Stefan Müller-Stach – författare

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21 produkter

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21 produkter

Arithmetic and Geometry of Algebraic Cycles
AvB. Brent Gordon,James D. Lewism. fl.
Inbunden, Engelska, 2000
2 441 kr
Skickas inom 10-15 vardagar
The NATO Advanced Study Institute on "The Arithmetic and Geometry of Algebraic Cycles" was held at the Banff Centre for Conferences in Banff (Al berta, Canada) from June 7 until June 19, 1998. This meeting was organized jointly with Centre de Recherches Mathematiques (CRM), Montreal, as one of the CRM Summer schools which take place annually at the Banff Center. The conference also served as the kick-off activity of the CRM 1998-99 theme year on Number Theory and Arithmetic Geometry. There were 109 participants who came from 17 countries: Belgium, Canada, China, France, Germany, Greece, India, Italy, Japan, Mexico, Netherlands, - mania, Russia, Spain, Switzerland, the United Kingdom and the United States. During a period of two weeks, 41 invited lectures and 20 contributed lec tures were presented. Four lectures by invited speakers were delivered every day, followed by two sessions of contributed talks. Many informal discussions and working sessions involving small groups were organized by individual partic ipants. In addition, participants' reprints and preprints were displayed through out in a lounge next to the auditorium, which further enhanced opportunities for communication and interaction.
Arithmetic and Geometry of Algebraic Cycles
AvB. Brent Gordon,James D. Lewism. fl.
Häftad, Engelska, 2000
2 441 kr
Skickas inom 10-15 vardagar
The NATO Advanced Study Institute on "The Arithmetic and Geometry of Algebraic Cycles" was held at the Banff Centre for Conferences in Banff (Al berta, Canada) from June 7 until June 19, 1998. This meeting was organized jointly with Centre de Recherches Mathematiques (CRM), Montreal, as one of the CRM Summer schools which take place annually at the Banff Center. The conference also served as the kick-off activity of the CRM 1998-99 theme year on Number Theory and Arithmetic Geometry. There were 109 participants who came from 17 countries: Belgium, Canada, China, France, Germany, Greece, India, Italy, Japan, Mexico, Netherlands, - mania, Russia, Spain, Switzerland, the United Kingdom and the United States. During a period of two weeks, 41 invited lectures and 20 contributed lec tures were presented. Four lectures by invited speakers were delivered every day, followed by two sessions of contributed talks. Many informal discussions and working sessions involving small groups were organized by individual partic ipants. In addition, participants' reprints and preprints were displayed through out in a lounge next to the auditorium, which further enhanced opportunities for communication and interaction.
Period Mappings and Period Domains
AvChris Peters,Stefan Muller-Stachm. fl.
E-bok
Engelska, 2017
900 kr
Läs direkt efter köp
This up-to-date introduction to Griffiths'' theory of period maps and period domains focusses on algebraic, group-theoretic and differential geometric aspects. Starting with an explanation of Griffiths'' basic theory, the authors go on to introduce spectral sequences and Koszul complexes that are used to derive results about cycles on higher-dimensional algebraic varieties such as the Noether–Lefschetz theorem and Nori''s theorem. They explain differential geometric methods, leading up to proofs of Arakelov-type theorems, the theorem of the fixed part and the rigidity theorem. They also use Higgs bundles and harmonic maps to prove the striking result that not all compact quotients of period domains are Kähler. This thoroughly revised second edition includes a new third part covering important recent developments, in which the group-theoretic approach to Hodge structures is explained, leading to Mumford–Tate groups and their associated domains, the Mumford–Tate varieties and generalizations of Shimura varieties.
Period Mappings and Period Domains
AvChris Peters,Stefan Muller-Stachm. fl.
E-bok
PDF, Engelska, 2017
900 kr
Läs direkt efter köp
This up-to-date introduction to Griffiths'' theory of period maps and period domains focusses on algebraic, group-theoretic and differential geometric aspects. Starting with an explanation of Griffiths'' basic theory, the authors go on to introduce spectral sequences and Koszul complexes that are used to derive results about cycles on higher-dimensional algebraic varieties such as the Noether–Lefschetz theorem and Nori''s theorem. They explain differential geometric methods, leading up to proofs of Arakelov-type theorems, the theorem of the fixed part and the rigidity theorem. They also use Higgs bundles and harmonic maps to prove the striking result that not all compact quotients of period domains are Kähler. This thoroughly revised second edition includes a new third part covering important recent developments, in which the group-theoretic approach to Hodge structures is explained, leading to Mumford–Tate groups and their associated domains, the Mumford–Tate varieties and generalizations of Shimura varieties.
Periods and Nori Motives
AvAnnette Huber,Stefan Müller-Stach
Inbunden, Engelska, 2017
923 kr
Skickas inom 5-8 vardagar
This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori’s abelian category of mixed motives. It develops Nori’s approach to mixed motives from scratch, thereby filling an important gap in the literature, and then explains the connection of mixed motives to periods, including a detailed account of the theory of period numbers in the sense of Kontsevich-Zagier and their structural properties.Period numbers are central to number theory and algebraic geometry, and also play an important role in other fields such as mathematical physics. There are long-standing conjectures about their transcendence properties, best understood in the language of cohomology of algebraic varieties or, more generally, motives. Readers of this book will discover that Nori’s unconditional construction of an abelian category of motives (over fields embeddable into the complex numbers) is particularly well suited for this purpose. Notably, Kontsevich's formal period algebra represents a torsor under the motivic Galois group in Nori's sense, and the period conjecture of Kontsevich and Zagier can be recast in this setting.Periods and Nori Motives is highly informative and will appeal to graduate students interested in algebraic geometry and number theory as well as researchers working in related fields. Containing relevant background material on topics such as singular cohomology, algebraic de Rham cohomology, diagram categories and rigid tensor categories, as well as many interesting examples, the overall presentation of this book is self-contained.
Periods and Nori Motives
AvStefan Muller-Stach,Annette Huber
E-bok
Engelska, 2017
1 891 kr
Läs direkt efter köp
This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori’s abelian category of mixed motives. It develops Nori’s approach to mixed motives from scratch, thereby filling an important gap in the literature, and then explains the connection of mixed motives to periods, including a detailed account of the theory of period numbers in the sense of Kontsevich-Zagier and their structural properties.Period numbers are central to number theory and algebraic geometry, and also play an important role in other fields such as mathematical physics. There are long-standing conjectures about their transcendence properties, best understood in the language of cohomology of algebraic varieties or, more generally, motives. Readers of this book will discover that Nori’s unconditional construction of an abelian category of motives (over fields embeddable into the complex numbers) is particularly well suited for this purpose. Notably, Kontsevich''s formal period algebra represents a torsor under the motivic Galois group in Nori''s sense, and the period conjecture of Kontsevich and Zagier can be recast in this setting.Periods and Nori Motives is highly informative and will appeal to graduate students interested in algebraic geometry and number theory as well as researchers working in related fields. Containing relevant background material on topics such as singular cohomology, algebraic de Rham cohomology, diagram categories and rigid tensor categories, as well as many interesting examples, the overall presentation of this book is self-contained.
Periods and Nori Motives
AvAnnette Huber,Stefan Müller-Stach
Häftad, Engelska, 2018
923 kr
Skickas inom 5-8 vardagar
This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori’s abelian category of mixed motives. It develops Nori’s approach to mixed motives from scratch, thereby filling an important gap in the literature, and then explains the connection of mixed motives to periods, including a detailed account of the theory of period numbers in the sense of Kontsevich-Zagier and their structural properties.Period numbers are central to number theory and algebraic geometry, and also play an important role in other fields such as mathematical physics. There are long-standing conjectures about their transcendence properties, best understood in the language of cohomology of algebraic varieties or, more generally, motives. Readers of this book will discover that Nori’s unconditional construction of an abelian category of motives (over fields embeddable into the complex numbers) is particularly well suited for this purpose. Notably, Kontsevich's formal period algebra represents a torsor under the motivic Galois group in Nori's sense, and the period conjecture of Kontsevich and Zagier can be recast in this setting.Periods and Nori Motives is highly informative and will appeal to graduate students interested in algebraic geometry and number theory as well as researchers working in related fields. Containing relevant background material on topics such as singular cohomology, algebraic de Rham cohomology, diagram categories and rigid tensor categories, as well as many interesting examples, the overall presentation of this book is self-contained.
Richard Dedekind
Was sind und was sollen die Zahlen? Stetigkeit und Irrationale Zahlen
AvStefan Muller-Stach
E-bok
PDF, Tyska, 2017
510 kr
Läs direkt efter köp
Die beiden Bücher „Was sind und was sollen die Zahlen?“ (1888) und „Stetigkeit und Irrationale Zahlen“ (1872) sind Dedekinds Beiträge zu den Grundlagen der Mathematik; er legte darin die Grundsteine der Mengenlehre und der Theorie der reellen und natürlichen Zahlen. Diese Schriften sind aus der modernen Mathematik nicht mehr wegzudenken. Dennoch wurde die Leistung Dedekinds nicht immer entsprechend gewürdigt und der Inhalt dieser Bücher ist auch heute noch vielen Mathematikern wenig bekannt. Dieses Buch enthält neben den Originaltexten eine ausführliche Erklärung der beiden Schriften und eine Interpretation in moderner Sprache, sowie eine kurze Biografie und eine Abschrift des berühmten Briefs an H. Keferstein. Dadurch bietet dieses Buch einen faszinierenden Einblick in das Leben und Schaffen dieses wegweisenden Wissenschaftlers und stellt sein Werk in Beziehung zu großen Zeitgenossen wie Cantor, Dirichlet, Frege, Hilbert, Kronecker und Riemann.
Der Code der Mathematik
Beweis und Wahrheit
AvStefan Müller-Stach
Häftad, Tyska, 2023
369 kr
Skickas inom 10-15 vardagar
Motiviert durch aktuelle Entwicklungen in der abhängigen Typentheorie und bei Unendlichkategorien präsentiert dieses Buch die Ideengeschichte der Begriffe Wahrheit, Beweis, Gleichheit und Äquivalenz. Neben ausgewählten Ideen von Platon, Aristoteles, Leibniz, Kant, Frege und anderen werden Resultate von Gödel und Tarski über Unvollständigkeit, Unentscheidbarkeit und Wahrheit in deduktiven Systemen und ihren semantischen Modellen vorgestellt. Der Hauptgegenstand dieses Textes ist die abhängige Typentheorie und neuere Entwicklungen in der Homotopy Type Theory. Diese Theorien beinhalten Identitätstypen, die neue Möglichkeiten für Gleichheit, Symmetrie, Äquivalenz und Isomorphie auf konzeptuelle Weise eröffnen. Die Interaktion von Typentheorie und Unendlichkategorien ist ein neues Paradigma für eine strukturelle Sichtweise auf die Mathematik. Sie fördert auch den neuen Trend zur Formalisierung von Mathematik in Form von Beweisassistenten.
Der Code der Mathematik
Beweis und Wahrheit
AvStefan Muller-Stach
E-bok
Tyska, 2023
348 kr
Läs direkt efter köp
Motiviert durch aktuelle Entwicklungen in der abhängigen Typentheorie und bei Unendlichkategorien präsentiert dieses Buch die Ideengeschichte der Begriffe Wahrheit, Beweis, Gleichheit und Äquivalenz. Neben ausgewählten Ideen von Platon, Aristoteles, Leibniz, Kant, Frege und anderen werden Resultate von Gödel und Tarski über Unvollständigkeit, Unentscheidbarkeit und Wahrheit in deduktiven Systemen und ihren semantischen Modellen vorgestellt. Der Hauptgegenstand dieses Textes ist die abhängige Typentheorie und neuere Entwicklungen in der Homotopy Type Theory. Diese Theorien beinhalten Identitätstypen, die neue Möglichkeiten für Gleichheit, Symmetrie, Äquivalenz und Isomorphie auf konzeptuelle Weise eröffnen. Die Interaktion von Typentheorie und Unendlichkategorien ist ein neues Paradigma für eine strukturelle Sichtweise auf die Mathematik. Sie fördert auch den neuen Trend zur Formalisierung von Mathematik in Form von Beweisassistenten.
Richard Dedekind
Was sind und was sollen die Zahlen? Stetigkeit und Irrationale Zahlen
AvStefan Müller-Stach
Häftad, Tyska, 2023
576 kr
Skickas inom 10-15 vardagar
Die beiden Bücher „Was sind und was sollen die Zahlen?“ (1888) und „Stetigkeit und Irrationale Zahlen“ (1872) sind Dedekinds Beiträge zu den Grundlagen der Mathematik; er legte darin die Grundsteine der Mengenlehre und der Theorie der reellen und natürlichen Zahlen. Diese Schriften sind aus der modernen Mathematik nicht mehr wegzudenken. Dennoch wurde die Leistung Dedekinds nicht immer entsprechend gewürdigt und der Inhalt dieser Bücher ist auch heute noch vielen Mathematikerinnen und Mathematikern wenig bekannt. Dieses Buch enthält neben den Originaltexten eine ausführliche Erklärung der beiden Schriften und eine Interpretation in moderner Sprache, sowie eine kurze Biografie und eine Abschrift des berühmten Briefs an H. Keferstein. Dadurch bietet dieses Buch einen faszinierenden Einblick in das Leben und Schaffen dieses wegweisenden Wissenschaftlers und stellt sein Werk in Beziehung zu großen Zeitgenossen wie Cantor, Dirichlet, Frege, Hilbert, Kronecker und Riemann.
Richard Dedekind
Was sind und was sollen die Zahlen? Stetigkeit und Irrationale Zahlen
AvStefan Muller-Stach
E-bok
PDF, Tyska, 2023
574 kr
Läs direkt efter köp
Die beiden Bücher „Was sind und was sollen die Zahlen?“ (1888) und „Stetigkeit und Irrationale Zahlen“ (1872) sind Dedekinds Beiträge zu den Grundlagen der Mathematik; er legte darin die Grundsteine der Mengenlehre und der Theorie der reellen und natürlichen Zahlen. Diese Schriften sind aus der modernen Mathematik nicht mehr wegzudenken. Dennoch wurde die Leistung Dedekinds nicht immer entsprechend gewürdigt und der Inhalt dieser Bücher ist auch heute noch vielen Mathematikerinnen und Mathematikern wenig bekannt. Dieses Buch enthält neben den Originaltexten eine ausführliche Erklärung der beiden Schriften und eine Interpretation in moderner Sprache, sowie eine kurze Biografie und eine Abschrift des berühmten Briefs an H. Keferstein. Dadurch bietet dieses Buch einen faszinierenden Einblick in das Leben und Schaffen dieses wegweisenden Wissenschaftlers und stellt sein Werk in Beziehung zu großen Zeitgenossen wie Cantor, Dirichlet, Frege, Hilbert, Kronecker und Riemann.
Del 11 - Mathematics Study Resources
Code of Mathematics
Proof and Truth
AvStefan Müller-Stach
Häftad, Engelska, 2024
616 kr
Skickas inom 10-15 vardagar
Inspired by recent developments in dependent type theory and infinity categories, this book presents a history of ideas around the topics of truth, proof, equality and equivalence. Besides selected ideas of Platon, Aristoteles, Leibniz, Kant, Frege and others, the results of Gödel and Tarski on incompleteness, undecidability and truth in deductive systems and their semantic models are covered. The main focus of this textbook is on dependent type theory and its recent variant homotopy type theory. Such theories contain identity types, which give a new understanding of equality, symmetry, equivalence and isomorphism in a conceptual way. The interaction of type theory and infinity category theory yields a new paradigm for a structural view on mathematics. This supports the tendencies towards formalising mathematics with the help of proof assistants.This book was first published in German. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.
Code of Mathematics
Proof and Truth
AvStefan Muller-Stach
E-bok
Engelska, 2024
797 kr
Läs direkt efter köp
Inspired by recent developments in dependent type theory and infinity categories, this book presents a history of ideas around the topics of truth, proof, equality and equivalence. Besides selected ideas of Platon, Aristoteles, Leibniz, Kant, Frege and others, the results of Gödel and Tarski on incompleteness, undecidability and truth in deductive systems and their semantic models are covered. The main focus of this textbook is on dependent type theory and its recent variant homotopy type theory. Such theories contain identity types, which give a new understanding of equality, symmetry, equivalence and isomorphism in a conceptual way. The interaction of type theory and infinity category theory yields a new paradigm for a structural view on mathematics. This supports the tendencies towards formalising mathematics with the help of proof assistants.
This book was first published in German. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.
Richard Dedekind
What Are and What Should the Numbers Be? Continuity and Irrational Numbers
AvStefan Müller-Stach
Inbunden, Engelska, 2024
1 777 kr
Skickas inom 10-15 vardagar
The two works titled "What Are and What Should the Numbers Be?" (1888) and "Continuity and Irrational Numbers" (1872) are Dedekind's contributions to the foundations of mathematics; therein, he laid the groundwork for set theory and the theory of real and natural numbers. These writings are indispensable in modern mathematics. However, Dedekind's achievements have not always been adequately acknowledged, and the content of these books is still little known to many mathematicians today.This volume contains not only the original texts but also a detailed analysis of the two writings and an interpretation in modern language, as well as a brief biography and a transcript of the famous letter to H. Keferstein. The extensive commentary offers a fascinating insight into the life and work of Dedekind's pioneering work and relates the latter to great contemporaries such as Cantor, Dirichlet, Frege, Hilbert, Kronecker, and Riemann.Researchers and students alike will find this work a valuable reference in the history of mathematics.
Richard Dedekind
What Are and What Should the Numbers Be? Continuity and Irrational Numbers
AvStefan Muller-Stach
E-bok
PDF, Engelska, 2024
2 224 kr
Läs direkt efter köp
The two works titled "What Are and What Should the Numbers Be?" (1888) and "Continuity and Irrational Numbers" (1872) are Dedekind''s contributions to the foundations of mathematics; therein, he laid the groundwork for set theory and the theory of real and natural numbers. These writings are indispensable in modern mathematics. However, Dedekind''s achievements have not always been adequately acknowledged, and the content of these books is still little known to many mathematicians today.
This volume contains not only the original texts but also a detailed analysis of the two writings and an interpretation in modern language, as well as a brief biography and a transcript of the famous letter to H. Keferstein. The extensive commentary offers a fascinating insight into the life and work of Dedekind''s pioneering work and relates the latter to great contemporaries such as Cantor, Dirichlet, Frege, Hilbert, Kronecker, and Riemann.
Researchers and students alike will find this work a valuable reference in the history of mathematics.
Gott q.e.d.?
Ein Lesebuch aus der gemeinsamen Geschichte von Mathematik und Theologie
AvStefan Müller-Stach,Tilman Sauerm. fl.
Inbunden, Tyska, 2027
379 kr
Kommande
Was haben Unendlichkeit, Zahlenverhältnisse und die Ordnung der Natur mit der Frage nach Gott zu tun? Für viele Denker der Antike, des Mittelalters und der frühen Neuzeit waren Mathematik und Theologie eng aufeinander bezogen. Zahlen galten nicht nur als Gegenstand mathematischer Erkenntnis, sondern auch als Schlüssel zum Verständnis der Welt und ihres Ursprungs. Diese Verbindung prägte über Jahrhunderte hinweg das gelehrte Denken – vom antiken Zahlendenken mitten hinein in das mittelalterliche Quadrivium mit Arithmetik, Geometrie, Musik und Astronomie, das dem Theologiestudium vorgeschaltet war. Auch die Beweise der Existenz Gottes gehen auf diese enge Verbindung zurück, die bis heute nachwirkt, aber außerhalb von Fachkreisen oft in Vergessenheit geraten ist. Doch auch wenn sich die Wege von Mathematik und Theologie in der klassischen Moderne trennten, so warfen Schlüsselfiguren der modernen mathematischen und physikalischen Welterklärung wie Einstein und Gödel die alten Fragen nach Ordnung, Rationalität und den Grenzen des Beweisbaren immer wieder neu auf. Das vorliegende Lesebuch macht mit seiner historischen Perspektive die ehemals enge Verbindung zwischen den beiden Disziplinen wieder neu zugänglich. Es versammelt zentrale Quellentexte von der Antike bis ins 20. Jahrhundert – überwiegend in neuen Übersetzungen – und erschließt sie durch Einleitungen, Kommentare und Literaturhinweise.
Elementare und algebraische Zahlentheorie
Ein moderner Zugang zu klassischen Themen
AvStefan Müller-Stach,Jens Piontkowski
Häftad, Tyska, 2011
400 kr
Skickas inom 10-15 vardagar
Das Buch wendet sich an alle, die in die klassischen Themen der Zahlentheorie einsteigen wollen. Neben den Standardthemen wie Primzahlen, Rechnen modulo n, quadratische Reste und Kettenbrüche werden auch die fortgeschrittenen Bereiche wie p-adische Zahlen, quadratische Formen und Zahlkörper am Beispiel der quadratischen Zahlkörper behandelt. Viel Wert wird auf die konkrete Berechenbarkeit bei allen Problemlösungen gelegt. Im Rahmen der Bachelor-/Master-Studiengänge eignet sich das Buch als Grundlage für zwei Semester: ein Aufbaumodul in elementarer Zahlentheorie mit einem Vertiefungsmodul in algebraischer Zahlentheorie. Die zweite Auflage enthält neben Verbesserungen viele neue Übungsaufgaben mit Lösungen oder Lösungshinweisen. Außerdem wurde ein Anhang über die Minkowski-Theorie ergänzt.
Elementare und algebraische Zahlentheorie
Ein moderner Zugang zu klassischen Themen
AvJens Piontkowski,Stefan Muller-Stach
E-bok
PDF, Tyska, 2011
399 kr
Läs direkt efter köp
Elementare und algebraische Zahlentheorie
Ein moderner Zugang zu klassischen Themen
AvJens Piontkowski,Stefan Muller-Stach
E-bok
PDF, Tyska, 2007
255 kr
Läs direkt efter köp
Arithmetic and Geometry of Algebraic Cycles
AvNoriko Yui,Shuji Saitom. fl.
E-bok
PDF, Engelska, 2012
3 054 kr
Läs direkt efter köp
The NATO Advanced Study Institute on "The Arithmetic and Geometry of Algebraic Cycles" was held at the Banff Centre for Conferences in Banff (Al berta, Canada) from June 7 until June 19, 1998. This meeting was organized jointly with Centre de Recherches Mathematiques (CRM), Montreal, as one of the CRM Summer schools which take place annually at the Banff Center. The conference also served as the kick-off activity of the CRM 1998-99 theme year on Number Theory and Arithmetic Geometry. There were 109 participants who came from 17 countries: Belgium, Canada, China, France, Germany, Greece, India, Italy, Japan, Mexico, Netherlands, - mania, Russia, Spain, Switzerland, the United Kingdom and the United States. During a period of two weeks, 41 invited lectures and 20 contributed lec tures were presented. Four lectures by invited speakers were delivered every day, followed by two sessions of contributed talks. Many informal discussions and working sessions involving small groups were organized by individual partic ipants. In addition, participants'' reprints and preprints were displayed through out in a lounge next to the auditorium, which further enhanced opportunities for communication and interaction.

Företag, bibliotek eller offentlig verksamhet?

Stefan Müller-Stach – författare

Arithmetic and Geometry of Algebraic Cycles

Arithmetic and Geometry of Algebraic Cycles

Period Mappings and Period Domains

Period Mappings and Period Domains

Periods and Nori Motives

Periods and Nori Motives

Periods and Nori Motives

Richard Dedekind

Der Code der Mathematik

Der Code der Mathematik

Richard Dedekind

Richard Dedekind

Code of Mathematics

Code of Mathematics

Richard Dedekind

Richard Dedekind

Gott q.e.d.?

Elementare und algebraische Zahlentheorie

Elementare und algebraische Zahlentheorie

Elementare und algebraische Zahlentheorie

Arithmetic and Geometry of Algebraic Cycles

Mina sidor

Mina sidor

Hjälp

Hjälp

Om Bokus

Om Bokus

Populärt

Populärt

Inspiration

Inspiration