McClung, William

Nebraska Wesleyan University 

Math/CS Dept.

Lincoln, NE 68504-2796

mcclung@nebrwesleyan.edu



Exploring Numbers



Burton, in his text, Elementary Number Theory, states that "nowhere else in 

the mathematical disciplines is rigorous proof so often preceded by 

patient, plodding experiment." I am working on a one-semester number theory 

text, Exploring Numbers, in which Mathematica will transform "patient" into 

"exciting" and "plodding" into "thorough" and "far-reaching." It will 

provide an experimental testbed in which the students will, in a guided 

fashion, examine numeric evidence to "verify," disprove, and generate 

conjectures. (Perhaps one measure of the success of this approach is the 

number of entirely student-generated conjectures.) Proofs of theorems would 

be attempted only after such experiments.  After students become familiar 

with a few Mathematica number-theoretic primitives, problems of the form 

"prove or disprove" could be assigned with students expected to generate 

appropriate experiments on their own. (Due to Wolfram Research's on-line 

library, MathSource, and the power of Mathematica's programming language, 

it is not difficult to provide easy-to-use primitives beyond those built in 

to the program.) While the course described is for math majors, number 

theory provides a familiar domain to all, and it is anticipated that the 

experiments could be successfully performed by a much larger audience. Thus 

a variant of this course for liberal arts students, deemphasizing student 

construction of proofs, could easily be fashioned.





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