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Presents the scientific methodology from the enlarged cybernetical perspective that recognizes the anisotropy of time, the probabilistic character of natural laws, and the entry that the incomplete determinism in Nature opens to the occurrence of innovation, growth, organization, teleology communication, control, contest and freedom. The new tier to the methodological edifice that cybernetics provides stands on the earlier tiers, which go back to the Ionians (c. 500 BC). However, the new insights reveal flaws in the earlier tiers, and their removal strengthens the entire edifice. The new concepts of teleological activity and contest allow the clear demarcation of the military sciences as those whose subject matter is teleological activity involving contest. The paramount question “what ought to be done”, outside the empirical realm, is embraced by the scientific methodology. It also embraces the cognitive sciences that ask how the human mind is able to discover, and how the sequence of discoveries might converge to a true description of reality.

Research in undergraduate mathematics education (RUME), the study of teaching and learning of college mathematics, is a new area of research in mathematics. Information to support this discipline is found in publications from all over the world, in the form of monographs, reports, research guidelines and resource manuals, as well as journal articles. Researchers in RUME require access to materials that are specific not only to their field, but also to the broader literature of mathematics, education, learning theories, instructional strategies, alternative assessment techniques, cognitive development and human behavior. This annotated bibliography is designed to be a template for a comprehensive and up‐to‐date collection of RUME resources. World Wide Web (Web) locations for many of the items are provided, as are descriptions of several Web sites that present information of interest to RUME researchers.

Set theory provides a foundational approach to mathematics, and mathematics provides an abstract way of looking at social reality. The first section presents some of the elementary concepts of set theory. The second section presents a variety of examples of social reality and shows how the abstract features of reality can be modelled by set theory. The third section shows how set theory can provide a way of looking at the accounts of social reality presented in humanities disciplines such as history and literature. The fourth section briefly indicates how set theory and the concept of a structure provide a foundational approach to mathematics. The fifth section looks at the debates surrounding realism and, albeit warily, espouses mathematical social science realism.

Surveys the use of mathematics in what are now commonly called the social sciences up to the time of the earliest use of the term “social science” in the late 1700s. Explains the rationale for the organization and structure of the paper and proceeds to reason for the broad definition of mathematics as it relates to the social sciences. The introduction also describes the periodization used. The next section contains a brief description of the state of what were to become the social sciences in the late 1700s. This is followed by a brief description of the state of mathematics at that time. Then follow sections demonstrating that mathematics was used by important developers of social thought from the earliest times right up to the dawn of the modern social sciences. Concludes with a discussion of some of the lessons to be learned from history. The most important lesson that history teaches us about the role of mathematics in the modern social sciences at the dawn of their existence is that the social sciences require the use of mathematics and could not exist without them.

Investigates the economic methodologies of Carl Menger, William Stanley Jevons and Gustav Schmoller with respect to the issue of whether mathematics is or is not an adequate language to express economic relationships. First, Menger’s and Jevons’s respective methodologies are identified as Aristotelian which means, inter alia, that economic properties are real, are naturally related to each other, exist as part of the observable world and can be separated (in thought or otherwise) from other properties. Second, it is shown how this general Aristotelian outlook has very different implications for Menger’s and Jevons’s thinking about mathematics. Third, these two “monogenetic” views are contrasted with Gustav Schmoller’s “polygenetic” approach which holds that a purely deductive economics, based on a small number of self‐evident principles, is inadequate for social purposes.

The physical universe is the embodiment of necessary mathematical forms by ever‐present flux. Interaction of these forms generates diversity, novelty, complexity, and higher levels of organization. Lattice order, group opposition, and topological transformation are generators necessary and sufficient to construct mathematics. Homologous cognitive structures generate human mental development. Process theory proposes that these mathematical generators also create nature. Lattice order is embodied as action, group opposition as two‐valued information, and topological transformation as spatial organization.

In this chapter, we present our ongoing efforts in developing and sustaining interdisciplinary STEM undergraduate programs at North Carolina A&T State University (NCA&T) – a state-supported HBCU and National Science Foundation (NSF) Historically Black Colleges and Universities Undergraduate Program (HBCU-UP) Institutional Implementation Project grantee. Through three rounds of NSF HBCU-UP implementation grants, a concerted effort has been made in developing interdisciplinary STEM undergraduate research programs in geophysical and environmental science (in round 1), geospatial, computational, and information science (in round 2), and mathematical and computational biology (in round 3) on NCA&T campus. We first present a brief history and background information about the interdisciplinary STEM undergraduate research programs developed and sustained at NCA&T, giving rationales on how these programs had been conceived, and summarizing what have been achieved. Next we give a detailed description on the development of undergraduate research infrastructure including building research facilities through multiple and leveraged funding sources, and engaging a core of committed faculty mentors and research collaborators. We then present, as case studies, some sample interdisciplinary research projects in which STEM undergraduate students were engaged and project outcomes. Successes associated to our endeavor in developing undergraduate research programs as well as challenges and opportunities on implementing and sustaining these efforts are discussed. Finally, we discuss the impact of well-structured undergraduate research training on student success in terms of academic performance, graduation rate and continuing graduate study, and summarize many of the learnings we have gained from implementation and delivery of undergraduate research experiences at HBCUs.

The aim is to report on the 175th Annual Meeting of the American Association for the Advancement of Science (AAAS), held in February 2009 in Chicago.

Provides a concise review of the conference, whose theme was Our Planet and Its Life: Origins and Futures.

Not surprisingly, because of the primary focus on Darwin and the ecology of the earth, there were few symposia that concentrated on the application of technology outside of the Life Sciences and of the Earth Sciences. However, in view of the current evolution of “cloud computing” and the formation of “mega grids,” there were two symposia devoted to these topics.

The paper is a useful summary of a conference of interest to library and information management professionals.

Although fuzzy logic is being extensively used in electronics and mathematical sciences, it has found little or no application in the social sciences, especially criminology. As a mathematical system, fuzzy logic generalizes the Boolean logic and can be a very useful tool for the social sciences where concepts and terms involve shades of meanings. Outlines the essential mathematics behind this approach and develops a technique that could be useful in building offender profiles from fuzzy descriptions provided by witnesses. Also suggests several other possible areas of applications of this mathematical system.

The purpose of this study is to formulate exploratory scenarios of Operations Research through the critical uncertainty approach and Soft Systems Methodology.

In this study, to formulate plausible scenarios, the discipline of operation research internal and external experts’ opinions of this field have been gathered through Delphi approach and uncertainty questionnaires. After use of the most important uncertainties, plausible scenarios of operations research have been mapped with the help of experts through co-thinking workshops.

Four scenarios are presented in this study. These scenarios include Solar System, Esfandiar's Eye, Rival’s Setraps and Legendary Simurgh. Naturally, the imagination of such a unitary future for all academic communities is an expectation far from reality, and given the conditions of each of these futures or any integration of them is imaginable.

Operations Research models have been faced with variously multiple changes since its emergence until now. Investigation into the future of operations research on the necessity for his planning has not received a reasonable notice in the literature. Sporadic activities that have been carried out are also lacking in the necessary methodology. Also, there has been no research about future study using the soft Operation Research tools (Soft Systems Methodology).