email: rbeveridge "at symbol" clatsopcc.edu
Education:
University of Maine, Orono, Maine
M.A. in Mathematics, May 2004
University of Maine, Orono, Maine
B.A. in Mathematics, May 2002
Oklahoma City University, Oklahoma City, Ok.
M. Ed. in Gifted and Talented Education, August 1992
University of Virginia, Charlottesville, Va.
B.A. in French Language and Literature, May 1987
Minor in Mathematics
Publication and other writing
"Friday the 13th and the Mathematics of the Gregorian Calendar."
Mathematical Connections , 2003, published by Augusta State University, Augusta, Georgia.
Mathematics, Communication and Secrecy
e : A Conceptually Defined Number
The Disquisitiones Arithmeticae of Carl Friedrich Gauss and the group Z(p)*
Teaching:
Clatsop Community College, Astoria, Oregon
Mathematics Instructor 2004-present
Courses:
MTH 060 Basic Mathematics II
MTH 070 Beginning Algebra
MTH 095 Intermediate Algebra
MTH 111 College Algebra
MTH 112 Trigonometry
MTH 116 Pre-Calculus
University of Maine, Orono, Maine
Teaching Assistant 2003-04
Courses:
MAT 108 Mathematics for Elementary Teachers
MAT 126 Calculus I
MAT 400 Mathematics for High School Teachers: An Advanced Perspective (TA)
University of Maine, Orono, Maine
NSF Teaching Fellow, Old Town and Orono, Maine, 2002- 03
University of Maine, Orono, Maine
Adjunct Instructor, 2000-2002
Courses:
MAT 101 The Nature and Language of Mathematics
MAT 111 College Algebra
Maine Central Institute, Pittsfield, Maine
Mathematics Teacher, 1999-2000
Courses:
Pre-Calculus with Trigonometry, Algebra I, II, Geometry
Ellsworth High School, Ellsworth, Maine
Mathematics Teacher 1998-99
Courses:
C++ Programming, Algebra II (Honors), Geometry (Honors), Algebra I, Pre-Algebra
Hopi Jr/Sr High School, Hopi Indian Reservation, Polacca, Arizona
Mathematics Teacher 1995-1997
Head of Mathematics Department 1997
Director of Gifted Program 1995, 1997
Courses:
Geometry, Algebra I, Pre-Algebra, Basic Math, 8th grade math, 7th grade math
The Desisto School, Stockbridge, Massachusetts
Mathematics Teacher 1994-95Courses: Algebra II, Geometry, Algebra I, Pre-Algebra, Financial Markets
Huntington Learning Center, Yorktown Heights, New York.
Mathematics Teacher 1993-94, 1998
Math Director 1995
Areas of Research Interest:
Analysis, Algebra, Number Theory and Cryptography
My interests in pure mathematics are not focused on a particular area of research. I have many different interests and work on them as time and opportunity allow. I tend to write historically motivated general interest articles that might appeal to non-mathematicians, mathematics teachers and students or mathematicians from another area of specialization.
In the spring of 2003, I researched ideas related to the application of analysis and topology to fractals using the work of Michael Barnsley and Gerald Edgar and presented this research in a series of two one-hour lectures.
I have also researched the distribution of complex primes and the properties of the Gaussian integers as a Euclidean Ring. Using Gauss' work in Disquisitiones Arithmeticae , I wrote a paper tracing the arguments Gauss used in proving that what is today known as the multiplicative group Z( p )* is cyclic for all primes p. In addition, I completed a paper that is a historical consideration of the application of the ideas of Gauss and Euler by Whitfield Diffie and Martin Hellman to create the fundamentals of public-key cryptography.
I became interested in cryptography as a result of reading the first section of Prof. Neal Koblitz's book A Course in Number Theory and Cryptography . I researched the RSA Cryptosystem and Diffie-Hellman key exchange and the algebraic number theory that underlies these processes. I later used this research as a basis for a unit on modular arithmetic that I taught in the MAT 101 course at the University of Maine. A second unit for MAT 101 was based on number systems in bases other than 10. The students calculated in other bases using standard algorithms and considered the creation of fractions in base 12 (duodecimals). This activity was subsequently adapted by Professor John Donovan for a week of lessons for his MAT 400 course for teachers in which I participated as a teaching assistant.
