2014, XXII, 672 p. 67 illus., 36 illus. in color.
Print (Book)
ISBN 978-94-007-4977-1
Print + eReference
ISBN 978-94-007-4979-5
* Covers all aspects of mathematics education through 500+ articles,
from short descriptions to in-depth pieces
* Guides readers through the range of methodologies, perspectives,
foci and cultures of mathematics education
* Updates on research and new developments in mathematics
education and references leading publications
The Encyclopedia of Mathematics Education is a comprehensive reference text, covering
every topic in the field with entries ranging from short descriptions to much longer
pieces where the topic warrants more elaboration. The entries provide access to
theories and to research in the area and refer to the leading publications for further
reading. Links will also be made to particular texts in Springer journals and e-books
through SpringerReference.com. The Encyclopedia is aimed at graduate students,
researchers, curriculum developers, policy makers, and others with interests in the field
of mathematics education. It is planned to be 700 pages in length in its hard copy form
but the text will subsequently be up-dated and developed on-line in a way that retains
the integrity of the ideas, the responsibility for which will be in the hands of the Editor-in-
Chief and the Editorial Board.
Editorial Board:
Michele Artigue
Ruhama Even
Melony Graven
Eva Jablonka
Robyn Jorgensen
Yoshinori Shimizu
Bharath Sriraman
Series: Monographs in Theoretical Computer Science. An EATCS Series
1st ed. 2015, XVIII, 264 p. 137 illus.
Hardcover
ISBN 978-3-319-25857-7
* Self-contained survey, useful for learning and reference
* Authors among key researchers in this field
* Suggests problems and directions for further research
This is the first comprehensive introduction to the theory of word-representable graphs,
a generalization of several classical classes of graphs, and a new topic in discrete
mathematics.
After extensive introductory chapters that explain the context and consolidate the
state of the art in this field, including a chapter on hereditary classes of graphs, the
authors suggest a variety of problems and directions for further research, and they
discuss interrelations of words and graphs in the literature by means other than wordrepresentability.
The book is self-contained, and is suitable for both reference and learning, with many
chapters containing exercises and solutions to seleced problems. It will be valuable for
researchers and graduate and advanced undergraduate students in discrete mathematics
and theoretical computer science, in particular those engaged with graph theory and
combinatorics, and also for specialists in algebra.
1st ed. 2015, IX, 252 p. 40 illus., 1 illus. in
Hardcover
ISBN 978-3-319-25821-8
* Introduces the basic concepts and results in number theory and
quantum computing
* Discusses three major intractable number-theoretic problems related
to the construction of modern public-key cryptography
* Discusses known quantum algorithms for solving the intractable
number-theoretic problems and for attacking the number-theoretic
cryptographic schemes
This book provides a comprehensive introduction to advanced topics in the
computational and algorithmic aspects of number theory, focusing on applications
in cryptography. Readers will learn to develop fast algorithms, including quantum
algorithms, to solve various classic and modern number theoretic problems. Key problems
include prime number generation, primality testing, integer factorization, discrete
logarithms, elliptic curve arithmetic, conjecture and numerical verification.
The author discusses quantum algorithms for solving the Integer Factorization Problem
(IFP), the Discrete Logarithm Problem (DLP), and the Elliptic Curve Discrete Logarithm
Problem (ECDLP) and for attacking IFP, DLP and ECDLP based cryptographic systems.
Chapters also cover various other quantum algorithms for Pell's equation, principal ideal,
unit group, class group, Gauss sums, prime counting function, Riemann's hypothesis and
the BSD conjecture.
Quantum Computational Number Theory is self-contained and intended to be used
either as a graduate text in computing, communications and mathematics, or as a basic
reference in the related fields. Number theorists, cryptographers and professionals
working in quantum computing, cryptography and network security will find this book a
valuable asset.
Series: Trends in Logic, Vol. 43
1st ed. 2016, VI, 283 p.
Hardcover
ISBN 978-3-319-22685-9
* Demonstrates the state of the art in proof-theoretic semantics
* Discusses topics including semantics as a methodological question
and general proof theory
* Presents each chapter as a self-contained description of a significant
research question in proof theoretic semantics
This volume is the first ever collection devoted to the field of proof-theoretic semantics.
Contributions address topics including the systematics of introduction and elimination
rules and proofs of normalization, the categorial characterization of deductions, the
relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes,
proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's
theory of constructions, paradoxical reasoning, and the defence of model theory.
The field of proof-theoretic semantics has existed for almost 50 years, but the term itself
was proposed by Schroeder-Heister in the 1980s. Proof-theoretic semantics explains
the meaning of linguistic expressions in general and of logical constants in particular
in terms of the notion of proof. This volume emerges from presentations at the Second
International Conference on Proof-Theoretic Semantics in Tubingen in 2013, where
contributing authors were asked to provide a self-contained description and analysis of a
significant research question in this area. The contributions are representative of the field
and should be of interest to logicians, philosophers, and mathematicians alike.
Series: Understanding Complex Systems
1st ed. 2016, XIV, 195 p. 83 illus., 65 illus. in
Hardcover
ISBN 978-3-319-24875-2
* Introduces and describes a new approach for modelling certain types
of complex dynamical systems
* Self-contained presentation and introductory level
* Useful as advanced text and as self-study guide
This self-contained text develops a Markov chain approach that makes the rigorous
analysis of a class of microscopic models that specify the dynamics of complex systems
at the individual level possible. It presents a general framework of aggregation in agentbased
and related computational models, one which makes use of lumpability and
information theory in order to link the micro and macro levels of observation. The starting
point is a microscopic Markov chain description of the dynamical process in complete
correspondence with the dynamical behavior of the agent-based model (ABM), which
is obtained by considering the set of all possible agent configurations as the state space
of a huge Markov chain. An explicit formal representation of a resulting gmicro-chainh
including microscopic transition rates is derived for a class of models by using the random
mapping representation of a Markov process. The type of probability distribution used
to implement the stochastic part of the model, which defines the updating rule and
governs the dynamics at a Markovian level, plays a crucial part in the analysis of gvoterlikeh
models used in population genetics, evolutionary game theory and social dynamics.
The book demonstrates that the problem of aggregation in ABMs - and the lumpability
conditions in particular - can be embedded into a more general framework that employs
information theory in order to identify different levels and relevant scales in complex
dynamical systems