Number Theory

Course Description

An examination of fundamental concepts of numbers, including divisibility, congruencies, the distribution of Primes, Pythagorean triples, the Euclidean Algorithm, the Fundamental Theorem of Arithmetic, Diophantine equations, and Goldbach’s conjecture. Emphasizes active student involvement in posing and testing conjectures, formulating counter examples, logical arguments and proofs.

Learning Outcomes

  • Describe a rationale and a set of strategies for the activity of problem-generation. Students will compare and contrast the framing of questions; e.g., those that attempt to get at the internal vs.; those that analyze the external character of the problem; those that require an exact vs. an approximate answer; those that make use of a pseudo-historical vs. metaphorical context.
  • Discuss the processes of inquiry; including how to get started, the processes of specializing and generalizing, the elements of justification.
  • Discuss the roles of affect in mathematical problem-solving.
  • Discuss divisibility properties of integers, the greatest common divisor, the least common multiple, and the Fundamental Theorem of Arithmetic.
  • Discuss prime numbers, gaps between primes, the twin prime conjecture, Goldbach’s conjecture.
  • Describe properties of congruencies (a is congruent to b modulo n) residue systems and examples (odometers, clocks).
  • Investigate Pythagorean triples and Diophantine equations.
  • Discuss the distinctions between rational vs. irrational number, geometrically and algebraically.
  • Demonstrate knowledge of the properties of the real number system and of its subsets

Prerequisites

Why Choose National University?

We’re proud to be a veteran-founded, San Diego-based nonprofit. Since 1971, our mission has been to provide accessible, achievable higher education to adult learners. Today, we educate students from across the U.S. and around the globe, with over 150,000 alumni worldwide.

Four-Week Classes

Focus on one subject at a time — one month at a time — and finish your degree faster.

100+ Degree Programs

Choose from associate, bachelor’s, and master’s degrees, plus credentials and certificates.

On Campus or Online

Study when and where it’s convenient for you with evening, weekend, and 100% online classes.

Year-Round Enrollment

Apply or transfer any time. Classes start monthly, and applications are accepted year round.

20+ Campus Locations

Attend class onsite at one of over 20 campus locations across California or in Nevada.

Military Friendly

As a Yellow Ribbon school, we offer tuition discounts to servicemembers and dependents.

College of Letters and Sciences

“Our faculty are established scholars and creators in their own fields. They are dedicated to making your entry into their disciplines a successful one, preparing you for your career as well as graduate study.”
College of Letters and Sciences
Rico M.
Class of 2014, Military Veteran