Due 2019-10-01
1st ed. 2019, VIII, 158 p. 4 illus.
Printed book
Softcover
ISBN 978-981-13-7996-3
A textbook for short introductory courses on nonclassical logic at the
undergraduate or graduate level
Offers a concise introduction to two major techniques in the study of
nonclassical logic: proof theory and algebraic methods, and highlights a
combination of proof theory with algebraic methods
Provides concrete examples showing how these techniques are applied in nonclassical logic
Demonstrates the complementary features of proof theory and algebraic
methods by describing both their differences and similarities, as well as their connections
This book offers a concise introduction to both proof-theory and algebraic methods, the core of
the syntactic and semantic study of logic respectively. The importance of combining these two
has been increasingly recognized in recent years. It highlights the contrasts between the deep,
concrete results using the former and the general, abstract ones using the latter. Covering
modal logics, many-valued logics, superintuitionistic and substructural logics, together with
their algebraic semantics, the book also provides an introduction to nonclassical logic for
undergraduate or graduate level courses. The book is divided into two parts: Proof Theory in
Part I and Algebra in Logic in Part II. Part Ipresents sequent systems and discusses cut
elimination and its applications in detail. It also provides simplified proof of cut elimination,
making the topic more accessible. The last chapter of Part I is devoted to clarification of the
classes of logics that are discussed in the second part. Part II focuses on algebraic semantics
for these logics. At the same time, it is a gentle introduction to the basics of algebraic logic
and universal algebra with many examples of their applications in logic. Part II can be read
independently of Part I, with only minimum knowledge required, and as such is suitable as a
textbook for short introductory courses on algebra in logic.
Due 2019-08-14
2019, VII, 562 p.
95 illus., 9 illus. in color.
Printed book
Hardcover
ISBN 978-3-030-20505-8
Uses natural situations to develop ideas relating to linear algebra
or differential equations
Uses an examples-oriented approach to develop an understanding of
increasingly complex theorems
Includes extensive visual and graphical aids to explain important ideas
This book is designed to serve as atextbook for a course on ordinary differential equations,
which is usually a required course in most science and engineering disciplines and follows
calculus courses. The book begins with linear algebra, including a number of physical
applications, and goes on to discuss first-order differential equations, linear systems of
differential equations, higher order differential equations, Laplace transforms, nonlinear systems
of differential equations, and numerical methods used in solving differential equations. The
style of presentation of the book ensures that the student with a minimum of assistance may
apply the theorems and proofs presented. Liberal use of examples and homework problems
aids the student in the study of the topics presented and applying them to numerous
applications in the real scientific world. This textbook focuses on the actual solution of ordinary
differential equations preparing the student to solve ordinary differential equations when
exposed to such equations in subsequent courses in engineering or pure science programs.
The book can be used as a text in a one-semester core course on differential equations,
alternatively it can also be used as a partial or supplementary text in intensive courses that
cover multiple topics including differential equations
Due 2019-10-03
1st ed. 2019, X, 85 p. 6 illus.
Printed book
Softcover
ISBN 978-981-13-9494-2
Spring, 1964
Was typeset from lecture notes originally handwritten by Kenkichi Iwasawa
for his course at Princeton University in 1964
Provides the details of Iwasawa's original method, unpublished until now, of
the adelic approach to Hecke's L-functions
Is an excellent textbook for studying to learn the analytic continuation and
functional equation of Hecke's L-functions and the class number formula of
Dedekind zeta functions
This volume contains the notes originally made by Kenkichi Iwasawa in his own handwriting
for his lecture course at Princeton University in 1964. These notes give a beautiful and
completely detailed account of the adelic approach to Hecke’s L-functions attached to any
number field, including the proof of analytic continuation, the functional equation of these Lfunctions,
and the class number formula arising from the Dedekind zeta function for a general
number field. This adelic approach was discovered independently by Iwasawa and Tate around
1950 and marked the beginning of the whole modern adelic approach to automorphic forms
and L-series. While Tate’s thesis at Princeton in 1950 was finally published in 1967 in the
volume Algebraic Number Theory, edited by Cassels and Frohlich, no detailed account of
Iwasawa’s work has been published until now, and this volume is intended to fill the gap in
the literature of one of the key areas of modern number theory. In the final chapter, Iwasawa
elegantly explains some important classical results, such as the distribution of prime ideals
and the class number formulae for cyclotomic fields
Due 2019-09-25
1st ed. 2019, XVIII, 162 p. 16 illus.
Printed book
Softcover
ISBN 978-3-030-25442-1
Promotes critical thinking skills to develop intuition about financial options
Highlights the mathematical concepts fundamental to finance by offering an
intuitive approach
Offers instructors potentially new to the area a valuable resource for teaching
a mathematical finance course
Simplifies complex mathematical concepts, such as the derivation of the
Black?Scholes equation and its solutions, by emphasizing the concepts behind a formula
This textbook invites the reader to develop a holistic grounding in mathematical finance, where
concepts and intuition play as important a role as powerful mathematical tools. Financial
interactions are characterized by a vast amount of data and uncertainty; navigating the
inherent dangers and hidden opportunities requires a keen understanding of what techniques
to apply and when. By exploring the conceptual foundations of options pricing, the author
equips readers to choose their tools with a critical eye and adapt to emerging challenges.
Introducing the basics of gambles through realistic scenarios, the text goes on to build the
core financial techniques of Puts, Calls, hedging, and arbitrage. Chapters on modeling and
probability lead into the centerpiece: the Black?Scholes equation. Omitting the mechanics of
solving Black?Scholes itself, the presentation instead focuses on an in-depth analysis of its
derivation and solutions. Advanced topics that follow include the Greeks, American options, and
embellishments. Throughout, the author presents topics in an engaging conversational style.
“Intuition breaks” frequently prompt students to set aside mathematical details and think
critically about the relevance of tools in context. Mathematics of Finance is ideal for
undergraduates from a variety of backgrounds, including mathematics, economics, statistics,
data science, and computer science. Students should have experience with the standard
calculus sequence, as well as a familiarity with differential equations and probability
Due 2019-10-04
1st ed. 2019, XV, 180 p. 32
illus., 31 illus. in color.
Printed book
Hardcover
ISBN 978-981-13-9226-9
Discusses recent developments in fractional calculus and fractional
differential equations
Focuses on applications in pure mathematics, applied mathematics, statistics,
and engineering
Covers topics on numerical analysis of fractional differential equations,
fractional Poisson processes, fractional calculus in complex domains, variableorder
fractional operators, and fractional-order delay differential equations
This book provides a broad overview of the latest developments in fractional calculus and
fractional differential equations (FDEs) with an aim to motivate the readers to venture into
these areas. It also presents original research describing the fractional operators of variable
order, fractional-order delay differential equations, chaos and related phenomena in detail.
Selected results on the stability of solutions of nonlinear dynamical systems of the noncommensurate
fractional order have also been included. Furthermore, artificial neural network
and fractional differential equations are elaborated on; and new transform methods (for
example, Sumudu methods) and how they can be employed to solve fractional partial
differential equations are discussed. The book covers the latest research on a variety of topics,
including: comparison of various numerical methods for solving FDEs, the Adomian
decomposition method and its applications to fractional versions of the classical Poisson
processes, variable-order fractional operators, fractional variational principles, fractional delay
differential equations, fractional-order dynamical systems and stability analysis, inequalities and
comparison theorems in FDEs, artificial neural network approximation for fractional operators,
and new transform methods for solving partial FDEs.
Due 2019-10-09
1st ed. 2019, XXV, 928 p. 212 illus.
Printed book
Hardcover
ISBN 978-981-13-9733-2
Provides a detailed, self-contained textbook on the theory and applications of
complex analysis
Discusses topics with a relevant historical background of the subject to motivate students
Includes complete definitions, proofs, and a wealth of solved examples and end-of-chapter problems
Is a valuable asset for undergraduate and graduate students of mathematics and engineering
This book offers an essential textbook on complex analysis. After introducing the theory of
complex analysis, it places special emphasis on the importance of Poincare theorem and
Hartog’s theorem in the function theory of several complex variables. Further, it lays the
groundwork for future study in analysis, linear algebra, numerical analysis, geometry, number
theory, physics (including hydrodynamics and thermodynamics), and electrical engineering. To
benefit most from the book, students should have some prior knowledge of complex numbers.
However, the essential prerequisites are quite minimal, and include basic calculus with some
knowledge of partial derivatives, definite integrals, and topics in advanced calculus such as
Leibniz’s rule for differentiating under the integral sign and to some extent analysis of infinite
series. The book offers a valuable asset for undergraduate and graduate students of
mathematics and engineering, as well as students with no background in
topological properties.