Architectural Form-Finding
Provides an illustrated, self-contained introduction to the differential
geometry of curves and surfaces
Connects abstract mathematical theory with real architectural objects
Richly illustrated with over 150 figures as well as 20 QR Codes linked to
animations
Many solved exercises to go beyond the theory
This textbook provides a thorough introduction to the differential geometry of parametrized
curves and surfaces, along with a wealth of applications to specific architectural elements.
Geometric elements in architecture respond to practical, physical and aesthetic needs. Proper
understanding of the mathematics underlying the geometry provides control over the
construction. This book relates the classical mathematical theory of parametrized curves and
surfaces to multiple applications in architecture. The presentation is mathematically complete
with numerous figures and animations illustrating the theory, and special attention is given to
some of the recent trends in the field. Solved exercises are provided to see the theory in
practice. Intended as a textbook for lecture courses,Parametric Geometry of Curves and
Surfacesis suitable for mathematically-inclined students in engineering, architecture and related
fields, and can also serve as a textbook for traditional differential geometry courses to
mathematics students. Researchers interested in the mathematics of architecture or computeraided
design will also value its combination of precise mathematics and architectural examples.
Due 2021-10-16
1st ed. 2021, X, 298 p. 189 illus., 165 illus. in color.
Hardcover
ISBN 978-3-030-81316-1
Product category : Undergraduate textbook
Series : Mathematics and the Built Environment
Mathematics : Differential Geometry
Connects quadratic fields with modern algebraic number theory
Applies the theory to solve Diophantine equations
Contains hundreds of exercises with solutions
Includes original historical commentary
This undergraduate textbook provides an elegant introduction to the arithmetic of quadratic
number fields, including many topics not usually covered in books at this level. Quadratic fields
offer an introduction to algebraic number theory and some of its central objects: rings of
integers, the unit group, ideals and the ideal class group. This textbook provides solid
grounding for further study by placing the subject within the greater context of modern
algebraic number theory. Going beyond what is usually covered at this level, the book
introduces the notion of modularity in the context of quadratic reciprocity, explores the close
links between number theory and geometry via Pell conics, and presents applications to
Diophantine equations such as the Fermat and Catalan equations as well as elliptic curves.
Throughout, the book contains extensive historical comments, numerous exercises (with
solutions), and pointers to further study. Assuming a moderate background in elementary
number theory and abstract algebra, Quadratic Number Fields offers an engaging first course
in algebraic number theory, suitable for upper undergraduate students.
Due 2021-10-12
1st ed. 2021, XI, 343 p. 16 illus., 8 illus. in color.
Softcover
ISBN 978-3-030-78651-9
Product category : Undergraduate textbook
Series : Springer Undergraduate Mathematics Series
Mathematics : Number Theory
Offers a path through the theory
Includes a list of basic notation
Inspires further research on the topic
This book sketches a path for newcomers into the theory of harmonic analysis on the real line.
It presents a collection of both basic, well-known and some less known results that may serve
as a background for future research around this topic. Many of these results are also a
necessary basis for multivariate extensions. An extensive bibliography, as well as hints to open
problems are included. The book can be used as a skeleton for designing certain special
courses, but it is also suitable for self-study.
Due 2021-10-07
1st ed. 2021, IX, 199 p.
Hardcover
ISBN 978-3-030-81891-3
Product category : Graduate/advanced undergraduate textbook
Series : Pathways in Mathematics
Mathematics : Fourier Analysis
Probabilistic and Thermodynamic Descriptions of non-Markovian
Processes far From Equilibrium
Nominated as an outstanding Ph.D. thesis by the Technische Universitat
Berlin, Berlin, Germany
Addresses and advances the challenging problem of strongly fluctuating
systems that include time delay
Predicts intriguing thermodynamic properties such as reversed heat flow in
non-Markovian systems
The nonequilibrium behavior of nanoscopic and biological systems, which are typically strongly
fluctuating, is a major focus of current research. Lately, much progress has been made in
understanding such systems from a thermodynamic perspective. However, new theoretical
challenges emerge when the fluctuating system is additionally subject to time delay, e.g. due to
the presence of feedback loops. This thesis advances this young and vibrant research field in
several directions. The first main contribution concerns the probabilistic description of timedelayed
systems; e.g. by introducing a versatile approximation scheme for nonlinear delay
systems. Second, it reveals that delay can induce intriguing thermodynamic properties such as
anomalous (reversed) heat flow. More generally, the thesis shows how to treat the
thermodynamics of non-Markovian systems by introducing auxiliary variables. It turns out that
delayed feedback is inextricably linked to nonreciprocal coupling, information flow, and to net
energy input on the fluctuating level.
Due 2021-10-01
1st ed. 2021, XXII, 285 p. 81 illus., 75 illus. in color.
Hardcover
ISBN 978-3-030-80770-2
Product category : Monograph
Series : Springer Theses
Mathematics : Probability Theory and Stochastic Processes
A thorough introduction to the combinatorial approach to Mahler measure
and more
Presents results that have not previously appeared in book form
Includes new tables of small Mahler measures and limit points
Appendices on prerequisites make the book self-contained
Mahler measure, a height function for polynomials, is the central theme of this book. It has
many interesting properties, obtained by algebraic, analytic and combinatorial methods. It is the
subject of several longstanding unsolved questions, such as Lehmerfs Problem (1933) and
Boydfs Conjecture (1981). This book contains a wide range of results on Mahler measure.
Some of the results are very recent, such as Dimitrovfs proof of the Schinzel?Zassenhaus
Conjecture. Other known results are included with new, streamlined proofs. Robinsonfs
Conjectures (1965) for cyclotomic integers, and their associated Cassels height function, are
also discussed, for the first time in a book. One way to study algebraic integers is to associate
them with combinatorial objects, such as integer matrices. In some of these combinatorial
settings the analogues of several notorious open problems have been solved, and the book
sets out this recent work. Many Mahler measure results are proved for restricted sets of
polynomials, such as for totally real polynomials, and reciprocal polynomials of integer
symmetric as well as symmetrizable matrices. For reference, the book includes appendices
providing necessary background from algebraic number theory, graph theory, and other
prerequisites, along with tables of one- and two-variable integer polynomials with small Mahler
measure. All theorems are well motivated and presented in an accessible way. Numerous
exercises at various levels are given, including some for computer programming. A wide range
of stimulating open problems is also included. At the end of each chapter there is a glossary
of newly introduced concepts and definitions. Around the Unit Circle is written in a friendly,
lucid, enjoyable style, without sacrificing mathematical rigour. It is intended for lecture courses
at the graduate level, and will also be a valuable reference for researchers interested in Mahler
measure.
Due 2021-10-13
1st ed. 2021, XVI, 432 p. 25 illus.
Softcover
ISBN 978-3-030-80030-7
Product category : Graduate/advanced undergraduate textbook
Series : Universitext
Mathematics : Number Theory
Generalizes the weighted Ricci curvature and develops comparison geometry
and geometric analysis in the Finsler context
Offers an accessible entry point to studying Finsler geometry for those
familiar with differentiable manifolds
Illustrates and compares three methods for studying lower Ricci curvature
bounds: Gamma-calculus, curvature-dimension condition, needle
decomposition
This monograph presents recent developments in comparison geometry and geometric analysis
on Finsler manifolds. Generalizing the weighted Ricci curvature into the Finsler setting, the
author systematically derives the fundamental geometric and analytic inequalities in the Finsler
context. Relying only upon knowledge of differentiable manifolds, this treatment offers an
accessible entry point to Finsler geometry for readers new to the area. Divided into three parts,
the book begins by establishing the fundamentals of Finsler geometry, including Jacobi fields
and curvature tensors, variation formulas for arc length, and some classical comparison
theorems. Part II goes on to introduce the weighted Ricci curvature, nonlinear Laplacian, and
nonlinear heat flow on Finsler manifolds. These tools allow the derivation of the Bochner?
Weitzenbock formula and the corresponding Bochner inequality, gradient estimates, Bakry?
Ledouxfs Gaussian isoperimetric inequality, and functional inequalities in the Finsler setting.
Part III comprises advanced topics: a generalization of the classical Cheeger?Gromoll splitting
theorem, the curvature-dimension condition, and the needle decomposition. Throughout,
geometric descriptions illuminate the intuition behind the results, while exercises provide
opportunities for active engagement. Comparison Finsler Geometry offers an ideal gateway to
the study of Finsler manifolds for graduate students and researchers. Knowledge of
differentiable manifold theory is assumed, along with the fundamentals of functional analysis.
Familiarity with Riemannian geometry is not required, though readers with a background in the
area will find their insights are readily transferrable.
Due 2021-09-25
1st ed. 2021, XXII, 312 p. 8 illus.
Hardcover
ISBN 978-3-030-80649-1
Product category : Monograph
Series : Springer Monographs in Mathematics
Mathematics : Differential Geometry
Covers topics such as elementary row operations and Gram?Schmidt
orthogonalization, rank factorization, OR-factorization, Schurtriangularization,
diagonalization of normal matrices, etc
Includes norms on matrices as a means to deal with iterative solutions of
linear systems and exponential of a matrix
Contains exercises and problems at the end of each chapter
This book is designed to serve as a textbook for courses offered to undergraduate and
postgraduate students enrolled in Mathematics. Using elementary row operations and GramSchmidt
orthogonalization as basic tools the text develops characterization of equivalence and
similarity, and various factorizations such as rank factorization, OR-factorization,
Schurtriangularization, Diagonalization of normal matrices, Jordan decomposition, singular value
decomposition, and polar decomposition. Along with Gauss-Jordan elimination for linear
systems, it also discusses best approximations and least-squares solutions. The book includes
norms on matrices as a means to deal with iterative solutions of linear systems and
exponential of a matrix. The topics in the book are dealt with in a lively manner. Each section
of the book has exercises to reinforce the concepts, and problems have been added at the end
of each chapter. Most of these problems are theoretical, and they do not fit into the running
text linearly. The detailed coverage and pedagogical tools make this an ideal textbook for
students and researchers enrolled in senior undergraduate and beginning postgraduate
mathematics courses.
Due 2021-09-19
1st ed. 2021, IX, 194 p. 2 illus., 1 illus. in color.
Hardcover
ISBN 978-3-030-80480-0
Product category : Graduate/advanced undergraduate textbook
Mathematics : Linear Algebra
Covers risk reduction management in complex systems
Describes an artificial intelligence approach to understand complex systems
Explains the relationship between transient chaos and crises
This book presents recent developments in nonlinear and complex systems. It provides recent
theoretic developments and new techniques based on a nonlinear dynamical systems approach
that can be used to model and understand complex behavior in nonlinear dynamical systems.
It covers information theory, relativistic chaotic dynamics, data analysis, relativistic chaotic
dynamics, solvability issues in integro-differential equations, and inverse problems for parabolic
differential equations, synchronization and chaotic transient. Presents new concepts for
understanding and modeling complex systems
Due 2021-09-30
1st ed. 2021, VIII, 242 p. 94 illus., 69 illus. in color.
Hardcover
ISBN 978-3-030-79411-8
Product category : Contributed volume
Series : Nonlinear Systems and Complexity
Mathematics : Mathematical Physics