This textbook covers a diversity of topics in graph and network theory, both from a theoretical standpoint, and from an applied modelling point of view. Mathematica® is used to demonstrate much of the modelling aspects. Graph theory and model building tools are developed in tandem with effective techniques for solving practical problems via computer implementation. The book is designed with three primary readerships in mind. Individual syllabi or suggested sequences for study are provided for each of three student audiences: mathematics, applied mathematics/operations research, and computer science. In addition to the visual appeal of each page, the text contains an abundance of gems. Most chapters open with real-life problem descriptions which serve as motivation for the theoretical development of the subject matter. Each chapter concludes with three different sets of exercises. The first set of exercises are standard and geared toward the more mathematically inclined reader. Many of these are routine exercises, designed to test understanding of the material in the text, but some are more challenging. The second set of exercises is earmarked for the computer technologically savvy reader and offer computer exercises using Mathematica. The final set consists of larger projects aimed at equipping those readers with backgrounds in the applied sciences to apply the necessary skills learned in the chapter in the context of real-world problem solving. Additionally, each chapter offers biographical notes as well as pictures of graph theorists and mathematicians who have contributed significantly to the development of the results documented in the chapter. These notes are meant to bring the topics covered to life, allowing the reader to associate faces with some of the important discoveries and results presented. In total, approximately 100 biographical notes are presented throughout the book. The material in this book has been organized into three distinct parts, each with a different focus. The first part is devoted to topics in network optimization, with a focus on basic notions in algorithmic complexity and the computation of optimal paths, shortest spanning trees, maximum flows and minimum-cost flows in networks, as well as the solution of network location problems. The second part is devoted to a variety of classical problems in graph theory, including problems related to matchings, edge and vertex traversal, connectivity, planarity, edge and vertex coloring, and orientations of graphs. Finally, the focus in the third part is on modern areas of study in graph theory, covering graph domination, Ramsey theory, extremal graph theory, graph enumeration, and application of the probabilistic method.

Study of the students of 9th standard in government and private schools in the Union Territory of Delhi.

This book discusses the importance of flag varieties in geometric objects and elucidates its richness as interplay of geometry, combinatorics and representation theory. The book presents a discussion on the representation theory of complex semisimple Lie algebras, as well as the representation theory of semisimple algebraic groups. In addition, the book also discusses the representation theory of symmetric groups. In the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. Many of the geometric results admit elegant combinatorial description because of the root system connections, a typical example being the description of the singular locus of a Schubert variety. This discussion is carried out as a consequence of standard monomial theory. Consequently, this book includes standard monomial theory and some important applications—singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. The two recent results on Schubert varieties in the Grassmannian have also been included in this book. The first result gives a free resolution of certain Schubert singularities. The second result is about certain Levi subgroup actions on Schubert varieties in the Grassmannian and derives some interesting geometric and representation-theoretic consequences.

Vols. 2 and 5 include appendices.

For centuries scientists and theologians have argued about the origin, structure, function, and purpose of the universe, with no end in sight. In the meantime, the average human being, when not overwhelmed by activities needed for mere survival, has wondered who we are, where we came from, and why were here. Dr. Michael Bohley believes that the answers we seek are hiding in plain sight, available to anyone with a healthy brain, regardless of level of education or specialization in certain obscure fields of science, theology, or philosophy. The answers are to be found within the sphere of our beliefs and how they help to shape the world around us.

The present volume contains selected papers from the 14th International Morphology Meeting held in Budapest, 13–16 May 2010, organized under the auspices of the Research Institute for Linguistics of the Hungarian Academy of Sciences. The selection of papers presented here addresses problems of language use in one or another sense, covering issues of regularity, irregularity and analogy, as well as the role of frequency in morphological complexity, morphological change and language acquisition. The languages discussed include Dutch, German, Greek, Hungarian, Lovari (Romani) and Russian. The contributors are Anna Anastassiadis-Symeonidis, Mario Andreou, Márton András Baló, Dunstan Brown, Gabriela Caballero, Anna Maria Di Sciullo, Wolfgang U. Dressler, Roger Evans, Alice C. Harris, László Kálmán, Katharina Korecky-Kröll, Sabine Laaha, Laura E. Lettner, Maria Mitsiaki, Péter Rácz, Angela Ralli, Péter Rebrus, Alan K. Scott, and Miklós Törkenczy.