First-Year Seminar: Number Theory

Number theory is the study of the most basic mathematical objects: the natural numbers (1, 2, 3, etc.). It begins by investigating simple patterns: for instance, which numbers can be written as sums of two squares? Do the primes go on forever? How can we be sure? The patterns and structures that emerge from studying the properties of numbers are so elegant, complex, and important that number theory has been called "the Queen of Mathematics." Once studied only for its intrinsic beauty, number theory has practical applications in cryptography and computer science. Topics include the Euclidean algorithm, modular arithmetic, Fermat's and Euler's Theorems, public-key cryptography, quadratic reciprocity. MATH 223 has a focus on learning to understand and write mathematical proofs; it can serve as valuable preparation for MATH 305.

Units: 1

Max Enrollment: 15

Prerequisites: Open to First-Years only.

Instructor: Lange

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Other Categories: FYS - First Year Seminar

Typical Periods Offered: Fall

Semesters Offered this Academic Year: Not Offered