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A SAMPLE RESEARCH PAPER/THESIS/DISSERTATION ON ASPECTS OF ELEMENTARY LINEARY ALGEBRA

by James Smith B.S., Southern Illinois University, 2010

A Research Paper/Thesis/Dissertation Submitted in Partial Fulfillment of the Requirements for the Master of Science Degree

Department of Mathematics in the Graduate School Southern Illinois University Carbondale July, 2006

(Please replace Name and Year with your information and delete all instructions) Copyright by NAME, YEAR All Rights Reserved **(This page is optional)**

RESEARCH PAPER/THESIS/DISSERTATION APPROVAL

TITLE (in all caps)

By (Author)

A Thesis/Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of (Degree) in the field of (Major)

Approved by: (Name of thesis/dissertation chair), Chair (Name of committee member 1) (Name of committee member 2) (Name of committee member 3) (Name of committee member 4)

Graduate School Southern Illinois University Carbondale (Date of Approval)

AN ABSTRACT OF THE DISSERTATION OF

NAME OF STUDENT, for the Doctor of Philosophy degree in MAJOR FIELD, presented on DATE OF DEFENSE, at Southern Illinois University Carbondale. (Do not use abbreviations.) TITLE: A SAMPLE RESEARCH PAPER ON ASPECTS OF ELEMENTARY LINEAR ALGEBRA MAJOR PROFESSOR: Dr. J. Jones (Begin the abstract here, typewritten and double-spaced. A thesis abstract should consist of 350 words or less including the heading. A page and one-half is approximately 350 words.)

iii

DEDICATION (NO REQUIRED FOR RESEARCH PAPER)

(The dedication, as the name suggests is a personal dedication of one’s work. The section is OPTIONAL and should be double-spaced if included in the thesis/dissertation.)

iv

ACKNOWLEDGMENTS
(NOT REQUIRED IN RESEARCH PAPER)

I would like to thank Dr. Jones for his invaluable assistance and insights leading to the writing of this paper. My sincere thanks also goes to the seventeen members of my graduate committee for their patience and understanding during the nine years of effort that went into the production of this paper. A special thanks also to Howard Anton [1], from whose book many of the examples used in this sample research paper have been quoted. Another special thanks to Prof. Ronald Grimmer who provided the previous thesis template upon which much of this is based and for help with graphics packages.

v

PREFACE
(DO NOT USE IN RESEARCH PAPER)

A preface or foreword may contain the author’s statement of the purpose of the study or special notes to the reader. This section is OPTIONAL and should be double-spaced if used in the thesis/dissertation.

vi

TABLE OF CONTENTS

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Systems of Linear Equations and Matrices . . . . . . . . . . . . . . . . . 1.1 Introductions to Systems of Linear Equations . . . . . . . . . . . . 1.2 Gaussian Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Further Results on Systems of Equations . . . . . . . . . . . . . . . 1.3.1 Some Important Theorems . . . . . . . . . . . . . . . . . . .

iii iv v vi viii ix 1 2 2 4 5 6 7 7 8 8 8 11 16 16 19

2 Determinants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 The Determinant Function . . . . . . . . . . . . . . . . . . . . . . . 2.2 Evaluating Determinants by Row Reduction . . . . . . . . . . . . . 2.2.1 Some Final Conclusions . . . . . . . . . . . . . . . . . . . .

2.3...
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