A publication of the Theta Foundation
Theta Foundation International Book Series of Mathematical Texts, Volume: 25
2018; 166 pp; Hardcover
MSC: Primary 00; 30; 42; 46; 47;
Print ISBN: 978-606-8443-11-9
The volume contains the proceedings of the First Northeastern Analysis Meeting, held in Brockport between October 14 and 16, 2016. It consists of a careful selection of papers covering a large range of subjects in mathematical analysis.
Among the topics discussed are: (1) classical complex function theory; (2) differential operators on trees; (3) integral operators; (4) operator theory on function spaces; (5) Fourier analysis; and (6) geometry of Banach spaces.
Anyone interested in analysis.
A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University
Courant Lecture Notes, Volume: 29
2019; 261 pp; Softcover
MSC: Primary 97; 15; 40; 20;
Print ISBN: 978-1-4704-4871-4
This book is the first of two volumes on linear algebra for graduate students in mathematics, the sciences, and economics, who have: a prior undergraduate course in the subject; a basic understanding of matrix algebra; and some proficiency with mathematical proofs. Proofs are emphasized and the overall objective is to understand the structure of linear operators as the key to solving problems in which they arise.
This first volume re-examines basic notions of linear algebra: vector spaces, linear operators, duality, determinants, diagonalization, and inner product spaces, giving an overview of linear algebra with sufficient mathematical precision for advanced use of the subject. This book provides a nice and varied selection of exercises; examples are well-crafted and provide a clear understanding of the methods involved. New notions are well motivated and interdisciplinary connections are often provided, to give a more intuitive and complete vision of linear algebra. Computational aspects are fully covered, but the study of linear operators remains the focus of study in this book.
Undergraduate and graduate students interested in an advanced understanding of linear algebra for graduate studies.
Contemporary Mathematics, Volume: 723
2019; 214 pp; Softcover
MSC: Primary 35; Secondary 11; 26; 60; 91
Print ISBN: 978-1-4704-4110-4
This volume contains the proceedings of the AMS Special Session on New Developments in the Analysis of Nonlocal Operators, held from October 28?30, 2016, at the University of St. Thomas, Minneapolis, Minnesota.
Over the last decade there has been a resurgence of interest in problems involving nonlocal operators, motivated by applications in many areas such as analysis, geometry, and stochastic processes.
Problems represented in this volume include uniqueness for weak solutions to abstract parabolic equations with fractional time derivatives, the behavior of the one-phase Bernoulli-type free boundary near a fixed boundary and its relation to a Signorini-type problem, connections between fractional powers of the spherical Laplacian and zeta functions from the analytic number theory and differential geometry, and obstacle problems for a class of not stable-like nonlocal operators for asset price models widely used in mathematical finance.
The volume also features a comprehensive introduction to various aspects of the fractional Laplacian, with many historical remarks and an extensive list of references, suitable for beginners and more seasoned researchers alike.
Graduate students and research mathematicians interested in analytic, geometric, and probabilistic aspects of nonlocal equations.
Contemporary Mathematics, Volume: 724
2019; 344 pp; Softcover
MSC: Primary 11; 14;
Print ISBN: 978-1-4704-4247-7
This volume contains a collection of papers on algebraic curves and their applications. While algebraic curves traditionally have provided a path toward modern algebraic geometry, they also provide many applications in number theory, computer security and cryptography, coding theory, differential equations, and more.
Papers cover topics such as the rational torsion points of elliptic curves, arithmetic statistics in the moduli space of curves, combinatorial descriptions of semistable hyperelliptic curves over local fields, heights on weighted projective spaces, automorphism groups of curves, hyperelliptic curves, dessins d'enfants, applications to Painleve equations, descent on real algebraic varieties, quadratic residue codes based on hyperelliptic curves, and Abelian varieties and cryptography.
This book will be a valuable resource for people interested in algebraic curves and their connections to other branches of mathematics.
Graduate students and research mathematicians interested in algebraic geometry, cryptography, and elliptic and hyperelliptic curves.
2019; 323 pp; Hardcover
MSC: Primary 00; 92; 39; 62;
Print ISBN: 978-1-4704-4869-1
Can we coexist with the other life forms that have evolved on this planet? Are there realistic alternatives to fossil fuels that would sustainably provide for human society's energy needs and have fewer harmful effects? How do we deal with threats such as emergent diseases?
Mathematical models?equations of various sorts capturing relationships between variables involved in a complex situation?are fundamental for understanding the potential consequences of choices we make. Extracting insights from the vast amounts of data we are able to collect requires analysis methods and statistical reasoning.
This book on elementary topics in mathematical modeling and data analysis is intended for an undergraduate gliberal arts mathematicsh-type course but with a specific focus on environmental applications. It is suitable for introductory courses with no prerequisites beyond high school mathematics. A great variety of exercises extends the discussions of the main text to new situations and/or introduces new real-world examples. Every chapter ends with a section of problems, as well as with an extended chapter project which often involves substantial computing work either in spreadsheet software or in the RR statistical package.
Undergraduate and graduate students and researchers interested in math modeling and data analysis with environmental applications.
Pure and Applied Undergraduate Texts, Volume: 34
2019; 142 pp; Hardcover
MSC: Primary 51;
Print ISBN: 978-1-4704-4760-1
This book on two-dimensional geometry uses a problem-solving approach to actively engage students in the learning process. The aim is to guide readers through the story of the subject, while giving them room to discover and partially construct the story themselves. The book bridges the study of plane geometry and the study of curves and surfaces of non-constant curvature in three-dimensional Euclidean space. One useful feature is that the book can be adapted to suit different audiences.
The first half of the text covers plane geometry without and with Euclid's Fifth Postulate, followed by a brief synthetic treatment of spherical geometry through the excess angle formula. This part only requires a background in high school geometry and basic trigonometry and is suitable for a quarter course for future high school geometry teachers. A brief foray into the second half could complete a semester course.
The second half of the text gives a uniform treatment of all the complete, simply connected, two-dimensional geometries of constant curvature, one geometry for each real number (its curvature), including their groups of isometries, geodesics, measures of lengths and areas, as well as formulas for areas of regions bounded by polygons in terms of the curvature of the geometry and the sum of the interior angles of the polygon. A basic knowledge of real linear algebra and calculus of several (real) variables is useful background for this portion of the text.
Undergraduates interested in secondary school mathematics teaching; also some engineering and physics majors.