Due 2019-04-18
1st ed. 2019, XXIV, 267 p. 1illus.
Hardcover
ISBN 978-3-030-11035-2
The first English translation of Resume des lecons sur le calcul infinitesimal
Complete with annotations throughout
Allows wider audience to experience Cauchy's original, complete text on
calculus
Provides historical supplement to traditional calculus texts
This book is a complete English translation of Augustin-Louis Cauchy's historic 1823text (his
first devoted to calculus),Resumedes lecons sur le calcul infinitesimal, "Summary ofLectures on
the Infinitesimal Calculus," originally written to benefit his Ecole Polytechnic studentsin Paris.
Within this single text, Cauchy succinctly lays out and rigorously develops all of the topicsone
encounters in an introductory study of the calculus, from his classic definition of the limit tohis
detailed analysis of the convergence properties of infinite series. In between, the reader willfind
a full treatment of differential and integral calculus, including the main theorems of
calculusand detailed methods of differentiating and integrating a wide variety of functions.
Real, singlevariable calculus is the main focus of the text, but Cauchy spends ample time
exploring theextension of his rigorous development to include functions of multiple variables
as well ascomplex functions. This translation maintains the same notation and terminology of
Cauchy's original work in thehope of delivering as honest and true a Cauchy experience as
possible so that the modern readercan experience his work as it may have been like 200 years
ago. This book can be used withadvantage today by anyone interested in the history of the
calculus and analysis. In addition, itwill serve as a particularly valuable supplement to a
traditional calculus text for those readers whodesire a way to create more texture in a
conventional calculus class through the introduction oforiginal historical sources.
Due 2019-04-27
4th ed. 2019, XXII, 827 p.
44 illus., 1 illus. in color.
Hardcover
ISBN 978-3-030-11297-4
Develops Kolmogorov theory in detail, and outlines a wide range of
illustrative applications
Examines major results from prominent researchers in the field
Details the practical application of KC in the similarity metric and information
diameter of multisets in phylogeny, language trees, music, heterogeneous
files, and clustering
Includes new and updated material on the Miller-Yu theorem, the Gacs-Kuera
theorem, the Day-Gacs theorem, the Lovasz local lemma, and the Slepian-Wolf
theorem
Discusses short lists computable from an input string containing the
incomputable Kolmogorov complexity of the input
This must-read textbook presents an essential introduction to Kolmogorov complexity (KC), a
central theory and powerful tool in information science that deals with the quantity of
information in individual objects. The text covers both the fundamental concepts and the most
important practical applications, supported by a wealth of didactic features. This thoroughly
revised and enhanced fourth edition includes new and updated material on, amongst other
topics, the Miller-Yu theorem, the Gacs-Kuera theorem, the Day-Gacs theorem, increasing
randomness, short lists computable from an input string containing the incomputable
Kolmogorov complexity of the input, the Lovasz local lemma, sorting, the algorithmic full
Slepian-Wolf theorem for individual strings, multiset normalized information distance and
normalized web distance, and conditional universal distribution
Due 2019-03-31
1st ed. 2019, XIV, 196 p. 13
illus., 11 illus. in color.
Hardcover
ISBN 978-3-030-12024-5
Elements of Commutative Algebra and Algebraic Geometry
Self-contained and concise primer
Geared towards applications in nonlinear control theory
Emphasizes tools from commutative algebra and algebraic geometry
This book is a short primer in engineering mathematics with a view on applications in
nonlinear control theory. In particular, it introduces some elementary concepts of commutative
algebra and algebraic geometry which offer a set of tools quite different from the traditional
approaches to the subject matter. This text begins with the study of elementary set and map
theory. Chapters 2 and 3 on group theory and rings, respectively, are included because of their
important relation to linear algebra, the group of invertible linear maps (or matrices) and the
ring of linear maps of a vector space. Homomorphisms and Ideals are dealt with as well at
this stage. Chapter 4 is devoted to the theory of matrices and systems of linear equations.
Chapter 5 gives some information on permutations, determinants and the inverse of a matrix.
Chapter 6 tackles vector spaces over a field, Chapter 7 treats linear maps resp. linear
transformations, and in addition the application in linear control theory of some abstract
theorems such as the concept of a kernel, the image and dimension of vector spaces are
illustrated. Chapter 8 considers the diagonalization of a matrix and their canonical forms.
Chapter 9 provides a brief introduction to elementary methods for solving differential equations
and, finally, in Chapter 10, nonlinear control theory is introduced from the point of view of
differential algebra.
Due 2019-03-25
1st ed. 2019, XV, 93 p.
Hardcover
ISBN 978-3-030-12095-5
Presents an English translation of a key 1985 Russian monograph by Leo Esakia
Details important insights into duality theory for Heyting algebras
Includes information about the planned contents of the lost second-volume
This book presents an English translation of a classic Russian text on duality theory for Heyting
algebras. Written by Georgian mathematician Leo Esakia, the text proved popular among
Russian-speaking logicians. This translation helps make the ideas accessible to a wider
audience and pays tribute to an influential mind in mathematical logic. The book discusses the
theory of Heyting algebras and closure algebras, as well as the corresponding intuitionistic and
modal logics. The author introduces the key notion of a hybrid that “crossbreeds” topology
(Stone spaces) and order (Kripke frames), resulting in the structures now known as Esakia
spaces. The main theorems include a duality between the categories of closure algebras and of
hybrids, and a duality between the categories of Heyting algebras and of so-called strict
hybrids. Esakia's book was originally published in 1985. It was the first of a planned twovolume
monograph on Heyting algebras. But after the break of the Soviet Union, the publishing
house closed and the project died with it. Fortunately, this important work now lives on in this
accessible translation. The Appendix of the book discusses the planned contents of the lost
second volume.
Due 2019-05-07
1st ed. 2019, X, 430 p. 5 illus.
Hardcover
ISBN 978-3-030-11526-5
Deepens readers’ foundations of geometry, physics and the theory of
continuum with an approach which is inextricably philosophical, historical and
scientific
Presents the first historical reconstitution of Weyl’s conferences on the
problem of space
Proposes an extensive philosophical approach to the different aspects of the
problem of space
Provides new insights and clarifications on complicated questions
This book investigates Hermann Weyl’s work on the problem of space from the early 1920s
onwards. It presents new material and opens the philosophical problem of space anew,
crossing the disciplines of mathematics, history of science and philosophy.With a Kantian
starting point Weyl asks: among all the infinitely many conceivable metrical spaces, which one
applies to the physical world? In agreement with general relativity, Weyl acknowledges that the
metric can quantitatively vary with the physical situation. Despite this freedom, Weyl “deduces”,
with group-theoretical technicalities, that there is only one “kind” of legitimate metric. This
construction was then decisive for the development of gauge theories. Nevertheless, the
question of the foundations of the metric of physical theories is only a piece of a wider
epistemological problem.Contributing authors mark out the double trajectory that goes through
Weyl’s texts, from natural science to philosophy and conversely, always through the mediation
of mathematics. Readers may trace the philosophical tradition to which Weyl refers and by
which he is inspired (Kant, Husserl, Fichte, Leibniz, Becker etc.), and explore the mathematical
tradition (Riemann, Helmholtz, Lie, Klein) that permitted Weyl to elaborate and solve his
mathematical problem of space. Furthermore, this volume analyzes the role of the interlocutors
with whom Weyl discussed the nature of physical space (Einstein, Cartan, De Sitter, Schrodinger,
Eddington). This volume features the work of top specialists and will appeal to postgraduates
and scholars in philosophy, the history of science, mathematics, or physics.
Due 2019-04-25
1st ed. 2019, VIII, 106 p.
15 illus.
Softcover
ISBN 978-3-030-12849-4
Fundamentals and Applications of Keystream Sequence Generators
Based on Irregular Decimation
Offers a rare, unified source of information on shrinking generators
Illustrates the theoretical aspects of this family of generators with a myriad
of applications
Presents open problems that might motivate further research on cryptology
This book offers a broad survey of all information made public - from 1993 until today - on
keystream sequence generators based on irregular decimation, which are referred to as
shrinking generators. Starting with an overview of cryptography, it describes each type of
generator - shrinking, self-shrinking, modified self-shrinking, generalized self-shrinking and the
DECIM algorithm - with examples and references. Further, the book discusses several attacks
on these generators and applications. It concludes by demonstrating how the output
sequences can be modeled by means of different families of one-dimensional cellular
automata, rendering the generators vulnerable to attacks. Intended for researchers and
graduate students, the book will hopefully inspire them to search for more details on this
family of generators and to address the open problems in this field.
Due 2019-04-19
1st ed. 2019, XVI, 321 p. 20
illus., 3 illus. in color.
Hardcover
ISBN 978-3-030-11520-3
Covers theoretical and computational aspects of ring theory, group theory, Lie
theory, commutative algebra, algebraic geometry, linear algebra, and
quantum groups
Includes a balance of original research articles and well-written survey papers
Honors the Southern Regional Algebra Conferences' tradition of embracing
new mathematics from across all areas in algebra
This proceedings volume covers a range of research topics in algebra from the Southern
Regional Algebra Conference (SRAC) that took place in March 2017. Presenting theory as well
as computational methods, featured survey articles and research papers focus on ongoing
research in algebraic geometry, ring theory, group theory, and associative algebras. Topics
include algebraic groups, combinatorial commutative algebra, computational methods for
representations of groups and algebras, group theory, Hopf-Galois theory, hypergroups, Lie
superalgebras, matrix analysis, spherical and algebraic spaces, and tropical algebraic geometry.
Since 1988, SRAC has been an important event for the algebra research community in the Gulf
Coast Region and surrounding states, building a strong network of algebraists that fosters
collaboration in research and education. This volume is suitable for graduate students and
researchers interested in recent findings in computational and theoretical methods in algebra
and representation theory.