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.

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.

This collection of essays charts the influence of the Lutheran Reformation on various (northern) European languages and texts written in them. The central themes of Languages in the Lutheran Reformation: Textual Networks and the Spread of Ideas are: how the ideas related to Lutheranism were adapted to the new areas, new languages, and new contexts during the Reformation period in the 16th and 17th centuries; and how the Reformation affected the standardization of the languages. Networks of texts, knowledge, and authors belong to the topics of the present volume. The contributions look into language use, language culture, and translation activities during the Reformation, but also in the prelude to the Reformation as well as after it, in the early modern period. The contributors are experts in the study of their respective languages, including Czech, Dutch, English, Estonian, Finnish, High German, Icelandic, Latvian, Lithuanian, Low German, Norwegian, Polish, and Swedish. The primary texts explored in the essays are Bible translations, but genres other than biblical are also discussed.

An adorably illustrated package featuring 40 mouthwatering recipes for cookies--from classic favorites and beautifully piped creations to luscious brownies and bars--this go-to guide will inspire showstopping treats for gifts, special occasions, and everyday snacks. If you're after the perfect cookie--whether gooey chocolate chip, thin and crispy oatmeal raisin, or classic French macaroon--this artfully curated collection of recipes delivers satisfaction on every page. The recipes are organized by type, including options for drop, shaped, piped, and rolled and cut cookies. You'll also find fantastic brownies and bars, from tart key lime squares and raspberry-almond linzer bars to blondies glazed with caramel and decadent brownies topped with chocolate frosting. A primer on mixing doughs and batters, expert baking tips, and suggestions for serving and shipping baked goods round out this delectable collection that will appeal to cookie lovers everywhere. Table of contents: Drop Cookies Classic Peanut Butter Cookies Oatmeal-Raisin Crisps Chewy Coconut Macaroons Chocolate Chip Cookie Sandwiches Triple-Chocolate-Chunk Cookies White Chocolate-Macadamia Cookies Shaped Cookies Buttery Vanilla Shortbread Fragrant Lavender Shortbread Crunchy Espresso Shortbread Mexican Wedding Cookies Spicy Ginger Snaps Cinnamon-Sugar Snickerdoodles Gooey Chocolate Crinkle Cookies Blackberry-Pecan Thumbprints Toasted Hazelnut Biscotti Double-Ginger Biscotti Chocolate, Pistachio & Cherry Biscotti Piped Cookies Cream-Filled Pecan Lace Cookies Almond-Filled Macaroons French-Style Pistachio Macaroons Chocolate-Almond Macaroons Butter Spritz Cookies Rolled & Cut Cookies Pinwheel Icebox Cookies Pink Raspberry Pinwheels Chocolate-Orange Stripe Cookies Sugar Cookie Cutouts Black-and-White Cookies Zesty Lime Sugar Cookies Chocolate Spice Cookies Apricot Rugelach Medjool Date Rugelach Chocolate Chip Rugelach Brownies & Bars Tangy Lemon Bars Coconut-Lemon Squares Tart Key Lime Squares Raspberry-Almond Linzer Bars Glazed Cinnamon Streusel Bars Blueberry Cheesecake Bars Frosted Chocolate Brownies Cream Cheese Marble Brownies Caramel-Glazed Blondies Fillings & Coatings Vanilla Glaze Chocolate Frosting Cooking Fillings Sweetened Whipped Cream