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Lavoisier Bokseller: New books in mathematics
2017-05-01T12:00:00+01:00
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Books in mathematics just arrived on Lavoisier Bookseller
© 2017 Lavoisier Bokseller
http://www.lavoisier.eu/books/mathematics/basic-algebra/knapp/description_1647891
Basic algebra
2017-05-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1649065.jpg" alt="Book's cover:Basic algebra" /><br />Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems. Basic Algebra presents the subject matter in a forward-looking way that takes into account its historical development. It is suitable as a text in a two-semester advanced undergraduate or first-year graduate sequence in algebra, possibly supplemented by some material from Advanced Algebra at the graduate level. It requires of the reader only familiarity with matrix algebra, an understanding of the geometry and reduction of linear equations, and an acquaintance with proofs.
http://www.lavoisier.eu/books/mathematics/statistical-implications-of-turing-s-formula/zhang/description_3615740
Statistical Implications of Turing′s Formula
2017-05-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1317011965.jpg" alt="Book's cover:Statistical Implications of Turing′s Formula" /><br />Features a broad introduction to recent research on Turing’s formula and
presents modern applications in statistics, probability, information
theory, and other areas of modern data science<br><br>Turing's formula is,
perhaps, the only known method for estimating the underlying
distributional characteristics beyond the range of observed data without
making any parametric or semiparametric assumptions. This book presents a
clear introduction to Turing’s formula and its connections to statistics.
Topics with relevance to a variety of different fields of study are
included such as information theory; statistics; probability; computer
science inclusive of artificial intelligence and machine learning; big
data; biology; ecology; and genetics.<br><br>The author provides
examinations of many core statistical issues within modern data science
from Turing's perspective. A systematic approach to long-standing problems
such as entropy and mutual information estimation, diversity index
estimation, domains of attraction on general alphabets, and tail
probability estimation is presented in light of the most up-to-date
understanding of Turing's formula.<br><br>Featuring numerous exercises and
examples throughout, the author provides a summary of the known properties
of Turing's formula and explains how and when it works well; discusses the
approach derived from Turing's formula in order to estimate a variety of
quantities, all of which mainly come from information theory, but are also
important for machine learning and for ecological applications; and uses
Turing's formula to estimate certain heavy-tailed distributions.
http://www.lavoisier.eu/books/mathematics/intuitive-probability-et-random-processes-using-matlab/kay/description_1270881
Intuitive probability & random processes using MATLAB
2017-05-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1271655.jpg" alt="Book's cover:Intuitive probability & random processes using MATLAB" /><br />Intuitive Probability and Random Processes using MATLAB® is an introduction to probability and random processes that merges theory with practice. Based on the author's belief that only "hands-on" experience with the material can promote intuitive understanding, the approach is to motivate the need for theory using MATLAB examples, followed by theory and analysis, and finally descriptions of "real-world" examples to acquaint the reader with a wide variety of applications. The latter is intended to answer the usual question "Why do we have to study this?" Other salient features are: heavy reliance on computer simulation for illustration and student exercises, the incorporation of MATLAB programs and code segments, discussion of discrete random variables followed by continuous random variables to minimize confusion, summary sections at the beginning of each chapter, in-line equation explanations, warnings on common errors and pitfalls, over 750 problems designed to help the reader assimilate and extend the concepts. This volume is intended for undergraduate and first-year graduate students in engineering. The practicing engineer as well as others having the appropriate mathematical background will also benefit from this book.
http://www.lavoisier.eu/books/mathematics/the-elements-of-statistical-learning-data-mining-inference-and-prediction-springer-series-in-statistics/hastie/description_1274454
The elements of statistical learning : data mining, inference and prediction (2nd Ed.)
2017-04-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1275229.jpg" alt="Book's cover:The elements of statistical learning : data mining, inference and prediction (2nd Ed.) " /><br />During the past decade there has been an explosion in computation and
information technology. With it have come vast amounts of data in a
variety of fields such as medicine, biology, finance, and marketing. The
challenge of understanding these data has led to the development of new
tools in the field of statistics, and spawned new areas such as data
mining, machine learning, and bioinformatics. Many of these tools have<br><br>This
book describes the important ideas in these areas in a common conceptual
framework. While the approach is statistical, the emphasis is on concepts
rather than mathematics. Many examples are given, with a liberal use of
color graphics. It should be a valuable resource for statisticians and
anyone interested in data mining in science or industry. The book's
coverage is broad, from supervised learning (prediction) to unsupervised
learning. The many topics include neural networks, support vector
machines, classification trees and boosting, the first comprehensive
treatment of this topic in any book.<br><br>This major new edition
features many topics not covered in the original, including graphical
models, random forests, ensemble methods, least angle regression and path
algorithms for the lasso, non-negative matrix factorization, and spectral
clustering. There is also a chapter on methods for "wide" data (p bigger
than n), including multiple testing and false discovery rates. Trevor
Hastie, Robert Tibshirani, and Jerome Friedman are professors of
statistics at Stanford University. They are prominent researchers in this
area: Hastie and Tibshirani developed generalized additive models and
wrote a popular book of that title. Hastie co-developed much of the
statistical modeling software and environment in R/S-PLUS and invented
principal curves and surfaces. Tibshirani proposed the lasso and is
co-author of the very successful An Introduction to the Bootstrap.
Friedman is the co-inventor of many data-mining tools including CART,
MARS, projection pursuit and gradient boosting.
http://www.lavoisier.eu/books/mathematics/elements-of-nonlinear-time-series-analysis-and-forecasting/de/description_3627447
Elements of Nonlinear Time Series Analysis and Forecasting
2017-04-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1317024456.jpg" alt="Book's cover:Elements of Nonlinear Time Series Analysis and Forecasting" /><br /><p>
This book provides an overview of the current state-of-the-art of
nonlinear time series analysis, richly illustrated with examples,
pseudocode algorithms and real-world applications. Avoiding
a “theorem-proof” format, it shows concrete applications on a variety of
empirical time series. The book can be used in graduate courses in
nonlinear time series and at the same time also includes interesting
material for more advanced readers. Though it is largely self-contained,
readers require an understanding of basic linear time series concepts,
Markov chains and Monte Carlo simulation methods.
</p>
<p>
The book covers time-domain and frequency-domain methods for the
analysis of both univariate and multivariate (vector) time series. It
makes a clear distinction between parametric models on the one hand, and
semi- and nonparametric models/methods on the other. This offers the
reader the option of concentrating exclusively on one of these nonlinear
time series analysis methods.
</p>
<p>
To make the book as user friendly as possible, major supporting concepts
and specialized tables are appended at the end of every chapter. In
addition, each chapter concludes with a set of key terms and concepts,
as well as a summary of the main findings. Lastly, the book offers
numerous theoretical and empirical exercises, with answers provided by
the author in an extensive solutions manual.
</p>
http://www.lavoisier.eu/books/mathematics/beginner-s-guide-to-spatial-temporal-and-spatial-temporal-ecological-data-analysis-with-r-inla/zuur/description_3616233
Beginner's Guide to Spatial, Temporal and Spatial-Temporal Ecological Data Analysis with R-INLA
2017-02-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1317012587.jpg" alt="Book's cover:Beginner's Guide to Spatial, Temporal and Spatial-Temporal Ecological Data Analysis with R-INLA " /><br />In Volume I we explain how to apply linear regression models, generalised
linear models (GLM), and generalised linear mixed - effects models ( GLMM)
to spatial, temporal, and spatial - temporal data. The models that will be
employed use the Gaussian and gamma distributions for continuous data, the
Poisson and negative binomial distributions for count data, the Bernoulli
distribution for absence – presence data, and the binomial distribution
for proportional data.
http://www.lavoisier.eu/books/mathematics/introduction-to-computational-chemistry-3rd-ed/jensen/description_3599469
Introduction to Computational Chemistry (3rd Ed.)
2017-02-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1316991570.jpg" alt="Book's cover:Introduction to Computational Chemistry (3rd Ed.) " /><br /><i>Introduction to Computational Chemistry - 3rd Edition </i>provides a
comprehensive account of the fundamental principles underlying different
computational methods. Fully revised and updated throughout to reflect
important method developments and improvements since publication of the
previous edition, this timely update includes the following significant
revisions and new topics:<br><br>- Polarizable force fields<br>-
Tight-binding DFT<br>- More extensive DFT functionals, excited states and
time dependent molecular properties<br>- Accelerated Molecular Dynamics
methods<br>- Tensor decomposition methods<br>- Cluster analysis<br>-
Reduced scaling and reduced prefactor methods
http://www.lavoisier.eu/books/mathematics/playing-around-resonance/fonda/description_3449709
Playing Around Resonance
2016-11-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1316948195.jpg" alt="Book's cover:Playing Around Resonance " /><br />This book provides an up-to-date description of the methods needed to face
the existence of solutions to some nonlinear boundary value problems. All
important and interesting aspects of the theory of periodic solutions of
ordinary differential equations related to the physical and mathematical
question of resonance are treated. The author has chosen as a model
example the periodic problem for a second order scalar differential
equation. In a paedagogical style the author takes the reader step by step
from the basics to the most advanced existence results in the field.
http://www.lavoisier.eu/books/mathematics/applied-biclustering-methods-for-big-and-high-dimensional-data-using-r/kasim/description_3541360
Applied Biclustering Methods for Big and High-Dimensional Data Using R
2016-10-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1316972018.jpg" alt="Book's cover:Applied Biclustering Methods for Big and High-Dimensional Data Using R" /><br />As big data has become standard in many application areas, challenges have
arisen related to methodology and software development, including how to
discover meaningful patterns in the vast amounts of data. Addressing these
problems, <i>Applied Biclustering Methods for Big and High-Dimensional
Data Using R</i> shows how to apply biclustering methods to find local
patterns in a big data matrix.<br><br>The book presents an overview of
data analysis using biclustering methods from a practical point of view.
Real case studies in drug discovery, genetics, marketing research,
biology, toxicity, and sports illustrate the use of several biclustering
methods. References to technical details of the methods are provided for
readers who wish to investigate the full theoretical background. All the
methods are accompanied with R examples that show how to conduct the
analyses. The examples, software, and other materials are available on a
supplementary website.
http://www.lavoisier.eu/books/mathematics/a-first-course-in-modular-forms-gradua-te-texts-in-mathematics-vol-228/diamond/description_1270528
A first course in modular forms, (Gradua te texts in mathematics, Vol. 228)
2016-09-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1271302.jpg" alt="Book's cover:A first course in modular forms, (Gradua te texts in mathematics, Vol. 228)" /><br />This book introduces the theory of modular forms with an eye toward the Modularity Theorem : All rational elliptic curves arise from modular forms. The topics covered include : elliptic curves as complex tori and as algebraic curves- modular curves as Riemann surfaces and as algebraic curves- Hecke operators and Atkin-Lehner theory- Hecke eigenforms and their arithmetic properties- the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms- elliptic and modular curves modulo p and the Eichler-Shimura Relation- the Galois representations associated to elliptic curves and to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory.
http://www.lavoisier.eu/books/mathematics/minimum-volume-ellipsoids/todd/description_3497961
Minimum-Volume Ellipsoids
2016-08-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1316942324.jpg" alt="Book's cover:Minimum-Volume Ellipsoids" /><br />The first book in the area, this volume addresses the problem of finding
an ellipsoid to represent a large set of points in high-dimensional space,
which has applications in computational geometry, data representations,
and optimal design in statistics. The book covers the formulation of this
and related problems, theoretical properties of their optimal solutions,
and algorithms for their solution. While algorithms of this kind have been
discovered and rediscovered over the past fifty years, their computational
complexities and convergence rates have only recently been investigated.
The optimization problems in the book have the entries of a symmetric
matrix as their variables, so the author's treatment also gives an
introduction to recent work in matrix optimization. This book will be of
interest to graduate students and researchers in operations research,
theoretical statistics, data mining, complexity theory, computational
geometry, and computational science.
http://www.lavoisier.eu/books/mathematics/encyclopedia-of-distances/deza/description_3611232
Encyclopedia of Distances
2016-08-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1317003839.jpg" alt="Book's cover:Encyclopedia of Distances" /><br /><p>
This 4-th edition of the leading reference volume on distance metrics is
characterized by updated and rewritten sections on some items suggested
by experts and readers, as well a general streamlining of content and
the addition of essential new topics. Though the structure remains
unchanged, the new edition also explores recent advances in the use of
distances and metrics for e.g. generalized distances, probability
theory, graph theory, coding theory, data analysis.
</p>
<p>
New topics in the purely mathematical sections include e.g. the Vitanyi
multiset-metric, algebraic point-conic distance, triangular ratio
metric, Rossi-Hamming metric, Taneja distance, spectral semimetric
between graphs, channel metrization, and Maryland bridge distance. The
multidisciplinary sections have also been supplemented with new topics,
including: dynamic time wrapping distance, memory distance, allometry,
atmospheric depth, elliptic orbit distance, VLBI distance measurements,
the astronomical system of units, and walkability distance.
</p>
<p>
Leaving aside the practical questions that arise during the selection of
a ‘good’ distance function, this work focuses on providing the research
community with an invaluable comprehensive listing of the main available
distances.
</p>
<p>
As well as providing standalone introductions and definitions, the
encyclopedia facilitates swift cross-referencing with easily navigable
bold-faced textual links to core entries. In addition to distances
themselves, the authors have collated numerous fascinating curiosities
in their Who’s Who of metrics, including distance-related notions and
paradigms that enable applied mathematicians in other sectors to deploy
research tools that non-specialists justly view as arcane. In expanding
access to these techniques, and in many cases enriching the context of
distances themselves, this peerless volume is certain to stimulate fresh
research.
</p>
http://www.lavoisier.eu/books/mathematics/crystal-structure-determination/massa/description_3450309
Crystal Structure Determination (3rd Ed.)
2016-07-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1316948695.jpg" alt="Book's cover:Crystal Structure Determination (3rd Ed.)" /><br />This textbook gives a concise introduction to modern crystal structure
determination, emphasising both its theoretical background and the way it
actually occurs. The theoretical and experimental sections are supported
by many illustrations, and lay emphasis on a good understanding rather
than rigorous mathematics.<br><br>The actual data collection techniques,
and the methods of data reduction, structure solution and refinement are
discussed from a practical point of view. Many tips and insigths help
readers to recognise and avoid possible errors and traps, and to judge the
quality of results.<br><br>In the third English edition, based on the
German eighth edition (Springer 2015), treatment of film methods, now
extinct, and of the nearly extinct four-circle diffractometers has been
omitted. Instead, the methods of obtaining and interpreting area detector
data have been expanded, and e.g. actual alternative direct methods and
time-resolved crystallography are included.
http://www.lavoisier.eu/books/mathematics/bayesian-designs-for-phase-i-ii-clinical-trials/yuan/description_3458727
Bayesian Designs for Phase I–II Clinical Trials
2016-06-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1316957707.jpg" alt="Book's cover:Bayesian Designs for Phase I–II Clinical Trials" /><br />Reliably optimizing a new treatment in humans is a critical first step in
clinical evaluation since choosing a suboptimal dose or schedule may lead
to failure in later trials. At the same time, if promising preclinical
results do not translate into a real treatment advance, it is important to
determine this quickly and terminate the clinical evaluation process to
avoid wasting resources.<br><br><i>Bayesian Designs for Phase I–II
Clinical Trials</i> describes how phase I–II designs can serve as a bridge
or protective barrier between preclinical studies and large confirmatory
clinical trials. It illustrates many of the severe drawbacks with
conventional methods used for early-phase clinical trials and presents
numerous Bayesian designs for human clinical trials of new experimental
treatment regimes.<br><br>The first two chapters minimize the technical
language to make them accessible to non-statisticians. These chapters
discuss the severe drawbacks of the conventional paradigm used for
early-phase clinical trials and explain the phase I–II paradigm for
optimizing dose, or more general treatment regimes, based on both efficacy
and toxicity. The remainder of the book covers a wide variety of clinical
trial methodologies, including designs to optimize the dose pair of a
two-drug combination, jointly optimize dose and schedule, identify optimal
personalized doses, optimize novel molecularly targeted agents, and choose
doses in two treatment cycles.<br><br>Written by research leaders from the
University of Texas MD Anderson Cancer Center, this book shows how
Bayesian designs for early-phase clinical trials can explore, refine, and
optimize new experimental treatments. It emphasizes the importance of
basing decisions on both efficacy and toxicity.
http://www.lavoisier.eu/books/mathematics/ggplot2-2nd-ed/wickham/description_3454485
ggplot2 (2nd Ed.)
2016-06-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1316953266.jpg" alt="Book's cover:ggplot2 (2nd Ed.)" /><br />This new edition to the classic book by ggplot2 creator Hadley Wickham
highlights compatibility with knitr and RStudio. ggplot2 is a data
visualization package for R that helps users create data graphics,
including those that are multi-layered, with ease. With ggplot2, it's easy
to: <br><br>- produce handsome, publication-quality plots with
automatic legends created from the plot specification<br>- superimpose
multiple layers (points, lines, maps, tiles, box plots) from different
data sources with automatically adjusted common scales<br>- add
customizable smoothers that use powerful modeling capabilities of R, such
as loess, linear models, generalized additive models, and robust regression<br>-
save any ggplot2 plot (or part thereof) for later modification or reuse<br>-
create custom themes that capture in-house or journal style requirements
and that can easily be applied to multiple plots<br>- approach a graph
from a visual perspective, thinking about how each component of the data
is represented on the final plot<br><br>This book will be useful to
everyone who has struggled with displaying data in an informative and
attractive way. Some basic knowledge of R is necessary (e.g., importing
data into R). ggplot2 is a mini-language specifically tailored for
producing graphics, and you'll learn everything you need in the book.
After reading this book you'll be able to produce graphics customized
precisely for your problems, and you'll find it easy to get graphics out
of your head and on to the screen or page.
http://www.lavoisier.eu/books/mathematics/hidden-markov-models-for-time-series-2nd-ed/zucchini/description_3580787
Hidden Markov Models for Time Series (2nd Ed.)
2016-06-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1316977071.jpg" alt="Book's cover:Hidden Markov Models for Time Series (2nd Ed.)" /><br /><p>
<i><b>Hidden Markov Models for Time Series: An Introduction Using R,
Second Edition</b></i><b> </b>illustrates the great flexibility of
hidden Markov models (HMMs) as general-purpose models for time series
data. The book provides a broad understanding of the models and their
uses.
</p>
<p>
After presenting the basic model formulation, the book covers
estimation, forecasting, decoding, prediction, model selection, and
Bayesian inference for HMMs. Through examples and applications, the
authors describe how to extend and generalize the basic model so that it
can be applied in a rich variety of situations.
</p>
<p>
The book demonstrates how HMMs can be applied to a wide range of types
of time series: continuous-valued, circular, multivariate, binary,
bounded and unbounded counts, and categorical observations. It also
discusses how to employ the freely available computing environment R to
carry out the computations.
</p>
http://www.lavoisier.eu/books/mathematics/degradation-processes-in-reliability/description_3434850
Degradation Processes in Reliability - volume 3
2016-06-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1316931600.jpg" alt="Book's cover:Degradation Processes in Reliability - volume 3" /><br />"Degradation process" refers to many types of reliability models, which
correspond to various kinds of stochastic processes used for deterioration
modeling. This book focuses on the case of a univariate degradation model
with a continuous set of possible outcomes. The envisioned univariate
models have one single measurable quantity which is assumed to be observed
over time. The first three chapters are each devoted to one degradation
model. The last chapter illustrates the use of the previously described
degradation models on some real data sets. For each of the degradation
models, the authors provide probabilistic results and explore simulation
tools for sample paths generation. Various estimation procedures are also
developed.
http://www.lavoisier.eu/books/mathematics/topologie-algebrique-chapitres-1-a-4/bourbaki/description_3624926
Topologie algébrique - Chapitres 1 à 4
2016-06-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1317021874.jpg" alt="Book's cover:Topologie algébrique - Chapitres 1 à 4" /><br /><p>
Ce livre des Éléments de mathématique est consacré à la Topologie
algébrique. Les quatre premiers chapitres présentent la théorie des
revêtements d'un espace topologique et du groupe de Poincaré. On
construit le revêtement universel d'un espace connexe pointé délaçable
et on établit l'équivalence de catégories entre revêtements de cet
espace et actions du groupe de Poincaré.
</p>
<p>
On démontre une version générale du théorème de van Kampen exprimant le
groupoïde de Poincaré d'un espace topologique comme un coégalisateur de
diagrammes de groupoïdes. Dans de nombreuses situations géométriques, on
en déduit une présentation explicite du groupe de Poincaré.
</p>
http://www.lavoisier.eu/books/mathematics/applied-survival-analysis-using-r/moore/description_3434849
Applied Survival Analysis Using R
2016-05-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1316931599.jpg" alt="Book's cover:Applied Survival Analysis Using R" /><br /><div class="springer-html">
<p>
<i>Applied Survival Analysis Using R</i> covers the main principles of
survival analysis, gives examples of how it is applied, and teaches
how to put those principles to use to analyze data using R as a
vehicle. Survival data, where the primary outcome is time to a
specific event, arise in many areas of biomedical research, including
clinical trials, epidemiological studies, and studies of animals. Many
survival methods are extensions of techniques used in linear
regression and categorical data, while other aspects of this field are
unique to survival data. This text employs numerous actual examples to
illustrate survival curve estimation, comparison of survivals of
different groups, proper accounting for censoring and truncation,
model variable selection, and residual analysis.<br><br>Because
explaining survival analysis requires more advanced mathematics than
many other statistical topics, this book is organized with basic
concepts and most frequently used procedures covered in earlier
chapters, with more advanced topics near the end and in the
appendices. A background in basic linear regression and categorical
data analysis, as well as a basic knowledge of calculus and the R
system, will help the reader to fully appreciate the information
presented. Examples are simple and straightforward while still
illustrating key points, shedding light on the application of survival
analysis in a way that is useful for graduate students, researchers,
and practitioners in biostatistics.<br>
</p>
</div>
http://www.lavoisier.eu/books/information-technology/advances-in-proof-theory/kahle/description_3416926
Advances in Proof Theory
2016-05-01T12:00:00+01:00
<img src="https://images.lavoisier.net/vignettes/1316912353.jpg" alt="Book's cover:Advances in Proof Theory" /><br />The aim of this volume is to collect original contributions by the best
specialists from the area of proof theory, constructivity, and computation
and discuss recent trends and results in these areas. Some emphasis will
be put on ordinal analysis, reductive proof theory, explicit mathematics
and type-theoretic formalisms, and abstract computations. The volume is
dedicated to the 60th birthday of Professor Gerhard Jäger, who has been
instrumental in shaping and promoting logic in Switzerland for the last 25
years. It comprises contributions from the symposium “Advances in Proof
Theory”, which was held in Bern in December 2013.<br><br>​Proof
theory came into being in the twenties of the last century, when it was
inaugurated by David Hilbert in order to secure the foundations of
mathematics. It was substantially influenced by Gödel's famous
incompleteness theorems of 1930 and Gentzen's new consistency proof for
the axiom system of first order number theory in 1936. Today, proof theory
is a well-established branch of mathematical and philosophical logic and
one of the pillars of the foundations of mathematics. Proof theory
explores constructive and computational aspects of mathematical reasoning;
it is particularly suitable for dealing with various questions in computer
science.