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A practical, accessible introduction to advanced geometry Exceptionally well-written and filled with historical and bibliographic notes, Methods of Geometry presents a practical and proof-oriented approach. The author develops a wide range of subject areas at an intermediate level and explains how theories that underlie many fields of advanced mathematics ultimately lead to applications in science and engineering. Foundations, basic Euclidean geometry, and transformations are discussed in detail and applied to study advanced plane geometry, polyhedra, isometries, similarities, and symmetry. An.

Front Cover; Computational Probability; Copyright Page; Table of Contents; Contributors; Preface; Chapter 1. Some Ideas in Computational Probability; References; Chapter 2. Computational Problems Related to the Galton- Watson Press; I. THE PROBABILITY DISTRIBUTIONS OF PHASE TYPE; 2. THE SUCCESSIVE GENERATION SIZES IN A GALTON-WATSON PROCESS; 3. A GALTON-WATSON PROCESS EMBEDDED INTHE MX /G/1 QUEUE; 4. THE MACIMUM GENERATION SIZE BEFORE EXTINCTION; 5. THE PROBABILITY OF EVENTUAL ABSORPTION; REFERENCES; Chapter 3. Central Limit Analogues for Markov Population Processes; 1. SUMMARY.

Selected peer-reviewed full text papers from the 3rd Borneo International Conference on Applied Mathematics and Engineering (3rd BICAME) Selected, peer-reviewed papers from the 3rd Borneo International Conference on Applied Mathematics and Engineering 2020 (3rd BICAME 2020), September 9-10, 2020, Balikpapan, Indonesia.

Bibliography: p. 221-233. ; This thesis is concerned with the problem of how to effectively address the complex issue of poverty in the context of limited resources. Poverty is a multi-dimensional problem that affects different communities in different ways. In order to use the available resources in such a way as to most effectively tackle poverty, a means of measuring and benchmarking outcomes as well as evaluating choices of intervention is required. However, smart methods of allocating scarce resources are not in themselves sufficient, if they are not regarded as legitimate by the participants of the process. The imperative of legitimacy demands that we both address the issue of quantitative rigour in resource allocation methods and that we look beyond and explore too the mechanics of effective participatory methods. The approach of developmental local government adopted by the new South African government post apartheid, places this complex problem in the sphere of local government. The primary tool available to local administrators for addressing poverty, amongst other issues, is that of integrated development planning. This process draws together the stakeholders who fall broadly into three groups of participants, namely the communities that live in the municipality, the municipal officials and the elected politicians, and allocates them the task of identifying and prioritising community and municipal issues, and developing appropriate plans to address them. This package of plans or projects is compiled into a municipal budget that targets priority issues for the area, in an integrated and coherent manner. This thesis proposes a new method for tackling this specific group decision making problem, namely Participative Multi-Criteria Decision Analysis. This method was developed in an action research setting in the municipality of Stellenbosch, South Africa, and applied to their 2001/2002 integrated development planning process. The method is grounded in the principles of participative action research in which the participation of all interested and affected patties is valued, and in which there is a commitment to work for change to the fundamental fabric of knowledge and power, leading to a greater empowerment of ordinary people. This participative framework strengthens the legitimacy of the approach by promoting a stronger sense of ownership of process and products by all participants. Within this participative framework, tools of multi-criteria decision analysis are used to support the decision making process by quantifying difficult decisions that need to be addressed. It is the synthesis of these two approaches (action research and multi-criteria decision analysis) that provides both legitimacy and rigour for this method within a highly contested and complex public decision making arena. In the spirit of action research, the method is developed by drawing on theory about developmental local government and poverty, as well as multi-criteria decision analysis. In the process of the research, over forty community workshops were held throughout the Stellenbosch municipal area. Community representatives identified and prioritised the issues of their areas; and in conjunction with municipal officials, developed and evaluated projects in response to these issues. These evaluations assisted the local council to compile the final budget for 2001/2002 in Stellenbosch. In this process, the communities (divided into nine development areas) also developed community development measurement scales which formed the basis for the project evaluations and an ongoing basis for monitoring progress in these communities. It unfolded during the course of this research that a fundamental component of this proposed participative public decision making approach is the role of a central co-ordinating person, not connected to or answerable to any of the constituent groups, who can manage the process of participation, promote an awareness of effective and informative data; ensure the appropriate use of quantification tools and maintain a focus on sustainable poverty alleviation. The method developed in this thesis was successfully applied to the process of identifying, prioritising and making choices about community issues in Stellenbosch, under conditions of significant polarisation of the constituent decision making groups, conclude that this method can be used to implement key aspects of integrated development planning as it addresses the issues of legitimacy and rigour in participative public decision making.

* A new approach that breaks new ground using psychophysics and mathematics in order to investigate human interaction * Identifies the critical direction of change, and the means to achieve it, in order to maintain a stable social environment that is going to require testable and provable theories that apply to our social space and the various cultures and groups that exist within it * An important text for graduate and advanced undergraduate students or classes, along with private and government analysts all operating within the areas of political theory, detection theory, social psychology, organizational behavior, psychophysics, and applied mathematics in the social and information sciences

This book contains a concise description of important mathematical methods of dynamics and suitable economic models. It covers discrete as well as continuous-time systems, linear and nonlinear models. Mixing traditional and modern materials, the study covers dynamics with and without optimization, naive and rational expectations, respectively. In addition to standard models of growth and cycles, the book also contains original studies on control of a multisector economy and expectations-driven multicohort economy. Numerous examples, problems (with solutions) and figures complete the book.

"The mathematical theory of persistence answers questions such as which species, in a mathematical model of interacting species, will survive over the long term. It applies to infinite-dimensional as well as to finite-dimensional dynamical systems, and to discrete-time as well as to continuous-time semiflows. This monograph provides a self-contained treatment of persistence theory that is accessible to graduate students. The key results for deterministic autonomous systems are proved in full detail such as the acyclicity theorem and the tripartition of a global compact attractor. Suitable conditions are given for persistence to imply strong persistence even for nonautonomous semiflows, and time-heterogeneous persistence results are developed using so-called 'average Lyapunov functions'. Applications play a large role in the monograph from the beginning. These include ODE models such as an SEIRS infectious disease in a meta-population and discrete-time nonlinear matrix models of demographic dynamics. Entire chapters are devoted to infinite-dimensional examples including an SI epidemic model with variable infectivity, microbial growth in a tubular bioreactor, and an age-structured model of cells growing in a chemostat."--Publisher's description

This book presents frontier research on the use of computational methods to model complex interactions in economics and finance. Artificial Intelligence, Machine Learning and simulations offer effective means of analyzing and learning from large as well as new types of data. These computational tools have permeated various subfields of economics, finance, and also across different schools of economic thought. Through 16 chapters written by pioneers in economics, finance, computer science, psychology, complexity and statistics/econometrics, the book introduces their original research and presents the findings they have yielded. Theoretical and empirical studies featured in this book draw on a variety of approaches such as agent-based modeling, numerical simulations, computable economics, as well as employing tools from artificial intelligence and machine learning algorithms. The use of computational approaches to perform counterfactual thought experiments are also introduced, which help transcend the limits posed by traditional mathematical and statistical tools. The book also includes discussions on methodology, epistemology, history and issues concerning prediction, validation, and inference, all of which have become pertinent with the increasing use of computational approaches in economic analysis

Voters today often desert a preferred candidate for a more viable second choice to avoid wasting their vote. Likewise, parties to a dispute often find themselves unable to agree on a fair division of contested goods. In Mathematics and Democracy, Steven Brams, a leading authority in the use of mathematics to design decision-making processes, shows how social-choice and game theory could make political and social institutions more democratic. Using mathematical analysis, he develops rigorous new procedures that enable voters to better express themselves and that allow disputants to divide goods