Due 2018-10-01
1st ed. 2018, X, 172 p. 55 illus.
Softcover
ISBN 978-3-319-96874-2
Series : Universitext
Includes tutorials and exercises for Macaulay 2
Provides hands-on experience with over 600 exercises
Broadens understanding of monomial ideals in polynomial rings
This textbook on combinatorial commutative algebra focuses on properties of monomial ideals
in polynomial rings and their connections with other areas of mathematics such as
combinatorics, electrical engineering, topology, geometry, and homological algebra. Aimed
toward advanced undergraduate students and graduate students who have taken a basic
course in abstract algebra that includes polynomial rings and ideals, this book serves as a core
text for a course in combinatorial commutative algebra or as preparation for more advanced
courses in the area. The text contains over 600 exercises to provide readers with a hands-on
experience working with the material; the exercises include computations of specific examples
and proofs of general results. Readers will receive a firsthand introduction to the computer
algebra system Macaulay2 with tutorials and exercises for most sections of the text, preparing
them for significant computational work in the area. Connections to non-monomialareas of
abstract algebra, electrical engineering, combinatorics and otherareas of mathematics are
provided whichgive the reader a sense of how theseideas reach into other areas.
Due 2018-10-11
1st ed. 2018, VII, 396 p. 5 illus.
Softcover
ISBN 978-981-13-1656-2
Series : Universitext
Gives a systematic introduction to the basic theory of financial mathematics,
with an emphasis on applications of martingale methods
Includes general theory of static risk measures, basic concepts and results on
markets of semimartingale model, and a numeraire-free and original
probability based framework for financial markets
An excellent introductory course of mathematical finance for graduate students
This book gives a systematic introduction to the basic theory of financial mathematics, with an
emphasis on applications of martingale methods in pricing and hedging of contingent claims,
interest rate term structure models, and expected utility maximization problems. The general
theory of static risk measures, basic concepts and results on markets of semimartingale model,
and a numeraire-free and original probability based framework for financial markets are also
included. The basic theory of probability and Ito's theory of stochastic analysis, as preliminary
knowledge, are presented.
Due 2018-10-06
1st ed. 2018, X, 313 p. 43
illus., 4 illus. in color.
Softcover
ISBN 978-3-319-95230-7
Series : Lecture Notes in Mathematics
Based on a workshop and a conference at CIRM in Luminy in 2016 attended
by both graduate students and very senior practitioners of the subject.
Features several excellent review articles which can be read by students
entering research in many areas of number theory.
Includes several high level research articles.
Begins with an article on the geometric Satake isomorphism, a key theorem in
the geometric Langlands program.
This volume presents a panorama of the diverse activities organized by V. Heiermann and D.
Prasad in Marseille at CIRM for the Chaire Morlet event during the first semester of 2016. It
assembles together expository articles on topics which previously could only been found in
research papers. Starting with a very detailed article by P. Baumann and S. Riche on the
geometric Satake correspondence, the book continues with three introductory articles on
distinguished representations due to P. Broussous, F. Murnaghan, and O. Offen, an expository
article of I. Badulescu on the Jacquet?Langlands correspondence, a paper of J. Arthur on
functoriality and the trace formula in the context of "Beyond Endoscopy", taken from the
Simons Proceedings, an article of W-W. Li attempting to generalize Godement?Jacquet theory,
and a research paper of C. Moeglin and D. Renard, applying the trace formula to the local
Langlands classification for classical groups. The book should be of interest to students as well
as professional researchers working in the broad area of representation theory.
Due 2018-10-04
1st ed. 2018, X, 275 p. 26
illus., 22 illus. in color.
Softcover
ISBN 978-3-319-97141-4
Series : C.I.M.E. Foundation Subseries
Brilliantly written tutorial on topics not covered elsewhere
Introduces the reader to optimization over networks which is an emergent
topic of contemporary importance with promising applications
Introduces the reader to complex modeling interdisciplinary paradigms as
Differential Variational Inequalities that are necessary to model complex timevarying,
paradigm shifting engineering situations
This book contains three well-written research tutorials that inform the graduate reader about
the forefront of current research in multi-agent optimization. These tutorials cover topics that
have not yet found their way in standard books and offer the reader the unique opportunity to
be guided by major researchers in the respective fields. Multi-agent optimization, lying at the
intersection of classical optimization, game theory, and variational inequality theory, is at the
forefront of modern optimization and has recently undergone a dramatic development. It
seems timely to provide an overview that describes in detail ongoing research and important
trends. This book concentrates on Distributed Optimization over Networks; Differential
Variational Inequalities; and Advanced Decomposition Algorithms for Multi-agent Systems. This
book will appeal to both mathematicians and mathematically oriented engineers and will be
the source of inspiration for PhD students and researchers.
Due 2018-09-30
1st ed. 2018, Approx. 305 p. 6 illus.
Softcover
ISBN 978-3-319-99066-8
Series : History of Mathematics Subseries
Describes the history of the Riemann hypothesis for function fields based on
letters exchanged between the main protagonists at the time
Provides a well-documented account of how mathematics develops in general
Written for mathematicians, but does not require specialist knowledge
This book tells the story of the Riemann hypothesis for function fields (or curves) starting with
Artin's 1921 thesis, covering Hasse's work in the 1930s on elliptic fields and more, and
concluding with Weil's final proof in 1948. The main sources are letters which were exchanged
among the protagonists during that time, found in various archives, mostly the University
Library in Gottingen. The aim is to show how the ideas formed, and how the proper notions
and proofs were found, providing a particularly well-documented illustration of how
mathematics develops in general. The book is written for mathematicians, but it does not
require any special knowledge of particular mathematical fields.