This is a unique book which systematically addresses the conceptual nature
of numbers
Combines mathematics, philosophy and history as tools to account for the
existence and essence of numbers
Draws on original analyses of key classical authors (Aristotle, Condillac,
Frege, Husserl...)
This book considers the manifold possible approaches, past and present, to our understanding
of the natural numbers. They are treated as epistemic objects: mathematical objects that have
been subject to epistemological inquiry and attention throughout their history and whose
conception has evolvedaccordingly. Although they are the simplest and most common
mathematical objects, as this book reveals, they have a very complex nature whose study
illuminates subtle features of the functioning of our thought. Using jointly history, mathematics
and philosophy to grasp the essence of numbers, the reader is led through their various
interpretations, presenting the ways they have been involved in major theoretical projects from
Thales onward. Some pertain primarily to philosophy (as in the works of Plato, Aristotle, Kant,
Wittgenstein...), others to general mathematics (Euclid's Elements,Cartesian algebraic geometry,
Cantorian infinities, set theory...). Also serving as an introduction to the works and thought of
major mathematicians and philosophers, from Plato and Aristotle to Cantor, Dedekind, Frege,
Husserl and Weyl, this book will be of interest to a wide variety of readers, from scholars with
ageneral interest in the philosophy or mathematics to philosophers andmathematicians
themselves.
Mathematics : History of Mathematics
Due 2020-11-11
1st ed. 2020, XI, 175 p. 1 illus.
Softcover
ISBN 978-3-030-56699-9
Product category : Monograph
Series : History of Mathematics Subseries
Presents select talks from the second international Aspects of TimeFrequency Analysis conference
Explores state-of-the-art topics in time-frequency analysis, with chapters
focusing on both comprehensive summaries as well as specific new results
Chapter authors are leaders in the field of harmonic analysis and its many
applications
This contributed volume features chapters based on talks given at the second international
conference titled Aspects of Time-Frequency Analysis (ATFA 19), held at Politecnico di Torino
from June 25th to June 27th, 2019. Written by experts in harmonic analysis and its
applications, these chapters provide a valuable overview of the state-of-the-art of this active
area of research. New results are collected as well, making this a valuable resource for readers
seeking to be brought up-to-date. Topics covered include: Signal analysis Quantum theory
Modulation space theory Applications to the medical industry Wavelet transform theory AntiWick
operators Landscapes of Time-Frequency Analysis: ATFA 2019 will be of particular
interest to researchers and advanced students working in time-frequency analysis and other
related areas of harmonic analysis.
Mathematics : Functional Analysis
Due 2020-12-29
1st ed. 2020, XIV, 218 p. 7 illus., 4 illus. in color.
Hardcover
ISBN 978-3-030-56004-1
Product category : Contributed volume
Series : Applied and Numerical Harmonic Analysis
Extensively rewritten new edition covering more advanced as well as recent
results
Provides a self-contained introduction to multiplicative number theory
Includes over 150 exercises, with hints and solutions
This textbook covers a wide array of topics in analytic and multiplicative number theory,
suitable for graduate level courses. Extensively revised and extended, this Advanced Edition
takes a deeper dive into the subject, with the elementary topics of the previous edition making
way for a fuller treatment of more advanced topics. The core themes of the distribution of
prime numbers, arithmetic functions, lattice points, exponential sums and number fields now
contain many more details and additional topics. In addition to covering a range of classical
and standard results, some recent work on a variety of topics is discussed in the book,
including arithmetic functions of several variables, bounded gaps between prime numbers a la
Yitang Zhang, Mordell's method for exponential sums over finite fields, the resonance method
for the Riemann zeta function, the Hooley divisor function, and many others. Throughout the
book, the emphasis is on explicit results. Assuming only familiarity with elementary number
theory and analysis at an undergraduate level, this textbook provides an accessible gateway to
a rich and active area of number theory. With an abundance of new topics and 50% more
exercises, all with solutions, it is now an even better guide for independent study.
Mathematics : Number Theory
Due 2021-01-09
2nd ed. 2020, X, 726 p. 6 illus.
Softcover
ISBN 978-3-030-54945-9
Product category : Graduate/advanced undergraduate textbook
Series : Universitext
Features an extensive range of real-world and relevant applications to
connect students to the concepts and theory, making the volume useful for
quantitative courses in a wide variety of majors (business, mathematics,
statistics, social sciences, sciences, and engineering, among others).
Includes updates on the latest methods in statistical practice, as well as the
latest in statistical software packages, in this new edition.
Includes sample syllabi for one- and two-term courses in mathematical
statistics, which serve as guides for instructors in smoothly adjusting to a new
text.
This 3rd edition of Modern Mathematical Statistics with Applications tries to strike a balance
between mathematical foundations and statistical practice. The book provides a clear and
current exposition of statistical concepts and methodology, including many examples and
exercises based on real data gleaned from publicly available sources. Here is a small but
representative selection of scenarios for our examples and exercises based on information in
recent articles: Use of the gBig Mac indexh by the publication The Economist as a humorous
way to compare product costs across nations Visualizing how the concentration of lead levels
in cartridges varies for each of five brands of e-cigarettes Describing the distribution of grip
size among surgeons and how it impacts their ability to use a particular brand of surgical
stapler Estimating the true average odometer reading of used Porsche Boxsters listed for sale
on www.cars.
Statistics : Statistical Theory and Methods
Due 2020-12-09
3rd ed. 2020, X, 1112 p. 234 illus., 160 illus. in color.
Hardcover
ISBN 978-3-030-55155-1
Product category : Graduate/advanced undergraduate textbook
Series : Springer Texts in Statistics
Provides a gentle introduction to combinatorics, finite geometry and related
topics
Covers a broad range of related topics including error-connecting codes,
cryptology and combinatorial game theory
Includes numerous examples and exercises that illustrate the theory
This undergraduate textbook is suitable for introductory classes in combinatorics and related
topics. The book covers a wide range of both pure and applied combinatorics, beginning with
the very basics of enumeration and then going on to Latin squares, graphs and designs. The
latter topic is closely related to finite geometry, which is developed in parallel. Applications to
probability theory, algebra, coding theory, cryptology and combinatorial game theory comprise
the later chapters. Throughout the book, examples and exercises illustrate the material, and
the interrelations between the various topics is emphasized. Readers looking to take first steps
toward the study of combinatorics, finite geometry, design theory, coding theory, or cryptology
will find this book valuable. Essentially self-contained, there are very few prerequisites aside
from some mathematical maturity, and the little algebra required is covered in the text. The
book is also a valuable resource for anyone interested in discrete mathematics as it ties
together a wide variety of topics.
Mathematics : Discrete Mathematics
Due 2020-12-18
1st ed. 2020, XIII, 370 p. 89 illus.
Softcover
ISBN 978-3-030-56394-3
Product category : Undergraduate textbook
Series : Springer Undergraduate Mathematics Series
An Introduction to the Theory and Applications of Propositional Sequent Calculi
Considers the methodology and techniques of sequent calculus to illustrate
its use in proving a wide range of metatheoretical results
Includes many results and their proofs that are often not well known or easily
accessible
Examines important and nonstandard generalized sequent calculi, like
hypersequent and structured sequent calculi.
This textbook offers a detailed introduction to the methodology and applications of sequent
calculi in propositional logic. Unlike other texts concerned with proof theory, emphasis is placed
on illustrating how to use sequent calculi to prove a wide range of metatheoretical results. The
presentation is elementary and self-contained, with all technical details both formally stated
and also informally explained. Numerous proofs are worked through to demonstrate methods
of proving important results, such as the cut-elimination theorem, completeness, decidability,
and interpolation. Other proofs are presented with portions left as exercises for readers,
allowing them to practice techniques of sequent calculus. After a brief introduction to classical
propositional logic, the text explores three variants of sequent calculus and their features and
applications. The remaining chapters then show how sequent calculi can be extended,
modified, and applied to non-classical logics, including modal, intuitionistic, subcultural, and
many-valued logics. Sequents and Trees is suitable for graduate and advanced undergraduate
students in logic taking courses on proof theory and its application to non-classical logics. It
will also be of interest to researchers in computer science and philosophers.
Mathematics : Structures and Proofs
Due 2020-12-13
1st ed. 2020, XIII, 341 p.
Hardcover
ISBN 978-3-030-57144-3
Product category : Graduate/advanced undergraduate textbook
Series : Studies in Universal Logic
Presents a series of surveys on topological and geometric subjects that
originate in the work of William Thurston, one of the greatest mathematicians
of modern times
Written by mathematicians who are at the forefront of research in their areas
Addressed to both students and researchers, each survey constitutes an
important reference on its research topic
This book consists of 16 surveys on Thurston's work and its later development. The authors
are mathematicians who were strongly influenced by Thurston's publications and ideas. The
subjects discussed include, among others, knot theory, the topology of 3-manifolds, circle
packings, complex projective structures, hyperbolic geometry, Kleinian groups, foliations,
mapping class groups, Teichmuller theory, anti-de Sitter geometry, and co-Minkowski geometry.
The book is addressed to researchers and students who want to learn about Thurstonfs wideranging
mathematical ideas and their impact. At the same time, it is a tribute to Thurston, one
of the greatest geometers of all time, whose work extended over many fields in mathematics
and who had a unique way of perceiving forms and patterns, and of communicating and
writing mathematics.
Mathematics : Geometry
Due 2020-12-09
1st ed. 2020, X, 590 p. 72 illus., 35 illus. in color.
Hardcover
ISBN 978-3-030-55927-4
Product category : Contributed volume