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Naive Lie Theory
Buch von John Stillwell
Sprache: Englisch

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Beschreibung
In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called "classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra.

This naive approach to Lie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. To compensate for the limitations of the naive approach, end of chapter discussions introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history.

John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).
In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called "classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra.

This naive approach to Lie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. To compensate for the limitations of the naive approach, end of chapter discussions introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history.

John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).
Zusammenfassung

Makes some basic Lie theory accessible

Unique choice of approach and topics

Introduces an advanced topic to undergraduates, at just the right pace

Author includes exercises and examples

Includes supplementary material: [...]

Inhaltsverzeichnis
Geometry of complex numbers and quaternions.- Groups.- Generalized rotation groups.- The exponential map.- The tangent space.- Structure of Lie algebras.- The matrix logarithm.- Topology.- Simply connected Lie groups.
Details
Erscheinungsjahr: 2008
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 232
Reihe: Undergraduate Texts in Mathematics
Inhalt: xv
217 S.
25 s/w Illustr.
25 s/w Zeichng.
ISBN-13: 9780387782140
ISBN-10: 0387782141
Sprache: Englisch
Herstellernummer: 12199891
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Stillwell, John
Auflage: 2008
Hersteller: Springer US
Springer New York
Undergraduate Texts in Mathematics
Maße: 241 x 160 x 19 mm
Von/Mit: John Stillwell
Erscheinungsdatum: 24.07.2008
Gewicht: 0,518 kg
preigu-id: 101866633
Zusammenfassung

Makes some basic Lie theory accessible

Unique choice of approach and topics

Introduces an advanced topic to undergraduates, at just the right pace

Author includes exercises and examples

Includes supplementary material: [...]

Inhaltsverzeichnis
Geometry of complex numbers and quaternions.- Groups.- Generalized rotation groups.- The exponential map.- The tangent space.- Structure of Lie algebras.- The matrix logarithm.- Topology.- Simply connected Lie groups.
Details
Erscheinungsjahr: 2008
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 232
Reihe: Undergraduate Texts in Mathematics
Inhalt: xv
217 S.
25 s/w Illustr.
25 s/w Zeichng.
ISBN-13: 9780387782140
ISBN-10: 0387782141
Sprache: Englisch
Herstellernummer: 12199891
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Stillwell, John
Auflage: 2008
Hersteller: Springer US
Springer New York
Undergraduate Texts in Mathematics
Maße: 241 x 160 x 19 mm
Von/Mit: John Stillwell
Erscheinungsdatum: 24.07.2008
Gewicht: 0,518 kg
preigu-id: 101866633
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