Number Theory and Cryptology for Middle Level Teachers
This course is designed and offered as part of the Math in the Middle Institute Partnership at the University of
Nebraska – Lincoln. Course developers are Kristin Pfabe, Professor of Mathematics at Nebraska Wesleyan
University, and Michelle Reeb Homp, Research Assistant Professor, Center for Science, Mathematics and Computer
Education, UNL.
AT A GLANCE
Target Audience: This course is designed for teachers of middle level mathematics. Comfort
with functions, algebraic representations and basic logic is strongly recommended. In the Math
in the Middle program, this course is preceded by Mathematics as a Second Language;
Functions, Algebra and Geometry; Experimentation, Conjecture and Reasoning; and Discrete
Mathematics for Middle Level Teachers.
Graduate Credit Hours: 3
Usual Delivery Format: This course follows the on-site, one-week, summer course design (see
Instructional Approach in the Descriptions of all Math in the Middle Courses folder) with class
meeting 8:00 – 5:00 M – F. The course can easily be adapted to other schedules with 40 hours of
contact time.
Texts/Materials:
1. Course notebook containing handouts and problems (see Course Notebook section )
2. Dunham, W. (1994). The mathematical universe. New York: Wiley & Sons.
Chapters A, F and P are assigned as readings.
3. NOVA movies: N is a Number, The Proof, and Decoding Nazi Secrets. Movies can be
ordered at http://www.publicvideostore.org/ (search by Program).
Description: This course focuses on basic number theory results which are needed to understand
the number theoretic RSA cryptography algorithm (an encryption algorithm which is in use today
to secure information sent via the internet). As the number theory results are developed,
connections to middle level curricula are emphasized and proofs are carefully selected so that
those which are included in the course are particularly relevant and accessible to middle level
teachers. This portion of the course promotes a deep understanding of the integers and their
properties in connection with the operations of multiplication and division. Elementary ciphers
(methods for encoding and decoding) are included to introduce the nature of cryptology in
preparation for understanding the RSA method. The cryptology related activities are readily
adaptable as enrichment activities for middle level students. The connection of number theory to
the RSA encryption algorithm allows the participants to see and understand a very relevant, realworld application of mathematics.
Course Goals: The goals of the course are to introduce the teacher participants to: (1) the basic
results of elementary number theory, (2) the rigor of mathematical definitions, reasoning and
proof, (3) the application of number theory to cryptology, (4) and the connections between
Number Theory and the middle school curriculum.
Copyright 2007. Number Theory and Cryptology for Middle Level Teachers. Developed by the Math in the Middle Institute
Partnership, University of Nebraska, Lincoln.
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Abbreviated Content Outline:
Day Topics
1
Course Introduction
Section 1: Integers and Divisibility
Section 2: Primes and Factorization
2
Introduction to Cryptology (substitution and transposition ciphers)
Section 3: Linear Diophantine Equations
3
Section 4: Congruence
Section 5: Linear Congruence Equations
4
Section 6: Fermat’s and Wilson’s Theorems
Section 7: Euler Phi-Function
5
Other Number Bases
RSA Public Key Cryptography
Instructional Style: The course is designed in an interactive-lecture style (similar to a Socratic
method) with problem sessions, examples and activities designed for cooperative groups
distributed consistently throughout.
References:
1. Dudley, U. (1978). Elementary Number Theory (2nd ed). New York: W. H. Freeman and
Company.
2. Walker, Judy (University of Nebraska – Lincoln), The Joy of Numbers
Acknowledgements:
This course has been significantly influenced by
 Professor Ron Rosier, who, using a grant from SONY, created a course entitled Joy of
Numbers at Georgetown University
and by
 Professor Judy Walker, who, using Rosier's materials, developed a
Joy of Numbers course at UNL, developed the cryptology content for All Girls/All Math at
UNL, and taught Number Theory for Elementary and Middle Level Teachers as part of an
NSF grant
Copyright 2007. Number Theory and Cryptology for Middle Level Teachers. Developed by the Math in the Middle Institute
Partnership, University of Nebraska, Lincoln.
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