading notions of physics,
one soon finds that the tangible and visible world dissolves -
rather unexpectedly - into invisible things and domains that are
beyond direct perception. A remarkable feature of our Universe is
that most of its constituents turn out to be invisible, and this
fact is brought out with great force by this book.Exploring the
Invisible Universe covers the gamut of topics in advanced modern
physics and provides extensive and well substantiated answers to
these questions and many more. Discussed in a non-technical, yet
also non-trivial manner, are topics dominated by invisible things -
such as Black Holes and Superstrings as well as Fields,
Gravitation, the Standard Model, Cosmology, Relativity, the Origin
of Elements, Stars and Planetary Evolution, and more. Just giving
the answer, as so many books do, is really not telling anything at
all. To truly answer the 'why' questions of nature, one needs to
follow the chain of reasoning that scientists have used to come to
the conclusions they have. This book does not shy away from
difficult-to-explain topics by reducing them to one-line answers
and power phrases suitable for a popular talk show. The
explanations are rigorous and straight to the point. This book is
rarely mathematical without being afraid, however, to use
elementary mathematics when called for. In order to achieve this, a
large number of detailed figures, specially developed for this book
and found nowhere else, convey insights that otherwise might either
be inaccessible or need lengthy and difficult-to-follow
explanations.After Exploring the Invisible Universe, a reader will
have a deeper insight into our current understanding of the
foundations of Nature and be able to answer all the questions above
and then some. To understand Nature and the cutting edge ideas of
contemporary physics, this is the book to have.
The Conference on Quantum Mechanics, Elementary Particles, Quantum
Cosmology and Complexity was held in honour of Professor Murray
Gell-Mann's 80th birthday in Singapore on 24-26 February 2010. The
conference paid tribute to Professor Gell-Mann's great achievements
in the elementary particle physics.This notable birthday volume
contains the presentations made at the conference by many eminent
scientists, including Nobel laureates C N Yang, G 't Hooft and K
Wilson. Other invited speakers include G Zweig, N Samios, M
Karliner, G Karl, M Shifman, J Ellis, S Adler and A Zichichi.About
Murray Gell-MannMurray Gell-Mann, born September 15, 1929, won the
1969 Nobel Prize in physics for his work on the theory of
elementary particles.His contributions span the entire history of
particle physics, from the early days of the particle zoo to the
modern day QCD. Along the way, even as he proposed new quantum
numbers to bring order into the zoo, he had fun in naming them. And
thus was born Strangeness, Flavor, Hadrons, Baryons, Leptons, the
Eightfold Way, Color, Quarks, Gluons and, with Harald Fritzsch, the
standard field theory of strong interactions, Quantum
Chromodynamics (QCD).He also proposed with Richard Feynman the V-A
theory of beta decay. Gell-Mann discovered the Current Algebra,
proposed (with Levy) the sigma model of pions and the see-saw
mechanism for the neutrino masses.
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