TITLE GOES HERE
[ If your title is more than one line, be sure to use single spacing between lines ]
By
YOUR NAME GOES HERE
A SENIOR RESEARCH PAPER PRESENTED TO THE DEPARTMENT OF MATHEMATICS
AND COMPUTER SCIENCE OF STETSON UNIVERSITY IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF BACHELOR OF SCIENCE
STETSON UNIVERSITY
YEAR OF SUBMISSION GOES HERE
ACKNOWLEDGMENTS
[ Put your acknowledgments here. Acknowledgments should be written in complete sentences. ]
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TABLE OF CONTENTS
ACKNOWLEDGEMENTS ----------------------------------------------------------------------------
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LIST OF TABLES ---------------------------------------------------------------------------------------
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LIST OF FIGURES -------------------------------------------------------------------------------------
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ABSTRACT ----------------------------------------------------------------------------------------------
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CHAPTERS
1. CHAPTER TITLE ---------------------------------------------------------------------------------1.1. Section Title ----------------------------------------------------------------------------------1.1.1. Subsection Title --------------------------------------------------------------------1.1.2. Subsection Title --------------------------------------------------------------------1.2. Section Title ----------------------------------------------------------------------------------1.2.1. Subsection Title --------------------------------------------------------------------1.2.2. Subsection Title ---------------------------------------------------------------------
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2. CHAPTER TITLE ---------------------------------------------------------------------------------2.1. Section Title ----------------------------------------------------------------------------------2.1.1. Subsection Title --------------------------------------------------------------------2.1.2. Subsection Title --------------------------------------------------------------------2.2. Section Title ----------------------------------------------------------------------------------2.3. Section Title -----------------------------------------------------------------------------------
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APPENDIX ----------------------------------------------------------------------------------------------
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REFERENCES -----------------------------------------------------------------------------------------
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BIOGRAPHICAL SKETCH -------------------------------------------------------------------------
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LIST OF TABLES
TABLE
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2.
3.
4.
5.
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LIST OF FIGURES
FIGURE
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Figure Title -----------------------------------------------------------------------------------------Figure Title -----------------------------------------------------------------------------------------Figure Title -----------------------------------------------------------------------------------------Figure Title -----------------------------------------------------------------------------------------Figure Title ------------------------------------------------------------------------------------------
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ABSTRACT
TITLE OF THE WORK, CENTERED, SINGLE SPACED,
IN ALL CAPITAL LETTERS, EXACTLY AS ON TITLE PAGE
By
Your Name as it appears on the Title Page
Month and year of graduation
(NOT month the work is submitted)
Advisors: Name [Names of other advisors if you have more than one, separated by commas]
Department: Mathematics and Computer Science
The double-spaced text of the abstract begins here. Note that the headings above should be single
spaced. The abstract should be a concise summary of the content of the paper, mentioning major
results if possible. It should be fully understandable without reference to the text. It should not
contain parenthetical or bracketed references. Mathematical notation and symbols should be used
sparingly, if at all. Abstracts should not exceed 150 words.
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CHAPTER 1
CHAPTER TITLE
Introductory text to introduce the chapter can go here. Be sure that all content is double-spaced.
Here is an example of how to include a reference within a chapter’s content: It was shown in [3]
that DES is not a group.
1.1. SECTION TITLE
You can have some text here too, introducing the section. If you don’t have subsections, then all
the content of the section will be here.
1.1.1. SUBSECTION TITLE
Introductory remarks goes here. Below is an example of how to present a theorem and its proof.
Theorem 1. There are an infinite number of primes.
Proof. Suppose there were only a finite number of primes p1, p2, . . . pn. Consider the number N
= p1p2 . . . pn+1. Note that N has remainder 1 when divided by any of p1, p2, . . . pn, so N is not
divisible by any of these primes. But this contradicts Theorem 5.2, which states that every
number has a unique prime factorization. 
[The square is an “end of proof” symbol. Feel free to be creative, but be consistent.]
Below is a more comprehensive example with mathematical notation
Theorem 2. An (n  n) matrix A is diagonalizable if and only if A has n linearly independent
vectors. In fact, A  PDP 1 , with D a diagonal matrix, if and only if the columns of P are n
linearly independent eigenvectors of A. In this case, the diagonal entries of D are eigenvalues of A
that correspond, respectively, to the eigenvectors in P.
Proof. First, observe that if P is an (n  n) matrix with columns v 1 , v 2 ,..., v n and if D is any
diagonal matrix with diagonal entries  1 ,  2 ,...,  n , then
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AP  Av 1 v 2 . . . v n 
  Av 1
Av 2 . . . Av n 
(1)
while
 1 0 . . . 0 
0  ... 0 
2


 .
.
.
. 
PD  P 

.
.
. 
 .
 .
.
.
. 


0 . . .  n 
 0
(2)
Suppose now that A is diagonalizable and A  PDP 1 . Then right-multiplying this relation by P,
we have AP  PD . In this case, (1) and (2) imply that
 Av 1
Av 2 . . . Av n    1 v 1  2 v 2 . . .  n v n 
(3)
Equating columns, we find that
Av 1   1 v 1 , Av 2   2 v 2 , . . ., Av n   n v n
(4)
Since P is nonsingular, its columns v 1 , v 2 ,..., v n must be linearly independent. Also, since these
columns are nonzero, (4) shows that  1 ,  2 ,...,  n are eigenvalues and v 1 , v 2 ,..., v n are
corresponding eigenvectors. This argument proves the “only if” parts of the first and second
statements, along with the third statement, of the theorem.
Finally, given any n eigenvectors v 1 , v 2 ,..., v n , use them to construct the columns of P and use
the corresponding eigenvalues  1 ,  2 ,...,  n to construct the matrix D. By (1) – (3), AP  PD .
This is true without any condition on the eigenvectors. If, in fact, the eigenvectors are linearly
independent, then P is invertible (by the Invertible Matrix Theorem), and AP  PD implies that
A  PDP 1 . This completes the proof. 
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Lemmas, propositions and conjectures should follow the same numbering (1, 2, 3 etc.) and font
style as theorems. Also, note the use of equation numbers in the proof above. Be sure to number
your equations either globally [i.e. (1), (2), etc.] or by Section [(1.2.1), (1.2.2) etc.]
1.1.2.
SUBSECTION TITLE
More stuff goes in this subsection presumably. Here is an example of a Figure in some text.
We call a collection of triangles 2-touching if every vertex of a triangle is the vertex of exactly 2
triangles. See Figure 1 for an example of a 2-touching collection.
Figure 1. A collection of 2-touching triangles
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APPENDIX A.
TITLE OF APPENDIX
10
APPENDIX B.
TITLE OF APPENDIX
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REFERENCES
[1] G. B. Dantzig, Linear Programming and Extensions. Princeton University Press, Princeton,
NJ, 1963. [printed books]
[2] E. Engelhardt, Some Problems on Paths in Graphs. Ph.D. Thesis, University of Washington,
Seattle, WA, 1988. [non-published articles or preprints]
[3] V. Klee and P. Kleindschmidt, “The d-step Conjecture and its Relatives.” Mathematics of
Operations Research, 12 (4), pp. 718-755, 1987. [published articles]
[4] J. Lincoln, Personal Communication. October 29, 2002. [conversations or e-mail]
.
.
.
[16] M. Richtel, “Backlash: How To Take Back Our Analog Brains.” New York Times on the
Web, June 10, 2001, July 21, 2001.
http://college1.nytimes.com/guests/articles/2001/06/10/851143.xml.
[online magazine column or newspaper]
[17] Encyclopedia of Integer Sequences, Ed. Neil Sloane. August 4, 2001.
http://www.research.att.com/~njas/sequences/index.html. [scholarly database]
.
.
.
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BIOGRAPHICAL SKETCH
[ Put your text here. It should be double-spaced and should not exceed one page. ]
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