ISBN: 978-1-4704-4400-6
MAA Textbooks, Volume 43
Published: 24 February 2019; Copyright Year: 2019
Pages: 402; Hardcover;
Subject Classification : Differential Equations
Textbook
Undergraduate students interested in teaching and learning differential equations
(both ordinary and PDE).
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.
ISBN: 978-1-4704-4245-3
Contemporary Mathematics, Volume 721
Published: 16 February 2019; Copyright Year: 2019;
Pages: approximately 299; Softcover
Algebra and Algebraic Geometry
Graduate students and research mathematicians interested in nonassociative algebraic
structures, Lie algebras, and Jordan algebras.
Nonassociative mathematics is a broad research area that studies mathematical
structures violating the associative law x(y z ) = (xy )z . The topics covered by nonassociative
mathematics include quasigroups, loops, Latin squares, Lie algebras, Jordan algebras, octonions,
racks, quandles, and their applications.
This volume contains the proceedings of the Fourth Mile High Conference on Nonassociative
Mathematics, held from July 29?August 5, 2017, at the University of Denver, Denver, Colorado.
Included are research papers covering active areas of investigation, survey papers covering
Leibniz algebras, self-distributive structures, and rack homology, and a sampling of applications
ranging from Yang-Mills theory to the Yang-Baxter equation and Laver tables.
An important aspect of nonassociative mathematics is the wide range of methods employed,
from purely algebraic to geometric, topological, and computational, including automated
deduction, all of which play an important role in this book.
ISBN: 978-1-4704-4212-5
Contemporary Mathematics, Volume 722
Published: 16 February 2019; Copyright Year: 2019;
Pages: 175; Softcover
Algebra and Algebraic Geometry
Number Theory
Graduate students and research mathematicians interested in arithmetic geometry
and coding theory.
For thirty years, the biennial international conference AGC2 T (Arithmetic,
Geometry, Cryptography, and Coding Theory) has brought researchers to Marseille to build
connections between arithmetic geometry and its applications, originally highlighting coding
theory but more recently including cryptography and other areas as well.
This volume contains the proceedings of the 16th international conference, held from June
19?23, 2017.
The papers are original research articles covering a large range of topics, including weight enumerators
for codes, function field analogs of the Brauer-Siegel theorem, the computation of
cohomological invariants of curves, the trace distributions of algebraic groups, and applications
of the computation of zeta functions of curves. Despite the varied topics, the papers share
a common thread: the beautiful interplay between abstract theory and explicit results.
ISBN: 978-1-4704-4384-9
MAA Textbooks, Volume 47
Published: 1 March 2019; Copyright Year:2019;
Pages: 383; Hardcover;
Algebra and Algebraic Geometry
Textbook
Undergraduate students interested in learning linear algebra.
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.
ISBN: 978-1-4704-4688-8
Graduate Studies in Mathematics, Volume 198
Published: 27 March 2019; Copyright Year: 2019;
Pages: approximately 418; Hardcover;
Algebra and Algebraic Geometry
Supplementary Text
Graduate students and researchers interested in arithmetic and non-archimedean
dynamics.
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.
ISBN: 978-1-4704-4350-4
MAA Textbooks, Volume 46
Published: 3 April 2019; Copyright Year: 2019;
Pages: approximately 597; Hardcover;
Algebra and Algebraic Geometry
Textbook
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.