An elementary treatment of the theory of spinning tops and by Harold Crabtree

By Harold Crabtree

The item of this publication is to convey in the diversity of the abler Mathematicians at our Public colleges and of First 12 months undergraduates on the Universities, a subject matter which has hitherto been thought of too tricky for any however the extra complex scholars in arithmetic, whereas even they've got in lots of situations did not derive extra excitement from the research of spinning tops than is contained in filing the matter to the motion of a sophisticated piece of Mathematical equipment which instantly, notwithstanding unintelligently, seems the proper end result.

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In the book version we engage a more sustained account of the possibilities, challenges, and indeed failures posed by such examples. It is our hope that, in thinking together with all of those who have contributed to our forums—face-toface at HASTAC gatherings as well as online with the Institute for the Future of the Book collaborative tool—we have begun a process, together, of envisioning better ways to think of the future of learning institutions in our digital age. Appendix: Portfolio of Virtual Learning Institutions: Models, Experiments, and Examples to Learn and Build On Gaming and Virtual Environments in Education Not only is educational gaming becoming seen as a viable alternative to a formal education, but other types of virtual environments and Massively Multiplayer Online Games are being recognized for their educational components.

Traditionally, institutions have been thought about in terms of rules, regulations, norms governing interactivity, production, and distribution within the institutional structure. Network culture and 34 The Future of Learning Institutions in a Digital Age associated learning practices and arrangements suggest that we think of institutions, especially those promoting learning, as mobilizing networks. The networks enable a mobilizing that stresses flexibility, interactivity, and outcome. And the mobilizing in turn encourages and enables networking interactivity that lasts as long as it is productive, opening up or giving way to new interacting networks as older ones ossify or newly emergent ones signal new possibilities.

We are not naive, and we realize also the challenges, limitations, and misdirections—in short, the opportunity costs—resulting from these developments. Some of this comes inevitably with the unsettling of long-established ways of doing things. When wellestablished modes of making knowledge sediment, they can become at least restrictive, if not unproductive. As new modes challenge, the old institutional structures can either dig in and refuse to respond other than to dismiss, or they can seek to work out renewed and renewing regimes disposed to take advantage of the possible productive elements.

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