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Books > Science & Mathematics > Mathematics > General
Exploring Monte Carlo Methods is a basic text that describes the
numerical methods that have come to be known as "Monte Carlo." The
book treats the subject generically through the first eight
chapters and, thus, should be of use to anyone who wants to learn
to use Monte Carlo. The next two chapters focus on applications in
nuclear engineering, which are illustrative of uses in other
fields. Five appendices are included, which provide useful
information on probability distributions, general-purpose Monte
Carlo codes for radiation transport, and other matters. The famous
"Buffon s needle problem" provides a unifying theme as it is
repeatedly used to illustrate many features of Monte Carlo
methods.
This book provides the basic detail necessary to learn how to
apply Monte Carlo methods and thus should be useful as a text book
for undergraduate or graduate courses in numerical methods. It is
written so that interested readers with only an understanding of
calculus and differential equations can learn Monte Carlo on their
own. Coverage of topics such as variance reduction, pseudo-random
number generation, Markov chain Monte Carlo, inverse Monte Carlo,
and linear operator equations will make the book useful even to
experienced Monte Carlo practitioners.
Provides a concise treatment of generic Monte Carlo methods
Proofs for each chapter
Appendixes include Certain mathematical functions; Bose Einstein
functions, Fermi Dirac functions, Watson functions"
This book is devoted to the study of stochastic measures (SMs). An
SM is a sigma-additive in probability random function, defined on a
sigma-algebra of sets. SMs can be generated by the increments of
random processes from many important classes such as
square-integrable martingales and fractional Brownian motion, as
well as alpha-stable processes. SMs include many well-known
stochastic integrators as partial cases.General Stochastic Measures
provides a comprehensive theoretical overview of SMs, including the
basic properties of the integrals of real functions with respect to
SMs. A number of results concerning the Besov regularity of SMs are
presented, along with equations driven by SMs, types of solution
approximation and the averaging principle. Integrals in the Hilbert
space and symmetric integrals of random functions are also
addressed.The results from this book are applicable to a wide range
of stochastic processes, making it a useful reference text for
researchers and postgraduate or postdoctoral students who
specialize in stochastic analysis.
The valuation of the liability structure can be determined by real
options because the shares of a company can be regarded as similar
to the purchase of a financial call option. Therefore, from this
perspective, debt can be viewed as the sale of a financial put
option. As a result, financial analysts are able to establish
different valuations of a company, according to these two financing
methods. Valuation of the Liability Structure by Real Options
explains how the real options method works in conjunction with
traditional methods. This innovative approach is particularly
suited to the valuation of companies in industries where an
underlying asset has high volatility (such as the mining or oil
industries) or where research and development costs are high (for
example, the pharmaceutical industry). Integration of the economic
value of net debt (rather than the accounting value) and
integration of the asset volatility are the main advantages of this
approach.
These materials were developed, in part, by a grant from the
federally-funded Mathematics and Science Partnership through the
Center for STEM Education. Some of the activities were adapted from
the National Council of Teachers of Mathematics Illuminations, the
National Library of Virtual Manipulatives, Hands-On Math Projects
with Real Applications by Judith A. Muschla and Gary R. Muschla,
Learning Math with Calculators: Activities for Grades 3-8 by Len
Sparrow and Paul Swan, and Mathematical Ideas by Charles D. Miller,
Vern E. Heeren and John Hornsby.
For anyone interested in the history and effects of the
introduction of so-called "Modern Mathematics" (or "Mathematique
Moderne," or "New Mathematics," etc.) this book, by Dirk De Bock
and Geert Vanpaemel, is essential reading. The two authors are
experienced and highly qualified Belgian scholars and the book
looks carefully at events relating to school mathematics for the
period from the end of World War II to 2010. Initially the book
focuses on events which helped to define the modern mathematics
revolution in Belgium before and during the 1960s. The book does
much more than that, however, for it traces the influence of these
events on national and international debates during the early
phases of the reform. By providing readers with translations into
English of relevant sections of key Continental documents outlining
the major ideas of leading Continental scholars who contributed to
the "Mathematique Moderne" movement, this book makes available to a
wide readership, the theoretical, social, and political backdrops
of Continental new mathematics reforms. In particular, the book
focuses on the contributions made by Belgians such as Paul Libois,
Willy Servais, Frederique Lenger, and Georges Papy. The influence
of modern mathematics fell away rapidly in the 1970s, however, and
the authors trace the rise and fall, from that time into the 21st
century, of a number of other approaches to school mathematics-in
Belgium, in other Western European nations, and in North America.
In summary, this is an outstanding, landmark publication displaying
the fruits of deep scholarship and careful research based on
extensive analyses of primary sources.
This book provides an insightful view of effective teaching
practices in China from an international perspective by examining
the grades 7-12 mathematics teacher preparation in the Shandong
province of China. It is an excellent reference book for teacher
educators, researchers, reformers, and teaching practitioners. A
qualitative research approach, involving in-depth interviews with
purposive sampling of ten grades 7-12 award-winning mathematics
teachers, was chosen to conduct the study. The participants are
from the Shandong province and have been awarded recognition for
his/her achievements in teaching grades 7-12 mathematics by the
different levels: school, district, city, province, or nation; and
his/her students have achieved high average scores in college
entrance exams or in high school entrance exams among the classes
at the same grade level. Data analysis revealed the following
findings: first, grades 7-12 mathematics teachers from the Shandong
province of China were prepared to teach through pre-service
training, in-service training, and informal learning. The
pre-service training can be characterized as emphasizing formal
mathematics training at advanced level. The in-service training is
integrated with teacher collaboration and teaching research, and
has the characteristics of diversity, continuity, and orientation
toward teaching practice. The in-service training also stimulates
teachers to conduct selfdirected learning. Second, the
award-winning grades 7-12 mathematics teachers are identified by
the following characteristics: they are passionate about
mathematics and share their passion through teaching; they actively
take part in teaching research through application of teaching
research in the classroom, collaboration with peers, and systematic
lesson preparation; they apply technology into teaching; and they
take an active role in teaching research in order to expand their
professional opportunities. Based on the findings of this study,
the following conclusions were reached: pre-service training and
in-service training are both necessary processes for mathematics
teachers to build up their knowledge base for effective teaching.
Pre-service training is just a starting point for the teaching
profession. In-service training, integrated with teacher
collaboration and teaching research should be a continuous activity
that is a part of a teacher's everyday life.
AN INTRODUCTION TO DIFFERENTIAL GEOMETRY WITH USE OF THE TENSOR
CALCULUS By LUTHER PFAHLER EISENHART. Preface: Since 1909, when my
Differential Geometry of Curves and Surfaces was published, the
tensor calculus, which had previously been invented by Ricci, was
adopted by Einstein in his General Theory of Relativity, and has
been developed further in the study of Riemannian Geometry and
various generalizations of the latter. In the present book the
tensor calculus of cuclidean 3-space is developed and then
generalized so as to apply to a Riemannian space of any number of
dimensions. The tensor calculus as here developed is applied in
Chapters III and IV to the study of differential geometry of
surfaces in 3-space, the material treated being equivalent to what
appears in general in the first eight chapters of my former book
with such additions as follow from the introduction of the concept
of parallelism of Levi-Civita and the content of the tensor
calculus. LUTHER PFAHLER EISENHART. Contents include: CHAPTER I
CURVES IN SPACE SECTION PAGE 1. Curves ami surfaces. The summation
convention 1 2. Length of a curve. Linear element, 8 3. Tangent to
a curve. Order of contact. Osculating plane 11 4. Curvature.
Principal normal. Circle of curvature 16 5. TBi normal. Torsion 19
6r The Frenet Formulas. The form of a curve in the neighborhood of
a point 25 7. Intrinsic equations of a curve 31 8. Involutes and
evolutes of a curve 34 9. The tangent surface of a curve. The polar
surface. Osculating sphere. . 38 10. Parametric equations of a
surface. Coordinates and coordinate curves trT a surface 44 11. 1
Tangent plane to a surface 50 tSffDovelopable surfaces. Envelope of
a one-parameter family ofsurfaces. . 53 CHAPTER II TRANSFORMATION
OF COORDINATES. TENSOR CALCULUS 13. Transformation of coordinates.
Curvilinear coordinates 63 14. The fundamental quadratic form of
space 70 15. Contravariant vectors. Scalars 74 16. Length of a
contravariant vector. Angle between two vectors 80 17. Covariant
vectors. Contravariant and covariant components of a vector 83 18.
Tensors. Symmetric and skew symmetric tensors 89 19. Addition,
subtraction and multiplication of tensors. Contraction.... 94 20.
The Christoffel symbols. The Riemann tensor 98 21. The Frenet
formulas in general coordinates 103 22. Covariant differentiation
107 23. Systems of partial differential equations of the first
order. Mixed systems 114 CHAPTER III INTRINSIC GEOMETRY OF A
SURFACE 24. Linear element of a surface. First fundamental
quadratic form of a surface. Vectors in a surface 123 25. Angle of
two intersecting curves in a surface. Element of area 129 26.
Families of curves in a surface. Principal directions 138 27. The
intrinsic geometry of a surface. Isometric surfaces 146 28. The
Christoffel symbols for a surface. The Riemannian curvature tensor.
The Gaussian curvature of a surface 149 29. Differential parameters
155 30. Isometric orthogonal nets. Isometric coordinates 161 31...
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