UNIVERSITY OF CALGARY. An Important Contribution to the Literature. Jane Mary Doe A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES

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UNIVERSITY OF CALGARY An Important Contribution to the Literature by Jane Mary Doe A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY GRADUATE PROGRAM IN PHILOSOPHY CALGARY, ALBERTA May, 2018 c Jane Mary Doe 2018

Abstract The abstract is a concise and accurate summary of the research contained in your thesis. It gives the reader a snapshot of your research by highlighting key points. It includes the problem, method of study, and general conclusion; relevant key words that will help people find your research. It must be no longer than 350 words (Note: hyphenated words or words separated by a slash are counted as two words). It must be double-spaced or one-half spaced, and not contain graphs, tables, or illustrations. ii

Preface The preface gives a statement of where the information included in your thesis came from. It gives credit to the authors who informed your work. A manuscript-based thesis must include an explanation of which parts of your thesis were already published and details of the publication. For example: Portions of the introductory text of Chapter 1 are used with permission from Smith et al. (2015) of which I am an author. Table 1.1 is modified from Supplementary Table 3 in Smith et al. (2014). Chapter 2 of this thesis has been published as J. Smith and J. Doe, Title of Article. Journal Name, vol. 1, issue 1. For a traditional thesis requiring ethics approval, include the name of the board that approved the research project, the title of the project, and the number of the approval certificate. For example: This thesis is original, unpublished, independent work by the author, J. Doe. The experiments reported in Chapters 2 4 were covered by Ethics Certificate number 007, issued by the University of Calgary Conjoint Health Ethics Board for the project Project Title on December 15, 2016. iii

Preface For a traditional thesis with no ethics approval required, simply state something along the lines of: This thesis is original, unpublished, independent work by the author, Jane M. Doe. iv

Acknowledgments The acknowledgments are a place for you to thank/recognize academics or organizations that supported you (remember you cannot make changes once your thesis is submitted, so be thoughtful!) You should include this when you want to acknowledge people who may or may not be formally recognized in your thesis elsewhere. People usually mentioned in the acknowledgments include your supervisor and committee, grant support, helpful fellow students, lab mates, or family members. Since we re using L A TEX and the memoir package, we should thank Don Knuth, Leslie Lamport, and Peter Wilson. 1 1 These are the authors of Knuth (1986); Lamport (1986); Wilson (2016). v

To mom. vi

Table of Contents Abstract............................................. Preface.............................................. ii iii Acknowledgments..................................... v Dedication........................................... Table of Contents...................................... List of Tables.......................................... List of Figures......................................... vi vii viii ix 1 Introduction....................................... 1 1.1 Literature Review................................ 1 1.2 Contributions of the Thesis......................... 4 2 Important Results................................... 7 2.1 The first result.................................. 7 2.2 The second result................................ 8 Notes............................................... 10 Bibliography......................................... 12 Appendix............................................ 13 vii

List of Tables 1.1 Letters and numbers................................ 5 viii

List of Figures 2.1 Circles and arrows.................................. 8 ix

Chapter 1 Introduction Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Anonymous The text above is an epigraph. In this typeface, you can have text in boldface, italics, bold italics, slanted, and SMALL CAPS. 1.1 Literature Review Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem. Nullam nec mi et neque pharetra sollicitudin. Praesent 1

1. Introduction Nunc quis urna dictum turpis accumsan semper. 1 Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem. Nullam nec mi et neque pharetra sollicitudin. Praesent Nunc quis urna dictum turpis accumsan semper. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem. Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor. Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris. Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit amet ipsum. Nunc quis urna dictum turpis accumsan semper. 2

1. Introduction Definition 1. A group G is said to be abelian (or commutative) if for every a, b G, a b = b a. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem. Nullam nec mi et neque pharetra sollicitudin. Praesent Nunc quis urna dictum turpis accumsan semper. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem. Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor. Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris. Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit amet ipsum. Nunc quis urna dictum turpis accumsan semper. 3

1. Introduction 1.2 Contributions of the Thesis Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem. Nullam nec mi et neque pharetra sollicitudin. Praesent Nunc quis urna dictum turpis accumsan semper. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem. Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor. Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris. Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit amet ipsum. Nunc quis urna dictum turpis accumsan semper. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem. Nullam nec mi et neque pharetra sollicitudin. Praesent 4

1. Introduction A B 1 2 Table 1.1: Letters and numbers Nunc quis urna dictum turpis accumsan semper. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem. Nullam nec mi et neque pharetra sollicitudin. Praesent Nunc quis urna dictum turpis accumsan semper. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem. Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dig- 5

1. Introduction nissim nibh lectus placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor. Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris. Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit amet ipsum. Nunc quis urna dictum turpis accumsan semper. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem. Nullam nec mi et neque pharetra sollicitudin. Praesent Nunc quis urna dictum turpis accumsan semper. 6

Chapter 2 Important Results 2.1 The first result Theorem 2 (Residue Theorem). Let f be analytic in the region G except for the isolated singularities a 1, a 2,..., a m. If γ is a closed rectifiable curve in G which does not pass through any of the points a k and if γ 0 in G, then 1 m f = n(γ; a k ) Res(f ; a k ). 2πi γ k=1 Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem. Nullam nec mi et neque pharetra sollicitudin. Praesent 7

2. Important Results Figure 2.1: Circles and arrows Nunc quis urna dictum turpis accumsan semper. 1 2.2 The second result The first half Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem. Nullam nec mi et neque pharetra sollicitudin. Praesent Nunc quis urna dictum turpis accumsan semper. 1 1 Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem. Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor. Praesent Duis fringilla tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris. Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit amet ipsum. Nunc quis urna dictum turpis accumsan semper. 8

2. Important Results The second half Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem. Nullam nec mi et neque pharetra sollicitudin. Praesent Nunc quis urna dictum turpis accumsan semper. 9

Notes Chapter 1 Introduction 1. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem. Nullam nec mi et neque pharetra sollicitudin. Praesent Nunc quis urna dictum turpis accumsan semper. Chapter 2 Important Results 1. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem. Nullam nec mi et neque pharetra sollicitudin. Praesent 10

Notes Nunc quis urna dictum turpis accumsan semper. 11

Bibliography Knuth, Donald E. 1986. The TeXbook. Boston: Addison-Wesley. Lamport, Leslie. 1986. LaTeX: A Document Preparation System. Reading, Mass.: Addison-Wesley. Wilson, Peter. 2016. The memoir class for configurable typesetting. URL https://ctan.org/pkg/memoir?lang=en. 12

Appendix An appendix is a way to include important information that would otherwise clutter up your thesis. It should be included when there is additional relevant information that won t fit in the body of your thesis. Any Appendix must also be mentioned in the body of your thesis (e.g., For a full list of interview questions used, please see the Appendix ). If your thesis only has one appendix, it must be titled Appendix. If your thesis has more than one appendix, add alphabetized letters, starting with Appendix A. The following are examples of things you might include in appendices: 1. Copyright permissions with signatures removed 2. Additional details of methodology and/or data 3. Diagrams of equipment that you developed 4. Digital files and/or artwork digital models 5. Blank copies of questionnaires or surveys used in your research 13