This book presents current research in the field of mathematics, with a particular emphasis on mathematical theories, models and groups. Topics discussed include particular swarm optimisation in theory and practice; detecting the commuting probability of the derived subgroup; peer group situations and games with interval uncertainty; groups of wraps and diffeomorphisms of manifolds over non-archimedean normed fields and the concept of a suitable insurance policy using leader-follower games.

Dieses Buch zeigt an einfachen Beispielen, wozu mathematisches Verstandnis (neben reinen Rechenfertigkeiten) in den Fachern der Betriebs- und Volkswirtschaftslehre gebraucht wird, um oekonomische Prozesse analysieren zu koennen. Es beschreibt zunachst die zentrale Bedeutung von Funktionen, fuhrt in lockerer Sprache in wissenschaftliches Modelldenken ein und erlautert die wichtige Abwagung zwischen Einfachheit und Genauigkeit der Modelle. Danach wird verdeutlicht, wie aus der Schule bekannte mathematische Konzepte (wie Exponential- und Logarithmusfunktionen, Ableitungen, Gleichungssysteme, Abstandsmasse und Wahrscheinlichkeiten) zu kraftvollen Verfahren zur Loesung wirtschaftswissenschaftlicher Probleme werden. Das Buch moechte Studienanfangern und interessierten Schulerinnen und Schulern elementare Grundfertigkeiten und Motivation geben, sich mit Mathe im Anwendungsbereich der OEkonomie zu beschaftigen.

Anhand vieler Anwendungsbeispiele aus den Wirtschafts- und Sozialwissenschaften
bietet dieses Buch eine praxisorientierte Einfuhrung in die deskriptive und induktive
Statistik sowie in die Grundlagen der Wahrscheinlichkeitsrechnung. Es verzichtet
weitgehend auf formale Beweise und ist so konzipiert, dass seine Inhalte auch in
einer einsemestrigen Veranstaltung behandelt werden konnen. Knapp 100 klausurtypische
Aufgaben mit ausfuhrlichen Losungen helfen bei der gezielten Prufungsvorbereitung.

"Optimierung" ist ein grundlegender Vorlesungszyklus in der angewandten Mathematik. Es geht dabei um die genaue und schnelle Berechnung der besten Entscheidung, wenn eine grosse Menge von Entscheidungsmoglichkeiten zur Auswahl steht. Mit diesem Buch liegt eine Sammlung von Ubungs- und Klausuraufgaben mit kompletten, mathematischen Losungen vor, die in langjahriger Lehrtatigkeit zusammengetragen wurde. Eine umfassende Sammlung, die das Bachelorwissen abdeckt. Sie eignet sich als Ubungsmaterial fur Studierende und als Anregungs- und Auswahlfundus fur Aufgabensteller. Die Aufgaben gehen direkt auf das Lehrniveau ein - kein Uberspringen von Schwierigkeiten - und sind so aufbereitet, dass eine Erfolgskontrolle fur die Studierenden moglich ist.
Erganzendes Lehrmaterial findet der Studierende im OnlinePLUS-Service des Verlages."

Mathematik gehoert zu den Grundfachern fur jeden Studierenden der Wirtschafts- und Sozialwissenschaften. Er benoetigt Kenntnisse der Analysis, der Linearen Algebra sowie der Funktion einer und mehrerer Variablen. Das zweibandige Taschenbuch, hervorgegangen aus Vorlesungen des Autors an der Universitat Regensburg, stellt den Studienstoff sehr anschaulich dar, unterstutzt durch eine Vielzahl von Beispielen und Abbildungen. Insbesondere wird auf die Anwendung verschiedener mathematischer Verfahren, auf konkrete Fragestellungen eingegangen. Das Buch richtet sich an alle Studenten der Wirtschafts- und Sozialwissenschaften an Unversitaten und Fachhochschulen sowie an den Praktiker, der sein Mathematikwissen auffrischen moechte. Es ist gleichermassen geeignet als Begleitbuch zu einer Vorlesung und zum Selbststudium. Fur das Verstandnis sind nur Kenntnisse der Oberstufenmathematik notwendig.

Addressed to 2nd- and 3rd-year students, this work by a world-famous teacher skillfully spans the pure and applied branches, so that applied aspects gain in rigor while pure mathematics loses none of its dignity. Equally essential as a text, a reference, or simply as a brilliant mathematical exercise. 1971 edition.

Un conjunto ameno de problemas, pasatiempos y enigmas que introducen, en forma de acertijos, todos los conceptos basicos de la logica.

Game theory, particularly the use of repeated games, N-person games, and incomplete information games have been popular research techniques in political science, sociology, and managementùbut difficult for new social researchers to useùuntil now. Aimed at making these topics accessible to all social scientist, Game Theory Topics shows how game theory can be productively applied to problems in the social sciences. Using a common social science gameùChickenùto illustrate game theory concepts, the authors introduce readers to games of incomplete information; how to build uncertainty into game theoretic models; the concept of Bayesian Nash equilibrium; and the role of repetition in game theory, including how game theoretic models can easily accommodate many players. Throughout the book, the authors use applications to social science problems to illustrate the points being developed in each chapter.

Monte Carlo Simulation is a method of evaluating substantive hypotheses and statistical estimators by developing a computer algorithm to simulate a population, drawing multiple samples from this pseudo-population, and evaluating estimates obtained from these samples. Christopher Z. Mooney explains the logic behind Monte Carlo Simulation and demonstrates its uses for social and behavioral research in conducting inference using statistics with only weak mathematical theory, testing null hypotheses under a variety of plausible conditions, assessing the robustness of parametric inference to violations of its assumptions, assessing the quality of inferential methods, and comparing the properties of two or more estimators. In addition, Mooney carefully demonstrates how to prepare computer algorithms using GAUSS code and illustrates these principles using several research examples.

Monte Carlo Simulation will enable researchers to effectively execute Monte Carlo Simulation and to interpret the estimated sampling distribution generated from its use.

Game Theory & Applications

The concepts of game theory (rationality etc) now pervade much of social science, so that Professor Zagare's exposition of game theory and its applications (intended to "convert the unconverted and initiate the uninitiated") is very welcome. He provides methods for analysing the structure of the game; considers zero and nonzero-sum games and the fundamental 'minimax theorem'; and investigates games with more than two players, including the possibility of coalitions between players. Diverse examples give the reader an idea of how the theory can be applied to a wide range of situations.

LEGOfied: Building Blocks as Media provides a multi-faceted exploration of LEGO fandom, addressing a blindspot in current accounts of LEGO and an emerging area of interest to media scholars: namely, the role of hobbyist enthusiasts and content producers in LEGO's emergence as a ubiquitous transmedia franchise. This book examines a range of LEGO hobbyism and their attendant forms of mediated self-expression and identity (their "technicities"): artists, aspiring Master Builders, collectors, and entrepreneurs who refashion LEGO bricks into new commodities (sets, tchotchkes, and minifigures). The practices and perspectives that constitute this diverse scene lie at the intersection of multiple transformations in contemporary culture, including the shifting relationships between culture industries and the audiences that form their most ardent consumer base, but also the emerging forms of entrepreneurialism, professionalization, and globalization that characterize the burgeoning DIY movement. What makes this a compelling project for media scholars is its mutli-dimensional articulation of how LEGO functions not just as a toy, cultural icon, or as transmedia franchise, but as a media platform. LEGOfied is centered around their shared experiences, qualitative observations, and semi-structured interviews at a number of LEGO hobbyist conventions. Working outwards from these conventions, each chapter engages additional modes of inquiry-media archaeology, aesthetics, posthumanist philosophy, feminist media studies, and science and technology studies-to explore the origins, permutations and implications of different aspects of the contemporary LEGO fandom scene.

Designed for the 21st century classroom, this textbook poses, refines, and analyzes questions of sustainability in a quantitative environment. Building mathematical knowledge in the context of issues relevant to every global citizen today, this text takes an approach that empowers students of all disciplines to understand and reason with quantitative information. Whatever conclusions may be reached on a given topic, this book will prepare the reader to think critically about their own and other people's arguments and to support them with careful, mathematical reasoning. Topics are grouped in themes of measurement, flow, connectivity, change, risk, and decision-making. Mathematical thinking is at the fore throughout, as students learn to model sustainability on local, regional, and global scales. Exercises emphasize concepts, while projects build and challenge communication skills. With no prerequisites beyond high school algebra, instructors will find this book a rich resource for engaging all majors in the mathematics classroom. From the Foreword No longer will you be just a spectator when people give you quantitative information-you will become an active participant who can engage and contribute new insights to any discussion.[...] There are many math books that will feed you knowledge, but it is rare to see a book like this one that will help you cultivate wisdom.[...] As the authors illustrate, mathematics that pays attention to human considerations can help you look at the world with a new lens, help you frame important questions, and help you make wise decisions. Francis Edward Su, Harvey Mudd College

Winner of the 2017 De Groot Prize awarded by the International Society for Bayesian Analysis (ISBA) A relatively new area of research, adversarial risk analysis (ARA) informs decision making when there are intelligent opponents and uncertain outcomes. Adversarial Risk Analysis develops methods for allocating defensive or offensive resources against intelligent adversaries. Many examples throughout illustrate the application of the ARA approach to a variety of games and strategic situations. Focuses on the recent subfield of decision analysis, ARA Compares ideas from decision theory and game theory Uses multi-agent influence diagrams (MAIDs) throughout to help readers visualize complex information structures Applies the ARA approach to simultaneous games, auctions, sequential games, and defend-attack games Contains an extended case study based on a real application in railway security, which provides a blueprint for how to perform ARA in similar security situations Includes exercises at the end of most chapters, with selected solutions at the back of the book The book shows decision makers how to build Bayesian models for the strategic calculation of their opponents, enabling decision makers to maximize their expected utility or minimize their expected loss. This new approach to risk analysis asserts that analysts should use Bayesian thinking to describe their beliefs about an opponent's goals, resources, optimism, and type of strategic calculation, such as minimax and level-k thinking. Within that framework, analysts then solve the problem from the perspective of the opponent while placing subjective probability distributions on all unknown quantities. This produces a distribution over the actions of the opponent and enables analysts to maximize their expected utilities.

The amazing story of one of the greatest math problems of all time and the reclusive genius who solved it
In the tradition of "Fermatas Enigma" and "Prime Obsession," George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri PoincarA(c) developed the PoincarA(c) Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldnat prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found.
Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius.

The Unpredictability of Gameplay explores the many forms of unpredictability in games and proposes a comprehensive theoretical framework for understanding and categorizing non-deterministic game mechanics. Rather than viewing all game mechanics with unpredictable outcomes as a single concept, Mark R. Johnson develops a three-part typology for such mechanics, distinguishing between randomness, chance, and luck in gameplay, assessing games that range from grand strategy and MMORPGs to slot machines and card games. He also explores forms of unanticipated unpredictability, where elements of games fail to function as intended and create new forms of gameplay in the process. Covering a range of game concepts using these frameworks, The Unpredictability of Gameplay then explores three illustrative case studies: 1) procedural generation, 2) replay value and grinding, and 3) player-made practices designed to reduce the level of luck in non-deterministic games. Throughout, Johnson demonstrates the importance of looking more deeply at unpredictability in games and game design and the various ways in which unpredictability manifests while offering an invaluable tool for game scholars and game designers seeking to integrate unpredictability into their work.

This textbook contains a rigorous exposition of the mathematical foundations of two of the most important topics in politics and economics: voting and apportionment, at the level of upper undergraduate and beginning graduate students. It stands out among comparable books by providing, in one volume, an extensive and mathematically rigorous treatment of these two topics. The text's three chapters cover social choice, yes-no voting, and apportionment, respectively, and can be covered in any order, allowing teachers ample flexibility. Each chapter begins with an elementary introduction and several examples to motivate the concepts and to gradually lead to more advanced material. Landmark theorems are presented with detailed and streamlined proofs; those requiring more complex proofs, such as Arrow's theorems on dictatorship, Gibbard's theorem on oligarchy, and Gardenfors' theorem on manipulation, are broken down into propositions and lemmas in order to make them easier to grasp. Simple and intuitive notations are emphasized over non-standard, overly complicated symbols. Additionally, each chapter ends with exercises that vary from computational to "prove or disprove" types. The Mathematics of Voting and Apportionment will be particularly well-suited for a course in the mathematics of voting and apportionment for upper-level undergraduate and beginning graduate students in economics, political science, or philosophy, or for an elective course for math majors. In addition, this book will be a suitable read for to any curious mathematician looking for an exposition to these unpublicized mathematical applications. No political science prerequisites are needed. Mathematical prerequisites (included in the book) are minimal: elementary concepts in combinatorics, graph theory, order relations, and the harmonic and geometric means. What is needed most is the level of maturity that enables the student to think logically, derive results from axioms and hypotheses, and intuitively grasp logical notions such as "contrapositive" and "counterexample."