Series: Sources and Studies in the History of Mathematics and Physical
Sciences
1st ed. 2019, XVIII, 460 p. 55 illus., 34
illus. in color.
Printed book
Hardcover
Provides pedagogical importance of scholarly work by Bhskarcrya, a great
Indian mathematician
Highlights the contribution of Bhskara to astronomy and mathematics
through illustrative examples
Collects selected papers presented at Bhskara 900 from renowned
contributors
This book covers the works of Bhskara, in particular, his monumental treatise on astronomy,
theSiddhntairomai, his astronomical handbook, theKaraakuthala, and his two mathematical
treatises, theLlavatand theBjagaita, on arithmetic and algebra, respectively. It is a collection of
selected papers presented atBhskara900, an international conference commemorate the 900th
birth anniversary of the great Indian mathematicianBhskarcrya.Bhskara-prabh, the radiance
ofBhskara, presents the Indian mathematical tradition and the place ofBhskarain it. The aim of
this book is to instill a sense of pride in younger generations of one of their most celebrated
thinkers, by sketching some details of his mathematical achievements and capturing their
imagination through his poetic flair. It is intended toraisea greater awareness among students
and teachers of Indiafs rich mathematical heritage.
Series: Algebra and Applications
1st ed. 2019, XX, 220 p. 111 illus.
Printed book
Hardcover
Compilation of both classical and new material on integral quadratic forms
Presents results as obtained in a representation theoretical setting, free from
that background
Gathers algorithms and criteria to verify numerical properties of quadratic
forms and their roots
Includes over 170 exercises
This monograph presents combinatorial and numerical issues on integral quadratic forms as
originally obtained in the context of representation theory of algebras and derived categories.
Some of these beautiful results remain practically unknown to students and scholars, and are
scattered in papers written between 1970 and the present day. Besides the many classical
results, the book also encompasses a few new results and generalizations. The material
presented will appeal to a wide group of researchers (in representation theory of algebras, Lie
theory, number theory and graph theory) and, due to its accessible nature and the many
exercises provided, also to undergraduate and graduate students with a solid foundation in
linear algebra and some familiarity on graph theory
Due 2019-03-16
1st ed. 2019, XII, 340 p.
108 illus., 106 illus. in color.
Hardcover
ISBN 978-3-030-11183-0
Textbook for convex optimization and non-convex optimization courses
Contains exercises with select solutions
Features model building, real problems, and applications of optimization
models
Provides numerical approaches to solve nonlinear optimization problems
This textbook on nonlinear optimization focuses on model building, real world problems, and
applications of optimization models to natural and social sciences. Organized into two parts,
this book may be used as a primary text for courses on convex optimization and non-convex
optimization. Definitions, proofs, and numerical methods are well illustrated and all chapters
contain compelling exercises. The exercises emphasize fundamental theoretical results on
optimality and duality theorems, numerical methods with or without constraints, and derivativefree
optimization. Selected solutions are given. Applications to theoretical results and numerical
methods are highlighted to help students comprehend methods and techniques.
Series: Texts & Monographs in Symbolic Computation
1st ed. 2019, XIII, 509 p. 134 illus., 54
illus. in color.
Printed book
Hardcover
Presents up-to-date reviews on modular forms and functions and their use in
particle physics
Combines knowledge from mathematical physics and mathematics
Written by international authors
This book includes review articles in the field of elliptic integrals, elliptic functions and modular
forms intending to foster the discussion between theoretical physicists working on higher loop
calculations and mathematicians working in the field of modular forms and functions and
analytic solutions of higher order differential and difference equations.
Due 2019-08-12
1st ed. 2019, Approx. 200 p.
20 illus.
Hardcover
ISBN 978-4-431-55904-7
Presents a practical method to use PCA and randomness measure based on
the RMT formula
Proposes a new and universal approach of big data analysis irrelevant to the
details of data types or fields
Uses real-world data to derive practical results for stock market forecasts and
computer security
This book presents the novel approach of analyzing large-sized rectangular-shaped numerical
data (so-called big data). The essence of this approach is to grasp the "meaning" of the data
instantly, without getting into the details of individual data. Unlike conventional approaches of
principal component analysis, randomness tests, and visualization methods, the authors'
approach has the benefits of universality and simplicity of data analysis, regardless of data
types, structures, or specific field of science. First, mathematical preparation is described. The
RMT-PCA and the RMT-test utilize the cross-correlation matrix of time series, C = XXT, where
Xrepresents a rectangular matrix of N rows and L columns and XT represents the transverse
matrix of X. Because C is symmetric, namely, C = CT, it can be converted to a diagonal matrix
of eigenvalues by a similarity transformation-1 = SCST using an orthogonal matrix S. When N is
significantly large, the histogram of the eigenvalue distribution can be compared to the
theoretical formula derived in the context of the random matrix theory (RMT, in abbreviation).
Then the RMT-PCA applied to high-frequency stock prices in Japanese and American markets is
dealt with. This approach proves its effectiveness in extracting "trendy" business sectors of the
financial market over the prescribed time scale.
Due 2019-03-26
1st ed. 2019, XXIV, 411 p.
96 illus., 45 illus. in color.
Hardcover
ISBN 978-3-030-11101-4
Highlights applications of enumerative combinatorics to varieties, Young
tableaux, partitions, queueing theory, tiling and graph theory
Presents recent methods in lattice path combinatorics
Discusses a wide breadth of topics and applications
Presents stimulating ideas of some of the exciting newcomers to the Lattice
Path Combinatorics Conference series
The most recent methods in various branches of lattice path and enumerative combinatorics
along with relevant applications are nicely grouped together and represented in this research
contributed volume. Contributions to this edited volume will be mainly research articles
however it will also include several captivating, expository articles (along with pictures) on the
life and mathematical work of leading researchers in lattice path combinatorics and beyond.
There will be four or five expository articles in memory ofShreeram Shankar Abhyankar and
Philippe Flajolet and honoringGeorge AndrewsandLajos Takacs. There may be another brief
articlein memory ofProfessors Jagdish Narayan Srivastava and Joti Lal Jain. New research
results include thekernel methoddeveloped by Flajolet and others for counting different classes
of lattice paths continues to produce new results in counting lattice paths.The recent
investigation of Fishburn numbers has led to interesting counting interpretations and a family
of fascinating congruences.Formulas for new methods to obtain the number of Fq-rational
points of Schubert varieties in Grassmannians continues to have research interest and will be
presented here. Topics to be included are far reaching and will include lattice path
enumeration, tilings, bijections between paths and other combinatoric structures, nonintersecting
lattice paths, varieties, Young tableaux, partitions, enumerative combinatorics,
discrete distributions, applications to queueing theory and other continuous time models, graph
theory and applications.Many leading mathematicians who spoke at the conference from which
this volume derives, are expected to send contributions including.