Reinterpreting History of Mathematics in North America 1607-1865
Presents the first history of mathematics written from "mathematics for all" vantage point
Introduces readers to a wide range of important but rare primary sources
Includes numerous photographs of key sections from major primary sources
This book presents a history of mathematic between 1607 and 1865 in that part of mainland
North America which is north of Mexico but excludes the present-day Canada and Alaska.
Unlike most other histories of mathematics now available, the emphasis is on the gradual
emergence of "mathematics for all" programs and associated changes in thinking which drove
this emergence. The book takes account of changing ideas about intended, implemented and
attained mathematics curricula for learners of all ages. It also pays attention to the
mathematics itself, and to how it was taught and learned.
Due 2021-11-07
1st ed. 2021, XVI, 350 p. 92 illus., 23 illus. in color.
Hardcover : ISBN 978-3-030-85723-3
Product category : Monograph
Series : History of Mathematics Education
Mathematics : History of Mathematics
Provides an applied and unified introduction to parametric, nonparametric
and semiparametric regression
Closes the gap between theory and application, featuring examples and
applications, and user-friendly software
Features data sets and software online at www.regressionbook.org
Now in its second edition, this textbook provides an applied and unified introduction to
parametric, nonparametric and semiparametric regression that closes the gap between theory
and application. The most important models and methods in regression are presented on a
solid formal basis, and their appropriate application is shown through numerous examples and
case studies. The most important definitions and statements are concisely summarized in
boxes, and the underlying data sets and code are available online on the book’s dedicated
website. Availability of (user-friendly) software has been a major criterion for the methods
selected and presented. The chapters address the classical linear model and its extensions,
generalized linear models, categorical regression models, mixed models, nonparametric
regression, structured additive regression, quantile regression and distributional regression
models. Two appendices describe the required matrix algebra, as well as elements of
probability calculus and statistical inference. In this substantially revised and updated new
edition the overview on regression models has been extended, and now includes the relation
between regression models and machine learning, additional details on statistical inference in
structured additive regression models have been added and a completely reworked chapter
augments the presentation of quantile regression with a comprehensive introduction to
distributional regression models. Regularization approaches are now more extensively
discussed in most chapters of the book. The book primarily targets an audience that includes
students, teachers and practitioners in social, economic, and life sciences, as well as students
and teachers in statistics programs, and mathematicians and computer scientists with interests
in statistical modeling and data analysis. It is written at an intermediate mathematical level
and assumes only knowledge of basic probability, calculus, matrix algebra and statistics.
Due 2021-10-30
2nd ed. 2021, XX, 690 p.200 illus., 3 illus. in color.
Hardcover : ISBN 978-3-662-63881-1
Product category : Graduate/advanced undergraduate textbook
Statistics : Statistical Theory and Methods
Features numerous contributions on Hilbert's axiomatic method
Authored by leading experts in the subject
Addressed to logicians, philosophers, physicists and computer scientists with
an interest in foundations
In this two-volume compilation of articles, leading researchers reevaluate the success of
Hilbert's axiomatic method, which not only laid the foundations for our understanding of
modern mathematics, but also found applications in physics, computer science and elsewhere.
The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a
meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of
Hilbert's return to his foundational studies, which ultimately resulted in the establishment of
proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used
the opportunity to bring Paul Bernays back to Gottingen as his main collaborator in
foundational studies in the years to come. The contributions are addressed to mathematical
and philosophical logicians, but also to philosophers of science as well as physicists and
computer scientists with an interest in foundations.
Due 2021-10-23
1st ed. 2021, XVI, 322 p. 15 illus., 7 illus. in color.
Hardcover : ISBN 978-3-030-77798-2
Product category : Contributed volume
Mathematics : Mathematical Logic and Foundations
Applications to Discontinuous Differential Equations
This book opens a novel and fruitful line of research based on a generalized degree theory
Expands available techniques employed to prove existence of solutions for
discontinuous problems
Presents many potential applications to other fields
This unique book contains a generalization of the Leray-Schauder degree theory which applies
for wide and meaningful types of discontinuous operators. The discontinuous degree theory
introduced in the first section is subsequently used to prove new, applicable, discontinuous
versions of many classical fixed-point theorems such as Schauder’s. Finally, readers will find in
this book several applications of those discontinuous fixed-point theorems in the proofs of new
existence results for discontinuous differential problems. Written in a clear, expository style,
with the inclusion of many examples in each chapter, this book aims to be useful not only as a
self-contained reference for mature researchers in nonlinear analysis but also for graduate
students looking for a quick accessible introduction to degree theory techniques for
discontinuous differential equations.
Due 2021-10-25
1st ed. 2021, VIII, 190 p. 9 illus. in color.
Hardcover : ISBN 978-3-030-81603-2
Product category : Monograph
Series : RSME Springer Series
Mathematics : Analysis
Nominated as an outstanding Ph.D. thesis by The University of Manchester, Manchester, United Kingdom
Provides a comprehensive introduction to the increasingly popular topic of field space covariance
Includes an in-depth discussion of the initial conditions problem of inflation
The ancient Greeks believed that everything in the Universe should be describable in terms of
geometry. This thesis takes several steps towards realising this goal by introducing geometric
descriptions of systems such as quantum gravity, fermionic particles and the origins of the
Universe itself. The author extends the applicability of previous work by Vilkovisky, DeWitt and
others to include theories with spin ? and spin 2 degrees of freedom. In addition, he
introduces a geometric description of the potential term in a quantum field theory through a
process known as the Eisenhart lift. Finally, the methods are applied to the theory of inflation,
where they show how geometry can help answer a long-standing question about the initial
conditions of the Universe. This publication is aimed at graduate and advanced undergraduate
students and provides a pedagogical introduction to the exciting topic of field space covariance
and the complete geometrization of quantum field theory
Due 2021-11-04
1st ed. 2021, XIX, 200 p. 7 illus., 6 illus. in color.
Hardcover ISBN 978-3-030-85268-9
Product category : Monograph
Series : Springer Theses
Physics : Elementary Particles, Quantum Field Theory
Includes over 400 great theorems from all areas of mathematics
Presents current mathematics research directions and results
Accessible to advanced undergraduates and above
Landscape of 21st Century Mathematics offers a detailed cross section of contemporary
mathematics. Important results of the 21st century are motivated and formulated, providing an
overview of recent progress in the discipline. The theorems presented in this book have been
selected among recent achievements whose statements can be fully appreciated without
extensive background. Grouped by subject, the selected theorems represent all major areas of
mathematics: number theory, combinatorics, analysis, algebra, geometry and topology,
probability and statistics, algorithms and complexity, and logic and set theory. The presentation
is self-contained with context, background and necessary definitions provided for each theorem,
all without sacrificing mathematical rigour. Where feasible, brief indications of the main ideas of
a proof are given. Rigorous yet accessible, this book presents an array of breathtaking recent
advances in mathematics. It is written for everyone with a background in mathematics, from
inquisitive university students to mathematicians curious about recent achievements in areas
beyond their own
Due 2021-10-15
1st ed. 2021, XIV, 429 p. 24 illus., 16 illus. in color.
Hardcover ISBN 978-3-030-80626-2
Product category : Monograph
Mathematics : Mathematics (general)
Quickly progresses from fundamental concepts to advanced modelling techniques
Provides Stan and Python codes for illustrating concepts
Presents exercises with solutions integrated into each chapter
These lecture notes provide a rapid, accessible introduction to Bayesian statistical methods. The
course covers the fundamental philosophy and principles of Bayesian inference, including the
reasoning behind the prior/likelihood model construction synonymous with Bayesian methods,
through to advanced topics such as nonparametrics, Gaussian processes and latent factor
models. These advanced modelling techniques can easily be applied using computer code
samples written in Python and Stan which are integrated into the main text. Importantly, the
reader will learn methods for assessing model fit, and to choose between rival modelling
approaches.
Due 2021-10-31
1st ed. 2021, X, 140 p. 31 illus., 30 illus. in color.
Hardcover : ISBN 978-3-030-82807-3
Product category : Graduate/advanced undergraduate textbook
Statistics : Bayesian Inference