The first biography to cover all aspects of Felix Klein’s life and work
Demonstrates all the ways in which Felix Klein played a pioneering role
Illustrate the wide variety of programs that Klein developed for mathematics,
its applications, its organization, and mathematical instruction
One of his prominent female collaborators was Emmy Noether, whose career
Klein promoted and whose famous Noether theorems he sought to make
known among physicists
Provides insight into the most important mathematical schools and research
directions in Germany as well as into the relationships between the
mathematicians themselves
About Felix Klein, the famous Greek mathematician Constantin Caratheodory once said: “It is
only by illuminating him from all angles that one can come to understand his significance.”
The author of this biography has done just this. A detailed study of original sources has made
it possible to uncover new connections; to create a more precise representation of this
important mathematician, scientific organizer, and educational reformer; and to identify
misconceptions. Because of his edition of Julius Plucker’s work on line geometry and due to
his own contributions to non-Euclidean geometry, Klein was already well known abroad before
he received his first full professorship at the age of 23. By exchanging ideas with his most
important cooperation partner, the Norwegian Sophus Lie, Klein formulated his Erlangen
Program. Various other visionary programs followed, in which Klein involved mathematicians
from Germany and abroad. Klein was the most active promoter of Riemann’s geometricphysical
approach to function theory, but he also integrated the analytical approaches of the
Weierstrass school into his arsenal of methods. Klein was a citizen of the world who repeatedly
travelled to France, Great Britain, Italy, the United States, and elsewhere. Despite what has
often been claimed, it must be emphasized that Klein expressly opposed national chauvinism.
He promoted mathematically gifted individuals regardless of their nationality, religion, or gender
1st ed. 2021, XX, 677 p.
Hardcover
ISBN 978-3-030-75784-7
Product category : Biography
Series : Vita Mathematica
Mathematics : History of Mathematics
Overviews key topics in foundations of quantum mechanics
Easy to understand presentations of core topics in fundamental physics
An unusually broad set of writings across topics in quantum interferometry
This book presents a collection of novel contributions and reviews by renowned researchers in
the foundations of quantum physics, quantum optics, and neutron physics. It is published in
honor of Michael Horne, whose exceptionally clear and groundbreaking work in the foundations
of quantum mechanics and interferometry, both of photons and of neutrons, has provided
penetrating insight into the implications of modern physics for our understanding of the
physical world. He is perhaps best known for the Clauser-Horne-Shimony-Holt (CHSH)
inequality. This collection includes an oral history of Michael Horne's contributions to the
foundations of physics and his connections to other eminent figures in the history of the
subject, among them Clifford Shull and Abner Shimony
Due 2021-08-17
1st ed. 2021, XIX, 223 p. 28 illus., 9 illus. in color.
Hardcover
ISBN 978-3-030-77366-3
Product category : Monograph
Series : Fundamental Theories of Physics
Physics : Quantum Physics
The first monograph applying machine learning to problems of geometry
Provides a data-driven introduction to computational algebraic geometry
Delivers a quick introduction to modern data science, with code in popular
software (Python, SageMath and Mathematica)
Includes background in geometry, algebra, and theoretical physics
Can artificial intelligence learn mathematics? The question is at the heart of this original
monograph bringing together theoretical physics, modern geometry, and data science. The
study of Calabi?Yau manifolds lies at an exciting intersection between physics and
mathematics. Recently, there has been much activity in applying machine learning to solve
otherwise intractable problems, to conjecture new formulae, or to understand the underlying
structure of mathematics. In this book, insights from string and quantum field theory are
combined with powerful techniques from complex and algebraic geometry, then translated into
algorithms with the ultimate aim of deriving new information about Calabi?Yau manifolds.
While the motivation comes from mathematical physics, the techniques are purely
mathematical and the theme is that of explicit calculations. The reader is guided through the
theory and provided with explicit computer code in standard software such as SageMath,
Python and Mathematica to gain hands-on experience in applications of artificial intelligence to
geometry. Driven by data and written in an informal style, The Calabi?Yau Landscape makes
cutting-edge topics in mathematical physics, geometry and machine learning readily accessible
to graduate students and beyond. The overriding ambition is to introduce some modern
mathematics to the physicist, some modern physics to the mathematician, and machine
learning to both.
Due 2021-08-13
1st ed. 2021, XVII, 206 p. 36 illus., 26 illus. in color.
Softcover
ISBN 978-3-030-77561-2
Product category : Monograph
Series : Lecture Notes in Mathematics
Mathematics : Algebraic Geometry
Provides a comprehensive introduction to polyfold theory
Generalizes nonlinear functional analysis and differential geometry
Describes a general nonlinear Fredholm theory in spaces with locally varying
dimensions
This book pioneers a nonlinear Fredholm theory in a general class of spaces called polyfolds.
The theory generalizes certain aspects of nonlinear analysis and differential geometry, and
combines them with a pinch of category theory to incorporate local symmetries. On the
differential geometrical side, the book introduces a large class of `smooth’ spaces and bundles
which can have locally varying dimensions (finite or infinite-dimensional). These bundles come
with an important class of sections, which display properties reminiscent of classical nonlinear
Fredholm theory and allow for implicit function theorems. Within this nonlinear analysis
framework, a versatile transversality and perturbation theory is developed to also cover
equivariant settings. The theory presented in this book was initiated by the authors between
2007-2010, motivated by nonlinear moduli problems in symplectic geometry. Such problems
are usually described locally as nonlinear elliptic systems, and they have to be studied up to a
notion of isomorphism. This introduces symmetries, since such a system can be isomorphic to
itself in different ways. Bubbling-off phenomena are common and have to be completely
understood to produce algebraic invariants. This requires a transversality theory for bubblingoff
phenomena in the presence of symmetries. Very often, even in concrete applications,
geometric perturbations are not general enough to achieve transversality, and abstract
perturbations have to be considered. The theory is already being successfully applied to its
intended applications in symplectic geometry, and should find applications to many other areas
where partial differential equations, geometry and functional analysis meet. Written by its
originators, Polyfold and Fredholm Theory is an authoritative and comprehensive treatise of
polyfold theory. It will prove invaluable for researchers studying nonlinear elliptic problems
arising in geometric contexts.
Due 2021-09-19
1st ed. 2021, X, 1010 p. 12 illus., 10 illus. in color.
Hardcover
ISBN 978-3-030-78006-7
Product category : Monograph
Series : Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge
/ A Series of Modern Surveys in Mathematics
Mathematics : Global Analysis and Analysis on Manifolds
A Volume in Honor of Lance Littlejohn's 70th Birthday
Celebrates Lance Littlejohn's achievements
Spans over many areas in analysis
Contains contributions of international specialists
The main topics of this volume, dedicated to Lance Littlejohn, are operatorand spectral theory,
orthogonal polynomials, combinatorics, number theory, andthe various interplays of these
subjects. Although the event, originally scheduledas the Baylor Analysis Fest, had to be
postponed due to the pandemic, scholarsfrom around the globe have contributed research in a
broad range of mathematicalfields. The collection will be of interest to both graduate students
and professionalmathematicians. Contributors are: G.E. Andrews, B.M. Brown, D. Damanik, M.L.
Dawsey, W.D.Evans, J. Fillman, D. Frymark, A.G. Garcia, L.G. Garza, F. Gesztesy, D. Gomez-Ullate,
Y. Grandati, F.A. Grunbaum, S. Guo, M. Hunziker, A. Iserles, T.F. Jones,K. Kirsten, Y. Lee, C. Liaw, F.
Marcellan, C. Markett, A. Martinez-Finkelshtein, D.McCarthy, R. Milson, D. Mitrea, I. Mitrea, M.
Mitrea, G. Novello, D. Ong,K. Ono,J.L. Padgett, M.M.M. Pang, T. Poe, A. Sri Ranga, K. Schiefermayr,
Q. Sheng, B.Simanek,J. Stanfill, L. Velazquez, M. Webb, J. Wilkening, I.G. Wood, M. Zinchenko.
Due 2021-09-16
1st ed. 2021, X, 290 p. 28 illus., 20 illus. in color.
Hardcover
ISBN 978-3-030-75424-2
Product category : Contributed volume
Series : Operator Theory: Advances and Applications
Mathematics : Operator Theory
Presents valuable resource for students and statisticians using survey
sampling
Offers new sampling designs
Provides sampling methods and application of statistical inference methods
in economics research
This short monograph provides a synthesis of new research on sampling designs that are
dependent on sample moments or the order statistics of auxiliary variables. The range of
survey sampling methods and their applications has gradually increased over time, and these
applications have led to new theoretical solutions that provide better sampling designs or
estimators. Recently, several important properties of sampling designs have been discovered,
and many new methods have been published.Offering an overview of these developments, this
book describes sampling designs dependent on the sample generalized variance of auxiliary
variables, examines properties of sampling designs proportional to functions of sample order
statistics of the auxiliary variable, and takes into account continuous sampling designs. The text
will be useful for students and statisticians whose work involves survey sampling, and it will
inspire those looking for new sampling designs dependent on auxiliary variables.
Due 2021-10-21
2nd ed. 2021, X, 102 p. 29 illus.
Softcover
ISBN 978-3-662-63412-7
Product category : Brief
Series : SpringerBriefs in Statistics
Statistics : Statistical Theory and Methods
https://doi.org/10.1142/12222 | May 2021
Pages: 160
ISBN: 978-981-123-472-9 (hardcover)
ISBN: 978-981-123-611-2 (softcover)
The author has published two texts on classical physics, Introduction to Classical Mechanics and Introduction to Electricity and Magnetism, both meant for initial one-quarter physics courses. The latter is based on a course taught at Stanford several years ago with over 400 students enrolled. These lectures, aimed at the very best students, assume a good concurrent course in calculus; they are otherwise self-contained. Both texts contain an extensive set of accessible problems that enhances and extends the coverage. As an aid to teaching and learning, the solutions to these problems have now been published in additional texts.
The present text completes the first-year introduction to physics with a set of lectures on Introduction to Quantum Mechanics, the very successful theory of the microscopic world. The Schrodinger equation is motivated and presented. Several applications are explored, including scattering and transition rates. The applications are extended to include quantum electrodynamics and quantum statistics. There is a discussion of quantum measurements. The lectures then arrive at a formal presentation of quantum theory together with a summary of its postulates. A concluding chapter provides a brief introduction to relativistic quantum mechanics. An extensive set of accessible problems again enhances and extends the coverage.
The goal of these three texts is to provide students and teachers alike with a good, understandable, introduction to the fundamentals of classical and quantum physics.
Preface
Motivation
Wave Packet for Free Particle
Include Potential V (x)
Scattering
Transition Rate
Quantum Electrodynamics
Quantum Statistics
Quantum Measurements
Formal Structure of Quantum Mechanics
Quantum Mechanics Postulates
Relativity
Problems
Appendix A: Electromagnetic Field in Normal Modes
Appendix B: Significant Names in Quantum Mechanics ? Theory and Applications
Bibliography
Index
Undergraduate students in physics.
https://doi.org/10.1142/12314 | June 2021
Pages: 384
ISBN: 978-981-123-827-7 (hardcover)
ISBN: 978-981-123-849-9 (softcover)
This textbook provides lecture materials of a comprehensive course in Classical Mechanics developed by the author over many years with input from students and colleagues alike. The richly illustrated book covers all major aspects of mechanics starting from the traditional Newtonian perspective, over Lagrangian mechanics, variational principles and Hamiltonian mechanics, rigid-body, and continuum mechanics, all the way to deterministic chaos and point-particle mechanics in special relativity. Derivation steps are worked out in detail, illustrated by examples, with ample explanations.
Developed by a classroom practitioner, the book provides a comprehensive overview of classical mechanics with judicious material selections that can be covered in a one-semester course thus streamlining the instructor's task of choosing materials for their course. The usefulness for instructors notwithstanding, the primary aim of the book is to help students in their understanding, with detailed derivations and explanations, and provide focused guidance for their studies by repeatedly emphasizing how various topics are tied together by common physics principles.
Preface
Newtonian Mechanics
Lagrangian Mechanics
Variational Principles
Hamiltonian Mechanics
Mechanics of Rigid Bodies
Small Oscillations
Continuum Mechanics
Beyond Classical Mechanics
Appendices:
Coordinates, Vector Operations, etc.
Dirac δ Distribution
Green's Function Method: An Example
Index
Advanced undergraduates and graduates in Physics.