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Pick up this book and dive into one of eight chapters relating
mathematics to fiber arts! Amazing exposition transports any
interested person on a mathematical exploration that is rigorous
enough to capture the hearts of mathematicians. The zenith of
creativity is achieved as readers are led to knit, crochet, quilt, or
sew a project specifically designed to illuminate the mathematics
through its physical realization. The beautiful finished pieces
provide a visual understanding of the mathematics that can be shared
with those who view them. If you love mathematics or fiber arts, this
book is for you!
Individual chapters are also available for purchase. Each
self-contained chapter contains directions for a complete project in
downloadable PDF format. See a list of all
chapters.
Undergraduate and graduate students and researchers interested in mathematical themes in needlework and fiber arts (e.g. crocheting, knitting, quilting).
I have long wondered whether it was possible to create art that expressed the beauty of science at a deep level. Most of the art I've seen celebrating science has lain strictly at the surface — mostly, images of scientific concepts that happen to have aesthetically attractive representations...Until someone told me about "Figuring Fibers." "Figuring Fibers" is a compilation of articles that demonstrate mathematical principles using fiber arts in a deep, thoughtful manner. It's unique in that it's written with mathematical rigor, yet is readable by the sufficiently bold layperson; and each article covers a deep, interesting mathematical idea and then demonstrates it/extends the idea using a fiber art technique.
-- Tien Chiu
This is a widely accessible introductory treatment of infinite series of real numbers, bringing the reader from basic definitions and tests to advanced results. An up-to-date presentation is given, making infinite series accessible, interesting, and useful to a wide audience, including students, teachers, and researchers. Included are elementary and advanced tests for convergence or divergence, the harmonic series, the alternating harmonic series, and closely related results. One chapter offers 107 concise, crisp, surprising results about infinite series. Another gives problems on infinite series, and solutions, which have appeared on the annual William Lowell Putnam Mathematical Competition. The lighter side of infinite series is treated in the concluding chapter where three puzzles, eighteen visuals, and several fallacious proofs are made available. Three appendices provide a listing of true or false statements, answers to why the harmonic series is so named, and an extensive list of published works on infinite series.
One chapter offers 107 concise, crisp, surprising results about infinite series. Recognizing the interest in problem solving that abounds with students of mathematics, the authors devote a chapter to problems of infinite series, and solutions ...
-- L'enseignement mathematique
Nilsystems play a key role in the structure
theory of measure preserving systems, arising as the natural objects
that describe the behavior of multiple ergodic averages. This book is
a comprehensive treatment of their role in ergodic theory, covering
development of the abstract theory leading to the structural
statements, applications of these results, and connections to other
fields.
Starting with a summary of the relevant dynamical background, the
book methodically develops the theory of cubic structures that give
rise to nilpotent groups and reviews results on nilsystems and their
properties that are scattered throughout the literature. These basic
ingredients lay the groundwork for the ergodic structure theorems, and
the book includes numerous formulations of these deep results, along
with detailed proofs. The structure theorems have many applications,
both in ergodic theory and in related fields; the book develops the
connections to topological dynamics, combinatorics, and number theory,
including an overview of the role of nilsystems in each of these
areas. The final section is devoted to applications of the structure
theory, covering numerous convergence and recurrence results.
The book is aimed at graduate students and researchers in ergodic
theory, along with those who work in the related areas of arithmetic
combinatorics, harmonic analysis, and number theory.
Graduate students and researchers interested in ergodic theory and its connections to combinatorics and number theory.
Combinatorial reciprocity is a very
interesting phenomenon, which can be described as follows: A
polynomial, whose values at positive integers count combinatorial
objects of some sort, may give the number of combinatorial objects of
a different sort when evaluated at negative integers (and suitably
normalized). Such combinatorial reciprocity theorems occur in
connections with graphs, partially ordered sets, polyhedra, and more.
Using the combinatorial reciprocity theorems as a leitmotif, this book
unfolds central ideas and techniques in enumerative and geometric
combinatorics.
Written in a friendly writing style, this is an
accessible graduate textbook with almost 300 exercises, numerous
illustrations, and pointers to the research literature. Topics include
concise introductions to partially ordered sets, polyhedral geometry,
and rational generating functions, followed by highly original
chapters on subdivisions, geometric realizations of partially ordered
sets, and hyperplane arrangements.
Advanced undergraduate students and graduate students learning combinatorics; instructors teaching such courses.
Algebra and Tiling is accessible to
undergraduate mathematics majors, as most of the tools necessary to
read the book are found in standard upper division algebra courses,
but teachers, researchers, and professional mathematicians will find
the book equally appealing. Beginners will find the exercises and the
appendices especially useful. The unsolved problems will challenge
both beginners and experts.
The book could serve as the basis of an undergraduate or graduate
seminar or a source of applications to enrich an algebra or geometry
course.
The prerequisites for this book are an acquaintance with the very basics of group and field theory. The appendices, on lattices, exact sequences, formal sums, and cyclotomic polynomials make this book quite self-contained and accessible to non-experts. There are plenty of historical remarks, making the exposition lively, and there are dozens of illustrations. The exercises and problems are abundant and stimulating.
-- Fabio Mainardi, MAA Reviews
Mathematical Reflections: Two Wonderful Years is a
compilation and revision of the 2016 and 2017 volumes from the online
journal of the same name. This book is aimed at high school students,
participants in math competitions, undergraduates, and anyone who has
a fire for mathematics. Passionate readers submitted many of the
problems, solutions, and articles and all require creativity,
experience, and comprehensive mathematical knowledge.
This book is a great resource for students training for advanced
national and international mathematics competitions such as USAMO and
IMO.
A publication of XYZ Press. Distributed in North America by the American Mathematical Society.
High school students, participants in math competitions, undergraduates, and anyone interested in mathematics.
Linear Algebra: Concepts and Applications is designed to be
used in a first linear algebra course taken by mathematics and science
majors. It provides a complete coverage of core linear algebra topics,
including vectors and matrices, systems of linear equations, general
vector spaces, linear transformations, eigenvalues, and eigenvectors.
All results are carefully, clearly, and rigorously proven. The
exposition is very accessible.
The applications of linear algebra are extensive and
substantial—several of those recur throughout the text in different
contexts, including many that elucidate concepts from multivariable
calculus. Unusual features of the text include a pervasive emphasis
on the geometric interpretation and viewpoint as well as a very
complete treatment of the singular value decomposition. The book
includes over 800 exercises and numerous references to the author's
custom software Linear Algebra Toolkit.
Undergraduate students interested in learning linear algebra.
Linear Algebra and Geometry is
organized around carefully sequenced problems that help students build
both the tools and the habits that provide a solid basis for further
study in mathematics. Requiring only high school algebra, it uses
elementary geometry to build the beautiful edifice of results and
methods that make linear algebra such an important field.
The materials in Linear Algebra and Geometry have been used, field
tested, and refined for over two decades. It is aimed at preservice
and practicing high school mathematics teachers and advanced high
school students looking for an addition to or replacement for
calculus. Secondary teachers will find the emphasis on developing
effective habits of mind especially helpful. The book is written in a
friendly, approachable voice and contains nearly a thousand problems.
Undergraduate students interested in learning linear algebra.
A thoroughly modern textbook for the
sophomore-level differential equations course. The examples and
exercises emphasize modeling not only in engineering and physics but
also in applied mathematics and biology. There is an early
introduction to numerical methods and, throughout, a strong emphasis
on the qualitative viewpoint of dynamical systems. Bifurcations and
analysis of parameter variation is a persistent theme.
Presuming previous exposure to only two semesters of calculus,
necessary linear algebra is developed as needed. The exposition is
very clear and inviting. The book would serve well
for use in a flipped-classroom pedagogical approach or for self-study
for an advanced undergraduate or beginning graduate student.
This second edition of Noonburg's best-selling textbook includes
two new chapters on partial differential equations, making the book
usable for a two-semester sequence in differential equations. It
includes exercises, examples, and extensive student projects taken
from the current mathematical and scientific literature.
Undergraduate students interested in teaching and learning differential equations (both ordinary and PDE).
The theory of complex dynamics in one variable, initiated by Fatou and
Julia in the early twentieth century, concerns the iteration of a
rational function acting on the Riemann sphere. Building on
foundational investigations of \(p\)-adic dynamics in the late twentieth
century, dynamics in one non-archimedean variable is the analogous
theory over non-archimedean fields rather than over the complex
numbers. It is also an essential component of the number-theoretic
study of arithmetic dynamics.
This textbook presents the fundamentals of non-archimedean
dynamics, including a unified exposition of Rivera-Letelier's
classification theorem, as well as results on wandering domains,
repelling periodic points, and equilibrium measures. The Berkovich
projective line, which is the appropriate setting for the associated
Fatou and Julia sets, is developed from the ground up, as are relevant
results in non-archimedean analysis. The presentation is accessible to
graduate students with only first-year courses in algebra and analysis
under their belts, although some previous exposure to non-archimedean
fields, such as the \(p\)-adic numbers, is recommended. The book should
also be a useful reference for more advanced students and researchers
in arithmetic and non-archimedean dynamics.
Graduate students and researchers interested in arithmetic and non-archimedean dynamics.