Due 2019-06-19
1st ed. 2019, X, 404 p. 50
illus.
Hardcover
ISBN 978-3-030-14807-2
Presents a new perspective on the history of mathematics teaching by looking
at descriptive geometry in the 19th century
Offers myriad international viewpoints on history of mathematics teaching
from renowned specialists across the field
Concerns relations between technics, arts and mathematics
This book seeks to explore the history of descriptive geometry in relation to its circulation in
19th century, which had been favoured by the transfers of the model of the Ecole
Polytechnique to other countries, and the diffusion of its teaching, from higher instruction to
technical and secondary teaching. In relation to thatweanalyse the role of the institutions ?
similar but definitely not identical in the different countries ? on the field under consideration.
Three main important aspects are underlined: the mathematical aspect, the aspect of teaching
in particular to non-mathematicians, and the institutions. Thebook contains 22 chapters
concerning different countries or areas, written by specialists of the history of the field.
Due 2019-07-19
1st ed. 2019, XVII, 217 p.
Hardcover
ISBN 978-3-030-14733-4
Emphasizes the modern approach to PDEs based on the notion of weak
solutions and Sobolev spaces
Covers a wide spectrum of topics in PDEs and Mathematical Physics
For many problems the reader is expected to prove simple statements
This book covers a diverse range of topics in Mathematical Physics, linear and nonlinear PDEs.
Though the text reflects the classical theory, the main emphasis is on introducing readers to
the latest developments based on the notions of weak solutions and Sobolev spaces. In
numerous problems, the student is asked to prove a given statement, e.g. to show the
existence of a solution to a certain PDE. Usually there is no closed-formula answer available,
which is why there is no answer section, although helpful hints are often provided. This
textbook offers a valuable asset for students and educators alike. As it adopts a perspective on
PDEs that is neither too theoretical nor too practical, it represents the perfect companion to a
broad spectrum of courses.
Due 2019-06-06
1st ed. 2019, XX, 312 p. 16 illus.
Softcover
ISBN 978-3-030-14052-6
Provides a rigorous yet intuitive and accessible introduction to abstract
algebra
Treats conceptually similar themes from different areas of algebra in a
unified manner
Includes numerous examples and over 700 exercises
This textbook offers an innovative approach to abstract algebra, based on a unified treatment
of similar concepts across different algebraic structures. This makes it possible to express the
main ideas of algebra more clearly and to avoid unnecessary repetition. The book consists of
two parts:The Language of AlgebraandAlgebra in Action.The unified approach to different
algebraic structures is a primary feature of the first part, which discusses the basic notions of
algebra at an elementary level. The second part is mathematically more complex, covering
topics such as the Sylow theorems, modules over principal integral domains, and Galois theory.
Intended for an undergraduate course or for self-study, the book is written in a readable,
conversational style, is rich in examples, and contains over 700 carefully selected exercises.
Due 2019-07-25
2019, Approx. 700 p.
155 illus., 113 illus. in color.
Softcover
ISBN 978-3-030-13750-2
Offers an essential introduction to the growing field of statistical applications
in finance
Addresses option pricing, analysis of financial time series, portfolio selection
and risk management, and various financial applications
Includes chapters on neural networks and deep learning, and cryptocurrencies
Using statistical software, readers can “learn by doing” and directly apply the
methods
Now in its fifth edition, this book offers a detailed yet concise introduction to the growing field
of statistical applications in finance. The reader will learn the basic methods for evaluating
option contracts, analyzing financial time series, selecting portfolios and managing risks based
on realistic assumptions about market behavior. The focus is both on the fundamentals of
mathematical finance and financial time series analysis, and on applications to specific
problems concerning financial markets, thus making the book the ideal basis for lectures,
seminars and crash courses on the topic. All numerical calculations are transparent and
reproducible using quantlets. For this new edition the book has been updated and extensively
revised and now includes several new aspects such as neural networks, deep learning, and
crypto-currencies. Both R and Matlab code, together with the data, can be downloaded from
the book’s product page and the Quantlet platform. The Quantlet platform quantlet.de, quantlet.
com, quantlet.org is an integrated QuantNet environment consisting of different types of
statistics-related documents and program codes. Its goal is to promote reproducibility and
offer a platform for sharing validated knowledge native to the social web. QuantNet and the
corresponding Data-Driven Documents-based visualization allow readers to reproduce the
tables, pictures and calculations inside this Springer book. “This book provides an excellent
introduction to the tools from probability and statistics necessary to analyze financial data.
Clearly written and accessible, it will be very useful to students and practitioners alike.” Yacine
Ait-Sahalia, Otto Hack 1903 Professor of Finance and Economics, Princeton University
Due 2019-05-30
1st ed. 2019, X, 280 p.
Softcover
ISBN 978-3-030-13757-1
Provides a detailed introduction to differential geometry on supermanifolds,
including bundles, connections and integration
Focuses on super Riemann surfaces, supergeometric analogues of Riemann
surfaces motivated by theoretical physics
Explains the relation between supergeometry and supersymmetry for the
superconformal action on super Riemann surfaces
This book treats the two-dimensional non-linear supersymmetric sigma model or spinning
string from the perspective of supergeometry. The objective is to understand its symmetries as
geometric properties of super Riemann surfaces, which are particular complex super manifolds
of dimension 1|1. The first part gives an introduction to the super differential geometry of
families of super manifolds. Appropriate generalizations of principal bundles, smooth families
of complex manifolds and integration theory are developed.The second part studies
uniformization, U(1)-structures and connections on Super Riemann surfaces and shows how
the latter can be viewed as extensions of Riemann surfaces by a gravitino field. A natural
geometric action functional on super Riemann surfaces is shown to reproduce the action
functional of the non-linear supersymmetric sigma model using a component field formalism.
The conserved currents of this action can be identified as infinitesimal deformations of the
super Riemann surface. This is in surprising analogy to the theory of Riemann surfaces and the
harmonic action functional on them. This volume is aimed at both theoretical physicists
interested in a careful treatment of the subject and mathematicians who want to become
acquainted with the potential applications of this beautiful theory.