Finite Reflection Groups

Finite Reflection Groups PDF

Author: L.C. Grove

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 142

ISBN-13: 1475718691

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Chapter 1 introduces some of the terminology and notation used later and indicates prerequisites. Chapter 2 gives a reasonably thorough account of all finite subgroups of the orthogonal groups in two and three dimensions. The presentation is somewhat less formal than in succeeding chapters. For instance, the existence of the icosahedron is accepted as an empirical fact, and no formal proof of existence is included. Throughout most of Chapter 2 we do not distinguish between groups that are "geo metrically indistinguishable," that is, conjugate in the orthogonal group. Very little of the material in Chapter 2 is actually required for the sub sequent chapters, but it serves two important purposes: It aids in the development of geometrical insight, and it serves as a source of illustrative examples. There is a discussion offundamental regions in Chapter 3. Chapter 4 provides a correspondence between fundamental reflections and funda mental regions via a discussion of root systems. The actual classification and construction of finite reflection groups takes place in Chapter 5. where we have in part followed the methods of E. Witt and B. L. van der Waerden. Generators and relations for finite reflection groups are discussed in Chapter 6. There are historical remarks and suggestions for further reading in a Post lude.

How long, O Lord? (2nd edition)

How long, O Lord? (2nd edition) PDF

Author: D A CARSON

Publisher: Inter-Varsity Press

Published: 2020-05-21

Total Pages: 353

ISBN-13: 1789740312

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My soul is in anguish. How long, O Lord, how long?' (Psalm 6:8) Personal tragedy and heartache. Accident, illness and infirmity. Drought, earthquake, tsunami. Terrorist atrocities. War, genocide, poverty, famine. All we have to do is live long enough, and we will suffer in one way or another. In this new edition of an excellent, widely appreciated study, Don Carson addresses the issue of evil and suffering with sensitivity, pastoral concern and biblical insight. He helps Christians prepare for the day when they have to experience a 'frowning providence', and face it with faith and hope because of an unshakable trust in the providence of God.

Coleridge, Philosophy and Religion

Coleridge, Philosophy and Religion PDF

Author: Douglas Hedley

Publisher: Cambridge University Press

Published: 2000-06-22

Total Pages: 346

ISBN-13: 1139428187

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Coleridge's relation to his German contemporaries constitutes the toughest problem in assessing his standing as a thinker. For the last half-century this relationship has been described, ultimately, as parasitic. As a result, Coleridge's contribution to religious thought has been seen primarily in terms of his poetic genius. This book revives and deepens the evaluation of Coleridge as a philosophical theologian in his own right. Coleridge had a critical and creative relation to, and kinship with, German Idealism. Moreover, the principal impulse behind his engagement with that philosophy is traced to the more immediate context of English Unitarian-Trinitarian controversy of the eighteenth and nineteenth centuries. The book re-establishes Coleridge as a philosopher of religion and as a vital source for contemporary theological reflection.

A Rhetoric of Reflection

A Rhetoric of Reflection PDF

Author: Kathleen Yancey

Publisher: University Press of Colorado

Published: 2016-08-15

Total Pages: 338

ISBN-13: 1607325160

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Reflection in writing studies is now entering a third generation. Dating from the 1970s, the first generation of reflection focused on identifying and describing internal cognitive processes assumed to be part of composing. The second generation, operating in both classroom and assessment scenes in the 1990s, developed mechanisms for externalizing reflection, making it visible and thus explicitly available to help writers. Now, a third generation of work in reflection is emerging. As mapped by the contributors to A Rhetoric of Reflection, this iteration of research and practice is taking up new questions in new sites of activity and with new theories. It comprises attention to transfer of writing knowledge and practice, teaching and assessment, portfolios, linguistic and cultural difference, and various media, including print and digital. It conceptualizes conversation as a primary reflective medium, both inside and outside the classroom and for individuals and collectives, and articulates the role that different genres play in hosting reflection. Perhaps most important in the work of this third generation is the identification and increasing appreciation of the epistemic value of reflection, of its ability to help make new meanings, and of its rhetorical power—for both scholars and students. Contributors: Anne Beaufort, Kara Taczak, Liane Robertson, Michael Neal, Heather Ostman, Cathy Leaker, Bruce Horner, Asao B. Inoue, Tyler Richmond, J. Elizabeth Clark, Naomi Silver, Christina Russell McDonald, Pamela Flash, Kevin Roozen, Jeff Sommers, Doug Hesse

Violence

Violence PDF

Author: Slavoj Zizek

Publisher: Macmillan

Published: 2008-07-22

Total Pages: 271

ISBN-13: 0312427182

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Philosopher, cultural critic, and agent provocateur Zizek constructs a fascinating new framework to look at the forces of violence in the world.

Mirror, Mirror

Mirror, Mirror PDF

Author: Mark Pendergrast

Publisher: Basic Books

Published: 2009-04-28

Total Pages: 448

ISBN-13: 0786729902

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Of all human inventions, the mirror is perhaps the one most closely connected to our own consciousness. As our first technology for contemplation of the self, the mirror is arguably as important an invention as the wheel. Mirror Mirror is the fascinating story of the mirror's invention, refinement, and use in an astonishing range of human activities -- from the fantastic mirrored rooms that wealthy Romans created for their orgies to the mirror's key role in the use and understanding of light. Pendergrast spins tales of the 2,500year mystery of whether Archimedes and his "burning mirror" really set faraway Roman ships on fire; the medieval Venetian glassmakers, who perfected the technique of making large, flat mirrors from clear glass and for whom any attempt to leave their cloistered island was punishable by death; Isaac Newton, whose experiments with sunlight on mirrors once left him blinded for three days; the artist David Hockney, who holds controversial ideas about Renaissance artists and their use of optical devices; and George Ellery Hale, the manic-depressive astronomer and telescope enthusiast who inspired (and gave his name to) the twentieth century's largest ground-based telescope. Like mirrors themselves, Mirror Mirror is a book of endless wonder and fascination.