Due 2018-08-07
1st ed. 2018, X, 199 p. 13 illus.
Softcover
ISBN 978-3-319-91511-1
Series ; Universitext
Provides an elementary treatment of the subject that establishes the
foundation for further study
Enriches understanding of the theory with numerous examples and
counterexamples
Includes many exercises for readers to practice techniques
Dissects proofs of difficult results into small steps to improve understanding
This concise text provides a gentle introduction to functional analysis. Chapters cover essential
topics such as special spaces, normed spaces, linear functionals, and Hilbert spaces. Numerous
examples and counterexamples aid in the understanding of key concepts, while exercises at
the end of each chapter provide ample opportunities for practice with the material. Proofs of
theorems such as the Uniform Bounded Theory, the Open Mapping Theorem, and the Closed
Graph Theorem are worked through step-by-step, providing an accessible avenue to
understanding these important results. The prerequisites for this book are linear algebra and
elementary real analysis, with two introductory chapters providing an overview of material
necessary for the subsequent text. Functional Analysis offers an elementary approach ideal for
the upper-undergraduate or beginning graduate student. Primarily intended for a one-semester
introductory course, this text is also a perfect resource for independent study or as the basis
for a reading course.
Due 2018-07-29
2nd ed. 2018, XV, 373 p. 44 illus.
Hardcover
ISBN 978-981-13-0658-7
Series ; Springer Undergraduate Mathematics Series
Examples and Applications
Easily accessible to both mathematics and non-mathematics majors who are
taking an introductory course on Stochastic Processes
Filled with numerous exercises to test students' understanding of key
concepts
A gentle introduction to help students ease into later chapters, also suitable
for self-study
Accompanied with computer simulation codes in R and Python
This book provides an undergraduate-level introduction to discrete and continuous-time Markov
chains and their applications, with a particular focus on the first step analysis technique and its
applications to average hittingtimes and ruin probabilities. It also discusses classical topics
such as recurrence and transience,stationary and limiting distributions, as well as branching
processes. It first examines in detail two important examples (gambling processes and random
walks) before presenting the general theory itself in the subsequent chapters. It also provides
an introduction to discrete-time martingalesand their relation to ruin probabilities and mean
exit times, together with a chapter on spatial Poisson processes. The conceptspresented are
illustrated by examples, 138 exercises and 9 problemswith their solutions.
Due 2018-08-09
1st ed. 2018, XVII, 543 p.
Softcover
ISBN 978-3-319-92003-0
Series ; Universitext
Provides necessary preliminaries
Explores basic and advanced material in functional analysis and operator
theory, including applications to Fourier series and the Fourier transform
Includes over 1500 exercises
Written by an expert on the topic and experienced lecturer, this textbook provides an elegant,
self-contained introduction to functional analysis, including several advanced topics and
applications to harmonic analysis. Starting from basic topics before proceeding to more
advanced material, the book covers measure and integration theory, classical Banach and
Hilbert space theory, spectral theory for bounded operators, fixed point theory, Schauder bases,
the Riesz-Thorin interpolation theorem for operators, as well as topics in duality and convexity
theory. Aimed at advanced undergraduate and graduate students, this book is suitable for both
introductory and more advanced courses in functional analysis. Including over 1500 exercises
of varying difficulty and various motivational and historical remarks, the book can be used for
self-study and alongside lecture courses.
Due 2018-10-13
1st ed. 2018, Approx. 885 p.
Hardcover
ISBN 978-3-319-90328-6
Series ;Sources and Studies in the History of Mathematics and Physical Sciences
the Dutch Correspondents
Contains a concise biography of Lorentz, as well as a full bibliography of his
writings and an insightful collection of his letters
Provides English translations for Dutch correspondence
Includes helpful annotations of the letters where their necessity has been
determined
This is the second and final volume of Dutch physicist Hendrik Antoon Lorentz's scientific
correspondence with Dutch colleagues, including Pieter Zeeman and Paul Ehrenfest. These 294
letters cover multiple subjects, ranging from pure mathematics to magneto-optics and wave
mechanics. They reveal much about their author, including Lorentz's surprisingly active
involvement in experimental matters in the first decades of his career. Letters are also devoted
to general relativity, Lorentz's 1908 lecture on radiation theory, and his receipt of the Nobel
Prize along with Zeeman in 1902. The letters are presented in their original language; Dutch
originals are accompanied by English translations. A concise biography of Lorentz is also
included.
Due 2018-10-12
1st ed. 2018, XV, 165 p. 10 illus.
Softcover
ISBN 978-3-319-92413-7
Series; Springer Undergraduate Mathematics Series
Provides a concise introduction to mathematical logic for mathematics students
Introduces models before formal proofs
Includes a detailed presentation of naive set theory as used in everyday
mathematical reasoning
Gives a detailed description of Gentzen-style proof trees and Godelfs
completeness theorem for first-order logic
Contains over 100 exercises of varying difficulty
This textbook provides a concise and self-contained introduction to mathematical logic, with a
focus on the fundamental topics in first-order logic and model theory. Including examples
from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates
the relevance and usefulness of logic in the study of these subject areas. The authors start
with an exposition of set theory and the axiom of choice as used in everyday mathematics.
Proceeding at a gentle pace, they go on to present some of the first important results in
model theory, followed by a careful exposition of Gentzen-style natural deduction and a
detailed proof of Godelfs completeness theorem for first-order logic. The book then explores
the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of
suggestions for further study. The present volume is primarily aimed at mathematics students
who are already familiar with basic analysis, algebra and linear algebra. It contains numerous
exercises of varying difficulty and can be used for self-study, though it is ideally suited as a
text for a one-semester university course in the second or third year.
Due 2018-11-11
1st ed. 2018, V, 305 p. 2 illus.
Softcover
ISBN 978-3-319-91997-3
Series :Springer Undergraduate Mathematics Series
Offers an elementary introduction that includes more advanced topics such as
Gabrielfs theorem on quivers
Based on the authorsf extensive undergraduate teaching experience
Provides numerous worked examples and more than 200 exercises (with
worked solutions to some of them)
This carefully written textbook provides an accessible introduction to the representation theory
of algebras, including representations of quivers. The book starts with basic topics on algebras
and modules, covering fundamental results such as the Jordan-Holder theorem on composition
series, the Artin-Wedderburn theorem on the structure of semisimple algebras and the Krull-
Schmidt theorem on indecomposable modules. The authors then go on to study
representations of quivers in detail, leading to a complete proof of Gabriel's celebrated theorem
characterizing the representation type of quivers in terms of Dynkin diagrams. Requiring only
introductory courses on linear algebra and groups, rings and fields, this textbook is aimed at
undergraduate students. With numerous examples illustrating abstract concepts, and including
more than 200 exercises (with solutions to about a third of them), the book provides an
example-driven introduction suitable for self-study and use alongside lecture courses.