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Explorations in Number Theory

Explorations in Number Theory
Explorations in Number Theory: Commuting through the Numberverse
English | 2022 | ISBN: 3030989305 | 385 Pages | PDF EPUB (True) | 19 MB
This innovative undergraduate textbook approaches number theory through the lens of abstract algebra. Written in an engaging and whimsical style, this text will introduce students to rings, groups, fields, and other algebraic structures as they discover the key concepts of elementary number theory. Inquiry-based learning (IBL) appears throughout the chapters, allowing students to develop insights for upcoming sections while simultaneously strengthening their understanding of previously covered topics.The text is organized around three core themes: the notion of what a "number" is, and the premise that it takes familiarity with a large variety of number systems to fully explore number theory; the use of Diophantine equations as catalysts for introducing and developing structural ideas; and the role of abstract algebra in number theory, in particular the extent to which it provides the Fundamental Theorem of Arithmetic for various new number systems. Other aspects of modern number theory - including the study of elliptic curves, the analogs between integer and polynomial arithmetic, p-adic arithmetic, and relationships between the spectra of primes in various rings - are included in smaller but persistent threads woven through chapters and exercise sets.

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Expanding the Gothic Canon Studies in Literature, Film and New Media

Expanding the Gothic Canon Studies in Literature, Film and New Media
Expanding the Gothic Canon: Studies in Literature, Film and New Media By Anna Kedra-Kardela (editor), Andrzej Slawomir Kowalczyk (editor)
2014 | 303 Pages | ISBN: 3631626398 | PDF | 2 MB
This volume offers a survey of analyses of Gothic texts, including literary works, feature films, a TV serial, and video games, with a view to showing the evolution and expansion of the Gothic convention across the ages and the media. The temporal scope of the book is broad: the chapters cover narratives from the early and mid-eighteenth century, predating the birth of the convention in 1764, through Romantic and Victorian novels, to the contemporary manifestations of the Gothic. Primarily designed for graduate and postgraduate students, the book sets out to acquaint them with both the convention and different theoretical approaches. The studies presented here could also prove inspirational for fellow scholars and helpful for university teachers, the book becoming an item on the reading lists in Gothic literature, film and media courses.

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Expanding the Canon

Expanding the Canon
Melissa Hoag, "Expanding the Canon"
English | ISBN: 1032068272 | 2022 | 286 pages | PDF | 9 MB
Directly addressing the underrepresentation of Black composers in core music curricula, Expanding the Canon: Black Composers in the Music Theory Classroom aims to both demonstrate why diversification is badly needed and help faculty expand their teaching with practical, classroom-oriented lesson plans that focus on teaching music theory with music by Black composers.

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