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1. |
Record Nr. |
UNINA9910483398203321 |
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Autore |
Ovchinnikov SergeiÌ |
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Titolo |
Real analysis : foundations / / SergeiÌ Ovchinnikov |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2021] |
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©2021 |
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ISBN |
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Edizione |
[1st ed. 2021.] |
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Descrizione fisica |
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1 online resource (XII, 178 p. 13 illus.) |
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Collana |
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Disciplina |
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Soggetti |
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Mathematical analysis |
Functions of real variables |
Ordered fields |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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1 Rational Numbers -- 2 Real Numbers -- 3 Continuous Functions -- 4 Differentiation -- 5 Integration -- 6 Infinite Series -- A Natural Numbers and Integers -- B Dedekind's Construction of Real Numbers. C A Panorama of Ordered Fields. |
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Sommario/riassunto |
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This textbook explores the foundations of real analysis using the framework of general ordered fields, demonstrating the multifaceted nature of the area. Focusing on the logical structure of real analysis, the definitions and interrelations between core concepts are illustrated with the use of numerous examples and counterexamples. Readers will learn of the equivalence between various theorems and the completeness property of the underlying ordered field. These equivalences emphasize the fundamental role of real numbers in analysis. Comprising six chapters, the book opens with a rigorous presentation of the theories of rational and real numbers in the framework of ordered fields. This is followed by an accessible exploration of standard topics of elementary real analysis, including continuous functions, differentiation, integration, and infinite series. Readers will find this text conveniently self-contained, with three appendices included after the main text, covering an overview of natural numbers and integers, Dedekind's construction of real numbers, historical notes, and selected topics in algebra. Real Analysis: |
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Foundations is ideal for students at the upper-undergraduate or beginning graduate level who are interested in the logical underpinnings of real analysis. With over 130 exercises, it is suitable for a one-semester course on elementary real analysis, as well as independent study. |
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2. |
Record Nr. |
UNINA9910136124203321 |
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Autore |
Tysdal Daniel Scott <1978-> |
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Titolo |
Fauxccasional Poems |
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Pubbl/distr/stampa |
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ISBN |
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Descrizione fisica |
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1 online resource (98 p.) |
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Disciplina |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Sommario/riassunto |
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In Fauxccasional Poems, Daniel Scott Tysdal imagines himself into poetic voices not his own, writing to commemorate events that never occurred, for the posterity of alternative universes -- and the delight of our own. From the reign of the first philosopher king once envisioned by Plato, to the twelfth-century Iroquois colonization of Europe, to Barack Obama's career as a poet, to the lasting peace to come under the rule of the Democratic Kampuchea Global Party, Tysdal envisions the paths not taken and what might have been. In these poems, the crew of the Enola Gayrefuse to drop the atomic bomb on Hiroshima, John F. Kennedy evades assassination, and Karl Marx moonlights as an agent provocateur for a capitalist consortium.In a dizzying display of poetic insight, technical prowess, and playful parody, Fauxccasional Poemsbrings these alternate universes to life, forcing the reader to ponder the contingency of history and how each moment brings us to a thousand turning points. Despite our certainties, nothing is ever as it |
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seems, and the future unfolds against our best designs. History is an unreliable vessel for the upwelling of our deepest hopes and fears, and in Tysdal's hands poetry shakes history by the lapels and shouts, "Wake up! Your time is now!" |
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