This course is designed as an introduction to Number Theory, with a focus on prime numbers and cryptography methods that rely on large prime numbers. It covers a range of ideas from Number Theory, starting with the division algorithm and modular arithmetic. Further topics include Diophantine Equations, the Fundamental Theorem of Arithmetic, the Chinese Remainder Theorem, Wilson’s Theorem, Fermat’s Little Theorem, the Euler Phi-function, and Euler’s Theorem and cryptography methods and their applications. Among the cryptography methods covered in the course, special focus will be placed on the RSA Algorithm which is wildly used in many computer systems.
This course includes a variety of mediums for learning, including on-campus class lectures/discussions, individual assignments, small group discussions, and group projects and presentations.
Upon successful completion of the course, you will be able to:
• Understand the concepts of divisibility, congruence, prime-factorization, and the prime number theorem
• Formulate and prove conjectures about numeric patterns
• Construct mathematical proofs of statements and find counterexamples to false statements in Number Theory
• Understand the distribution of prime numbers among integers
• Understand the techniques of Number Theory used in cryptography methods that rely on large prime numbers
The course will provide you with a solid foundation for higher-level mathematics. At the end of the course, you will know what it’s like to think and work like a mathematician.
A solid background in algebra is needed. No Calculus experience is required.
Online sections of Pre-College courses are offered in one of the following modalities: Asynchronous, Mostly asynchronous, or Blended. Please review full information regarding the experience here.