Linear Algebra and Analytic Geometry
Martin Mustermann
Linear Algebra and Analytic Geometry
Eine Diplomarbeit uber ¨
Linear Algebra and Analytic Geometry
Humboldt-Universit¨at zu Berlin Mathematisch-Naturwissenschaftliche Fakult¨at II Institut fur ¨ Mathematik
Geschrieben von Martin Mustermann Geboren am 4. Dezember 1984 in Paris Betreut durch Prof. Dr. Max Beispiel
Berlin, den 1. Juli 2010
Copyright by Martin Mustermann.
[email protected]
Erkl¨arung Ich erkl¨are, dass ich die vorliegende Arbeit selbstst¨andig und nur unter Verwendung der angegebenen Literatur und Hilfsmittel angefertigt habe. Weiterhin erkl¨are ich mich einverstanden, dass ein Exemplar dieser Diplomarbeit in der Bibliothek des Institutes fur ¨ Mathematik der Humboldt-Universit¨at zu Berlin verbleibt. Berlin, den 1. Juli 2010
The introductory quotation has been cited by Tito Tonietti in a letter to the editor of The Mathematical Intelligencer, volume 7 (1985), number 4, page 8 from a letter by Hermann Weyl to Freeman Dyson.
Layout by Tillmann Berg. www.mathematik.hu-berlin.de/∼berg/TBthesis This work is typeset in Hermann Zapf’s beautiful Palatino font. The spread is inspired by Johannes Gutenberg as described by Jan Tschichold. Produced using LATEX together with the memoir class. Gedruckt in Germany.
Abstract This work is concerned with providing a nice LATEX-layout for everyone writing a Bachelor, Master or Diploma thesis. Change the texts in this file to suit your needs!
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Contents Abstract
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Contents iii Introduction iv Results and Overview 1
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Bibliography
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Index
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Introduction Usually a short introduction to your thesis will be expected. It should contain a short description of what you are doing, why you are doing it and who else has done something similar. Also, some acknowledgments will be nice. Acknowledgment. I want to thank Professor Dr. Max Beispiel for support and proofreading. Also, I thank Mrs. Picky for suggesting many improvements for this work.
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Results and Overview The First Chapter & The Second Chapter You can use this list to generate a per chapter overview of your thesis. Third Chapter If you want to add a list of Theorems and Results, you can nest anouther list as follows: Corollary 1. For every even-dimensional rectangular flat torus and every nondegenerate rectangular line bundle ω over this torus is independent of a and is called the spectrum of ω. Corollary 2. For every even integer n ≥ 4 there exists an n-dimensional flat torus M and two topologically distinct but isospectral nondegenerate rectangular line bundles over M. The expression of the transplantation in Corollary 2 can be simplified for a Z2 -invariant connection and r1 = · · · = rm = 1 such that it does not contain any infinite sums.
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My work always tried to unite the truth with the beautiful; but when I had to chose one or the other, I usually chose the beautiful. Hermann Weyl
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Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Definition 1.1. The definition of a manifold can be found in the very nice book [Lee02]. The point of this definition is to show how the predefined environments look and to generate some quotation such that the bibliography at the end of the text is not empty. Duis autem vel eum iriure dolor in hendrerit in vulputate velit esse molestie consequat, vel illum dolore eu feugiat nulla facilisis at vero eros et accumsan et iusto odio dignissim qui blandit praesent luptatum zzril delenit augue duis dolore te feugait nulla facilisi. Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat. Duis autem vel eum iriure dolor in hendrerit in vulputate velit esse molestie consequat, vel illum dolore eu feugiat nulla facilisis at vero eros et 1
accumsan et iusto odio dignissim qui blandit praesent luptatum zzril delenit augue duis dolore te feugait nulla facilisi. Nam liber tempor cum soluta nobis eleifend option congue nihil imperdiet doming id quod mazim placerat facer possim assum. Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat. Duis autem vel eum iriure dolor in hendrerit in vulputate velit esse molestie consequat, vel illum dolore eu feugiat nulla facilisis. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, At accusam aliquyam diam diam dolore dolores duo eirmod eos erat, et nonumy sed tempor et et invidunt justo labore Stet clita ea et gubergren, kasd magna no rebum. sanctus sea sed takimata ut vero voluptua. est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat. Consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus.
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Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Duis autem vel eum iriure dolor in hendrerit in vulputate velit esse molestie consequat, vel illum dolore eu feugiat nulla facilisis at vero eros et accumsan et iusto odio dignissim qui blandit praesent luptatum zzril delenit augue duis dolore te feugait nulla facilisi. Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat. Duis autem vel eum iriure dolor in hendrerit in vulputate velit esse molestie consequat, vel illum dolore eu feugiat nulla facilisis at vero eros et accumsan et iusto odio dignissim qui blandit praesent luptatum zzril delenit augue duis dolore te feugait nulla facilisi.
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Bibliography [Lee02] John M. Lee. Introduction to Smooth Manifolds. Springer, First edition, September 2002.
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Index facilisi, 3 lorem ipsum, 1 manifold, 1
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