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This textbook offers an introduction to the theory of Drinfeld modules, mathematical objects that are fundamental to modern number theory. After the first two chapters conveniently recalling prerequisites from abstract algebra and non-Archimedean analysis, Chapter 3 introduces Drinfeld modules and the key notions of isogenies and torsion points. Over the next four chapters, Drinfeld modules are studied in settings of various fields of arithmetic importance, culminating in the case of global fields. Throughout, numerous number-theoretic applications are discussed, and the analogies between classical and function field arithmetic are emphasized. Drinfeld Modules guides readers from the basics to research topics in function field arithmetic, assuming only familiarity with graduate-level abstract algebra as prerequisite. With exercises of varying difficulty included in each section, the book is designed to be used as the primary textbook for a graduate course on the topic, and may also provide a supplementary reference for courses in algebraic number theory, elliptic curves, and related fields. Furthermore, researchers in algebra and number theory will appreciate it as a self-contained reference on the topic.
Number theory. --- Algebra. --- Algebraic geometry. --- Number Theory. --- Algebraic Geometry. --- Algebraic geometry --- Geometry --- Mathematics --- Mathematical analysis --- Number study --- Numbers, Theory of --- Algebra --- Drinfeld modules. --- Modules (Algebra) --- Mòduls de Drinfeld
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This book constitutes the thoroughly refereed post-workshop proceedings of the 8th International Workshop on the Arithmetic of Finite Field, WAIFI 2022, held in Chengdu, China, in August – September 2022. The 19 revised full papers and 3 invited talks presented were carefully reviewed and selected from 25 submissions. The papers are organized in topical sections: structures in finite fields; efficient finite field arithmetic; coding theory; cryptography; sequences.
Finite fields (Algebra) --- Modular fields (Algebra) --- Algebra, Abstract --- Algebraic fields --- Galois theory --- Modules (Algebra)
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This collection of previously unpublished papers explores the implications of Chomsky's Minimalist framework for the modularity of grammar.
Psycholinguistics --- Grammar --- Generative grammar --- Grammar, Comparative and general --- Modularity (Psychology) --- Language, Psychology of --- Language and languages --- Psychology of language --- Speech --- Linguistics --- Psychology --- Thought and thinking --- Grammar, Generative --- Grammar, Transformational --- Grammar, Transformational generative --- Transformational generative grammar --- Transformational grammar --- Syntax --- Faculty psychology --- Modules (Psychology) --- Human information processing --- Psychological aspects --- Derivation --- Psycholinguistics. --- Generative grammar. --- Syntax. --- Philology --- Grammar, Comparative and general Syntax
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An incomparable look at how Chinese artists have used mass production to assemble exquisite objects from standardized partsChinese workers in the third century BC created seven thousand life-sized terracotta soldiers to guard the tomb of the First Emperor. In the eleventh century AD, Chinese builders constructed a pagoda from as many as thirty thousand separately carved wooden pieces. As these examples show, throughout history, Chinese artisans have produced works of art in astonishing quantities, and have done so without sacrificing quality, affordability, or speed of manufacture. In this book, Lothar Ledderose takes us on a remarkable tour of Chinese art and culture to explain how artists used complex systems of mass production to assemble extraordinary objects from standardized parts or modules. He reveals how these systems have deep roots in Chinese thought and reflect characteristically Chinese modes of social organization. Combining invaluable aesthetic and cultural insights with a rich variety of illustrations, Ten Thousand Things make a profound statement about Chinese art and society.
. --- Book of Changes (Yijing). --- Building Standards (Yingzao fashi). --- European co-invention of. --- Julien, Stanislas. --- Leibniz, Gottfried Wilhelm. --- Nan Yue kingdom, tomb of. --- Shang module systems in. --- West, the. --- Yijing (Book of Changes). --- Yingzao fashi (Building Standards). --- aesthetics of. --- applied and minor. --- as art form. --- as central to life of literati. --- cities, modular-grid layout of. --- collecting of. --- collectors and collecting of. --- developments in. --- during Qin. --- early trend toward. --- establishment of European industry for. --- factories (Chinese). --- factory system of production for. --- learning from Chinese art production. --- literacy (Chinese). --- mass production, in China. --- modular production of. --- modular production. --- modularity of. --- modules. --- names of, inscribed on objects. --- period. --- standardization. --- wall paintings in. --- writing central to life of. --- Art, Chinese --- Mass production --- Technique.
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