This paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well-known that for finite ordinals ∑bT<αβ is the number of 2-element subsets of an α-element set. It is shown here that for any well-ordered set of arbitrary infinite order type α, ∑bT<αβ is the ordinal of the set M of 2-element subsets, where M is ordered in some natural way. The result is then extended to evaluating the ordinal of the set of all n-element (...) subsets for each natural number n ≥ 2. Moreover, series ∑β<αf are investigated and evaluated, where α is a limit ordinal and the function f belongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α appears to be quite problematic. (shrink)
This text provides a straightforward, lively but rigorous, introduction to truth-functional and predicate logic, complete with lucid examples and incisive exercises, for which Warren Goldfarb is renowned.
The role of paleontology in evolutionary biology between the publication of The Origin of Species in 1859 and the Evolutionary Synthesis of the 1940s is frequently described as mostly misguided failure. However, a significant number of American and British PDPS invertebrate paleontologists of this period did devote considerable attention to evolution, and their evolutionary theories and conclusions were a good deal more diverse and nuanced than previous histories have suggested. This paper brings into focus a number of important but underrecognized (...) aspects of the history of paleontology within the history of biology, including that PDPS paleontologists were not all as theoretically backward as they have been portrayed; that the post-Synthesis narrative of the history of evolution should be continually reevaluated, in part to decouple historical understanding from the agendas of authors who have used history to advance particular views of evolution; and that there is a much richer story to be told about the history of evolutionary biology in both the pre- and post-Synthesis eras. (shrink)
A guide for scientists who would like to contribute to the professional development of science teachers for elementary schools. Based on information from over 180 programs, describes what activities work and why, and suggests how to identify programs teachers have found to be effective and take the initial steps to become involved. Also provides vignettes illustrating the daily work of science teachers. Annotation copyright by Book News, Inc., Portland, OR.
Farmer participatory approaches were used to identify problems and needs as perceived by local people and to develop strategies to achieve fodder security in south Indian villages. Indigenous knowledge systems as they relate to agroforestry were explored. The farmer participatory approaches have laid the foundations for selecting appropriate agroforestry technologies and developing suitable fodder security policy options. Potential benefits and risks as a result of implementing agroforestry projects were also discussed.
This book includes a selection of contributions to the Iowa State University Symposium on agricultural bioethics in november 1987. The papers are grouped in the sections "Safety and regulatory issues", "Impact on scientific and industrial communities", "Public perceptions", "Economic prospects", "Social considerations" and "Ethical dilemmas".