Elementary Number Theory: Primes, Congruences, and Secrets by William Stein. Springer Publishing, 2009.  ISBN 978-0387855240

Students do not need to purchase the textbook.  The author has made a free PDF available on his website https://wstein.org/ent/.

You will do some computations for this course using Sage, a powerful mathematics software. Please register at https://cocalc.com. Once registered, your instructor will have you added to the class in CoCalc. No programming experience is required for this course.

Divisibility, prime numbers, congruences, quadratic reciprocity, cryptography, introduction to Sage for number theoretic computations, Diophantine equations. 3 hours.

Upon successful completion of the course, each participant should be able to:

• Prove statements about divisibility of integers.
• Solve linear congruences and systems of linear congruences.
• Understand the connection between the ring of integers and the ring of integers modulo n. 
• Understand the basics of encryption schemes based on factoring large numbers. 
• Use quadratic reciprocity to solve quadratic congruences.
• Understand the basic of encryption schemes based on elliptic curves.
• Use Sage to perform number theoretic computations.