Divisors and Sandpiles - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Divisors and Sandpiles write by Scott Corry. This book was released on 2018-07-23. Divisors and Sandpiles available in PDF, EPUB and Kindle. Divisors and Sandpiles provides an introduction to the combinatorial theory of chip-firing on finite graphs. Part 1 motivates the study of the discrete Laplacian by introducing the dollar game. The resulting theory of divisors on graphs runs in close parallel to the geometric theory of divisors on Riemann surfaces, and Part 1 culminates in a full exposition of the graph-theoretic Riemann-Roch theorem due to M. Baker and S. Norine. The text leverages the reader's understanding of the discrete story to provide a brief overview of the classical theory of Riemann surfaces. Part 2 focuses on sandpiles, which are toy models of physical systems with dynamics controlled by the discrete Laplacian of the underlying graph. The text provides a careful introduction to the sandpile group and the abelian sandpile model, leading ultimately to L. Levine's threshold density theorem for the fixed-energy sandpile Markov chain. In a precise sense, the theory of sandpiles is dual to the theory of divisors, and there are many beautiful connections between the first two parts of the book. Part 3 addresses various topics connecting the theory of chip-firing to other areas of mathematics, including the matrix-tree theorem, harmonic morphisms, parking functions, M-matrices, matroids, the Tutte polynomial, and simplicial homology. The text is suitable for advanced undergraduates and beginning graduate students.
SOFSEM 2019: Theory and Practice of Computer Science
SOFSEM 2019: Theory and Practice of Computer Science - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook SOFSEM 2019: Theory and Practice of Computer Science write by Barbara Catania. This book was released on 2019-01-10. SOFSEM 2019: Theory and Practice of Computer Science available in PDF, EPUB and Kindle. This book constitutes the refereed proceedings of the 45th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2019, held in Nový Smokovec, Slovakia, in January 2019. The 34 full papers presented together with 6 invited talks were carefully reviewed and selected from 92 submissions. They presented new research results in the theory and practice of computer science in the each sub-area of SOFSEM 2019: Foundations of theoretical Computer Science, foundations of data science and engineering, and foundations of software engineering.
A Project-Based Guide to Undergraduate Research in Mathematics
A Project-Based Guide to Undergraduate Research in Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Project-Based Guide to Undergraduate Research in Mathematics write by Pamela E. Harris. This book was released on 2020-04-17. A Project-Based Guide to Undergraduate Research in Mathematics available in PDF, EPUB and Kindle. This volume provides accessible and self-contained research problems designed for undergraduate student projects, and simultaneously promotes the development of sustainable undergraduate research programs. The chapters in this work span a variety of topical areas of pure and applied mathematics and mathematics education. Each chapter gives a self-contained introduction on a research topic with an emphasis on the specific tools and knowledge needed to create and maintain fruitful research programs for undergraduates. Some of the topics discussed include:• Disease modeling• Tropical curves and surfaces• Numerical semigroups• Mathematics EducationThis volume will primarily appeal to undergraduate students interested in pursuing research projects and faculty members seeking to mentor them. It may also aid students and faculty participating in independent studies and capstone projects.
The Mathematics of Chip-Firing
The Mathematics of Chip-Firing - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Mathematics of Chip-Firing write by Caroline J. Klivans. This book was released on 2018-11-15. The Mathematics of Chip-Firing available in PDF, EPUB and Kindle. The Mathematics of Chip-firing is a solid introduction and overview of the growing field of chip-firing. It offers an appreciation for the richness and diversity of the subject. Chip-firing refers to a discrete dynamical system — a commodity is exchanged between sites of a network according to very simple local rules. Although governed by local rules, the long-term global behavior of the system reveals fascinating properties. The Fundamental properties of chip-firing are covered from a variety of perspectives. This gives the reader both a broad context of the field and concrete entry points from different backgrounds. Broken into two sections, the first examines the fundamentals of chip-firing, while the second half presents more general frameworks for chip-firing. Instructors and students will discover that this book provides a comprehensive background to approaching original sources. Features: Provides a broad introduction for researchers interested in the subject of chip-firing The text includes historical and current perspectives Exercises included at the end of each chapter About the Author: Caroline J. Klivans received a BA degree in mathematics from Cornell University and a PhD in applied mathematics from MIT. Currently, she is an Associate Professor in the Division of Applied Mathematics at Brown University. She is also an Associate Director of ICERM (Institute for Computational and Experimental Research in Mathematics). Before coming to Brown she held positions at MSRI, Cornell and the University of Chicago. Her research is in algebraic, geometric and topological combinatorics.
Tropical and Non-Archimedean Geometry
Tropical and Non-Archimedean Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Tropical and Non-Archimedean Geometry write by Omid Amini. This book was released on 2014-12-26. Tropical and Non-Archimedean Geometry available in PDF, EPUB and Kindle. Over the past decade, it has become apparent that tropical geometry and non-Archimedean geometry should be studied in tandem; each subject has a great deal to say about the other. This volume is a collection of articles dedicated to one or both of these disciplines. Some of the articles are based, at least in part, on the authors' lectures at the 2011 Bellairs Workshop in Number Theory, held from May 6-13, 2011, at the Bellairs Research Institute, Holetown, Barbados. Lecture topics covered in this volume include polyhedral structures on tropical varieties, the structure theory of non-Archimedean curves (algebraic, analytic, tropical, and formal), uniformisation theory for non-Archimedean curves and abelian varieties, and applications to Diophantine geometry. Additional articles selected for inclusion in this volume represent other facets of current research and illuminate connections between tropical geometry, non-Archimedean geometry, toric geometry, algebraic graph theory, and algorithmic aspects of systems of polynomial equations.
