# Number Theory

A careful study of major topics in elementary number theory, including divisibility, factorization, prime numbers, perfect numbers, congruences, Diophantine equations and primitive roots. Meets the Critical Perspectives: Quantitative Reasoning requirement. Meets the Critical Learning: FRL requirement.

*Prerequisite:* Mathematics 129 or Mathematics 204 or 2 credits of college level calculus with consent of instructor.

Degree requirement — Critical Learning: FRL, Critical Perspectives: Q

1 unit — Erickson

## Previously Featured Offering

Number Theory serves as an in-depth introduction to mathematic discovery and practice. Students will dive into the number explorations of mathematicians before them and learn how number theory applies to daily life!

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!

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!

## Offerings

Term | Block | Title | Instructor | Location | Student Limit/Available | Updated |
---|---|---|---|---|---|---|

Fall 2022 | Block 3 | Number Theory | Molly Moran | Tutt Science Building 229 | 25 / 2 | 03/26/2023 |

Spring 2023 | Block 7 | Number Theory | Eddie Price | Tutt Science Building 101 | 25 / 0 | 03/26/2023 |

Fall 2023 | Block 2 | Number Theory | Stefan Erickson | TBA | 25 / 25 | 03/26/2023 |

Spring 2024 | Block 5 | Number Theory | Stefan Erickson | TBA | 25 / 25 | 03/26/2023 |

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Last updated: 03/26/2023