XYZ Series, Volume: 41
2021; 530 pp; Softcover
MSC: Primary 00; 97
Print ISBN: 978-1-7358315-1-0
This book casts light on the topic of polynomials from numerous angles.
The authors present important theoretical facts in harmony with their showcased applications.
There are 8 chapters, 252 solved examples, 105 end-of-chapter problems, all with
detailed solutions, as well as 77 additional problems that further enhance the book's exposition.
This book is best suited for motivated high school and college students,
teachers, or anyone with a passion for mathematics.
XYZ Series, Volume: 42
2021; 184 pp; Softcover
MSC: Primary 00; 97;
Print ISBN: 978-1-7358315-2-7
This book has 13 chapters of problems. Chapters 14 through 26 comprise of the solutions
to the previous 13 chapters. The authors also present several solutions for a large part of
the problems in order to provide a full picture of these essential algebraic techniques and
their accompanying theorems. The authors really strived to illustrate the beauty and
interconnectedness of algebra by including these problems, all of which they created,
and delicately arranging the chapters. Whether you are preparing for Olympiad level competitions
such as USA(J)MO, are formally studying mathematics, or if algebra simply piques your interest,
we are confident that you will appreciate these topics and awesome problems.
This book is best suited for motivated high school and college students, teachers,
or anyone with a passion for mathematics.
Mathematical Surveys and Monographs, Volume: 260
2021; 311 pp; Softcover
MSC: Primary 16; 11; Secondary 12; 20
Print ISBN: 978-1-4704-6516-2
Hopf algebras have been shown to play a natural role in studying questions of integral
module structure in extensions of local or global fields. This book surveys the state
of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed
as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and
Local Galois Module Theory, which was published in 2000.
The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois
structures on Galois field extensions, as well as the connection between this topic and
the theory of skew braces. Part II is more number theoretical and studies the application
of Hopf algebras to questions of integral module structure in extensions of local or global fields.
Graduate students and researchers with a general background in graduate-level algebra,
algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview
of the current state of this exciting area and the suggestions for numerous avenues for
further research and investigation.
Graduate students and researchers interested in Hopf algebras.
Pure and Applied Undergraduate Texts, Volume: 53
2022; 270 pp; Softcover
MSC: Primary 60; 91;
Print ISBN: 978-1-4704-6488-2
A First Course in Stochastic Calculus is a complete guide for advanced undergraduate
students to take the next step in exploring probability theory and for master's students i
n mathematical finance who would like to build an intuitive and theoretical understanding
of stochastic processes. This book is also an essential tool for finance professionals who
wish to sharpen their knowledge and intuition about stochastic calculus.
Louis-Pierre Arguin offers an exceptionally clear introduction to Brownian motion and
to random processes governed by the principles of stochastic calculus. The beauty and
power of the subject are made accessible to readers with a basic knowledge of probability,
linear algebra, and multivariable calculus. This is achieved by emphasizing numerical
experiments using elementary Python coding to build intuition and adhering to a rigorous
geometric point of view on the space of random variables. This unique approach is used to
elucidate the properties of Gaussian processes, martingales, and diffusions. One of the book's
highlights is a detailed and self-contained account of stochastic calculus applications to option pricing in finance.
Undergraduate and graduate students interested in advanced probability
and the applications of stochastic calculus to finance. Finance professionals
who want to develop their knowledge and intuition of stochastic calculus.
Louis-Pierre Arguin's masterly introduction to stochastic calculus seduces the reader
with its quietly conversational style; even rigorous proofs seem natural and easy.
Full of insights and intuition, reinforced with many examples, numerical projects,
and exercises, this book by a prize-winning mathematician and great teacher fully
lives up to the author's reputation. I give it my strongest possible recommendation.
-- Jim Gatheral, Baruch College
I happen to be of a different persuasion, about how stochastic processes should be
taught to undergraduate and MA students. But I have long been thinking to go against
my own grain at some point and try to teach the subject at this
level-yogether with its applications to finance one semester. Louis-Pierre Arguin's
excellent and artfully designed text will give me the ideal vehicle to do so.
-- Ioannis Karatzas, Columbia University, New York
AMS/MAA Textbooks, Volume: 68
2021; 334 pp; Softcover
MSC: Primary 00;
Print ISBN: 978-1-4704-6514-8
Proofs and Ideas serves as a gentle introduction to advanced mathematics for students
who previously have not had extensive exposure to proofs. It is intended to ease the student's
transition from algorithmic mathematics to the world of mathematics that is built around proofs and concepts.
The spirit of the book is that the basic tools of abstract mathematics are best developed in
context and that creativity and imagination are at the core of mathematics. So, while the book
has chapters on statements and sets and functions and induction, the bulk of the book focuses
on core mathematical ideas and on developing intuition. Along with chapters on elementary
combinatorics and beginning number theory, this book contains introductory chapters on real analysis,
group theory, and graph theory that serve as gentle first exposures to their respective areas.
The book contains hundreds of exercises, both routine and non-routine.
This book has been used for a transition to advanced mathematics courses at California State University,
Northridge, as well as for a general education course on mathematical reasoning at Krea University, India.
Undergraduate students interested in an introduction to proofs.
This book is a continuation of Asymptotic Geometric Analysis, Part I,
which was published as volume 202 in this series.
Mathematical Surveys and Monographs, Volume: 261
2021; 645 pp; Softcover
MSC: Primary 52; 46; 60;
Print ISBN: 978-1-4704-6360-1
Asymptotic geometric analysis studies properties of geometric objects, such as normed spaces,
convex bodies, or convex functions, when the dimensions of these objects increase to infinity.
The asymptotic approach reveals many very novel phenomena which influence other fields in
mathematics, especially where a large data set is of main concern, or a number of parameters
which becomes uncontrollably large. One of the important features of this new theory is in
developing tools which allow studying high parametric families.
Among the topics covered in the book are measure concentration, isoperimetric constants
of log-concave measures, thin-shell estimates, stochastic localization, the geometry of Gaussian
measures, volume inequalities for convex bodies, local theory of Banach spaces, type and cotype,
the Banach-Mazur compactum, symmetrizations, restricted invertibility, and functional versions of
geometric notions and inequalities.
Graduate students and researchers interested in analysis and geometry of high dimensional spaces.
Collected Works, Volume: 27
2021; Hardcover
MSC: Primary 57; 53; 20; 37; 68;
Print ISBN: 978-1-4704-5164-6
This set contains the Collected Works of William P. Thurston with Commentary, Volumes I-II,
and The Geometry and Topology of Three-Manifolds.
William Thurston's work has had a profound influence on mathematics.
He connected whole mathematical subjects in entirely new ways and changed the way
mathematicians think about geometry, topology, foliations, group theory, dynamical systems,
and the way these areas interact. His emphasis on understanding and imagination in mathematical
learning and thinking are integral elements of his distinctive legacy.
This four-part collection brings together in one place Thurston's major writings,
many of which are appearing in publication for the first time. Volumes I-II contain commentaries by the Editors.
Volume IV includes a preface by Steven P. Kerckhoff.
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Contemporary Mathematics, Volume: 775
2021; 319 pp; Softcover
MSC: Primary 53; 83; 46; 37; 55; 35; 47; 17; 11; 22;
Print ISBN: 978-1-4704-6536-0
Articles in this volume are based on presentations given at the IV Meeting of Mexican Mathematicians Abroad
(IV Reunin de Matemticos Mexicanos en el Mundo), held from June 10-15,
2018, at Casa Matemtica Oaxaca (CMO), Mexico.
This meeting was the fourth in a series of ongoing biannual meetings bringing
together Mexican mathematicians working
abroad with their peers in Mexico.
This book features surveys and research articles from five broad research areas: algebra, analysis, combinatorics,
geometry, and topology. Their topics range from general relativity and mathematical physics to interactions
between logic and ergodic theory. Several articles provide a panoramic view of the fields and problems on
which the authors are currently working on, showcasing diverse research lines complementary to those
currently pursued in Mexico. The research-oriented manuscripts provide either alternative approaches
to well-known problems or new advances in active research fields.
Graduate students and research mathematicians interested in algebra, analysis, combinatorics, and geometry and topology.