Carl Gauss once said that “Mathematics is the queen of the sciences and number theory is the queen of mathematics.” It is thus only appropriate that the mathematics department at CC uses our course MA251: Number Theory as an introduction to careful rigorous mathematics and proof. This opens exciting new vistas to the students who take the course and in the process learn that mathematics is not just more calculus.

The course concentrates on surprising and beautiful results about the integers . . . -2, -1, 0, 1, 2, 3, … . Euclid in ancient Greece first proved that each integer greater than 1 can be factored uniquely into primes, integers that cannot be further factored. Euclid also proved that there are infinitely many primes, which is only the beginning of the many profound questions about the primes (2, 3, 5, 7, 11, ...) that have still not been answered, despite the antiquity of the subject. For example, are there infinitely many Twin Primes, like 3 and 5, 5 and 7, 11 and 13, 17 and 19 and so?

Interestingly, many modern methods of cryptography are constructed using the methods learned in MA251. Number theory is not only elegant and beautiful, but applicable too!