MA251 - 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: Any two of: Mathematics 117, Mathematics 217, Mathematics 120, Mathematics 125, Mathematics 126. Mathematics 129 or equivalent.
Degree requirement — Critical Learning: FRL, Critical Perspectives: Q
1 unit — Erickson
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Explore the number theory of the positive integers that have been studied since the time of the ancient Greeks and before. Investigate unsolved problems and conjectures that remain unproven to this day about them. Some of the deepest mathematical problems ever thought about by humans belong to this subject!
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 |
|---|---|---|---|---|---|---|
| Spring 2025 | Block 5 | Number Theory | Stefan Erickson | Tutt Science Building 223 | 25 / 6 | 12/23/2024 |
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