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This book provides simple introduction to quantitative finance for
students and junior quants who want to approach the typical
industry problems with practical but rigorous ambition. It shows a
simple link between theoretical technicalities and practical
solutions. Mathematical aspects are discussed from a practitioner
perspective, with a deep focus on practical implications, favoring
the intuition and the imagination. In addition, the new post-crisis
paradigms, like multi-curves, x-value adjustments (xVA) and
Counterparty Credit Risk are also discussed in a very simple
framework. Finally, real world data and numerical simulations are
compared in order to provide a reader with a simple and handy
insight on the actual model performances.
A huge chasm has developed between modern science and undergraduate
education. The result of this chasm is that students who are
graduating from college are unable to exploit the many
opportunities offered by modern science and technology. Modern
science and technology widely uses the methods of classical
physics, but these modern applications are not reflected in the
physics problems often suggested to students. Solving practical
problems is a very effective way to inform students about
contemporary science, to illustrate the important relationships
between modern and classical physics, and to prepare them for
future activity in the modern technological environment. The aim of
this book is to try to bridge this chasm between modern science and
technology and an undergraduate course in physics.The first part of
the book gives an overview of 'hot' directions in modern physics
and technology. The second part includes a brief review of
undergraduate physics, followed by problems which are related to
those directions. These problems, which are based on some of the
latest developments in science and technology, can be solved using
the classical physics accessible in a standard undergraduate
program. Where necessary, the problems have detailed solutions.The
second edition of Modern Physics and Technology for Undergraduates
includes six new subsections dealing with the most recent
developments in science, and a fully updated and expanded list of
problems.
A huge chasm has developed between modern science and undergraduate
education. The result of this chasm is that students who are
graduating from college are unable to exploit the many
opportunities offered by modern science and technology. Modern
science and technology widely uses the methods of classical
physics, but these modern applications are not reflected in the
physics problems often suggested to students. Solving practical
problems is a very effective way to inform students about
contemporary science, to illustrate the important relationships
between modern and classical physics, and to prepare them for
future activity in the modern technological environment. The aim of
this book is to try to bridge this chasm between modern science and
technology and an undergraduate course in physics.The first part of
the book gives an overview of 'hot' directions in modern physics
and technology. The second part includes a brief review of
undergraduate physics, followed by problems which are related to
those directions. These problems, which are based on some of the
latest developments in science and technology, can be solved using
the classical physics accessible in a standard undergraduate
program. Where necessary, the problems have detailed solutions.The
second edition of Modern Physics and Technology for Undergraduates
includes six new subsections dealing with the most recent
developments in science, and a fully updated and expanded list of
problems.
We consider quantum dynamical systems (in general, these could be
either Hamiltonian or dissipative, but in this review we shall be
interested only in quantum Hamiltonian systems) that have, at least
formally, a classical limit. This means, in particular, that each
time-dependent quantum-mechanical expectation value X (t) has as i
cl Ii -+ 0 a limit Xi(t) -+ x1 )(t) of the corresponding classical
sys- tem. Quantum-mechanical considerations include an additional
di- mensionless parameter f = iiiconst. connected with the Planck
constant Ii. Even in the quasiclassical region where f~ 1, the dy-
namics of the quantum and classicalfunctions Xi(t) and XiCcl)(t)
will be different, in general, and quantum dynamics for expectation
val- ues may coincide with classical dynamics only for some finite
time. This characteristic time-scale, TIi., could depend on several
factors which will be discussed below, including: choice of
expectation val- ues, initial state, physical parameters and so on.
Thus, the problem arises in this connection: How to estimate the
characteristic time- scale TIi. of the validity of the
quasiclassical approximation and how to measure it in an
experiment? For rather simple integrable quan- tum systems in the
stable regions of motion of their corresponding classical phase
space, this time-scale T" usually is of order (see, for example,
[2]) const TIi. = p,li , (1.1) Q where p, is the dimensionless
parameter of nonlinearity (discussed below) and a is a constant of
the order of unity.
Quantum computing promises to solve problems which are intractable
on digital computers. Highly parallel quantum algorithms can
decrease the computational time for some problems by many orders of
magnitude. This important book explains how quantum computers can
do these amazing things. Several algorithms are illustrated: the
discrete Fourier transform, Shor's algorithm for prime
factorization; algorithms for quantum logic gates; physical
implementations of quantum logic gates in ion traps and in spin
chains; the simplest schemes for quantum error correction;
correction of errors caused by imperfect resonant pulses;
correction of errors caused by the nonresonant actions of a pulse;
and numerical simulations of dynamical behavior of the quantum
Control-Not gate. An overview of some basic elements of computer
science is presented, including the Turing machine, Boolean
algebra, and logic gates. The required quantum ideas are explained.
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