MODULAR ARITHMETIC

The class meets twice a week for 1 hour each time.

Congruences and their properties
Residue classes
Exponentiation: Fermat's Little Theorem and Euler's Theorem
Applications: Wilson's Theorem, diophantine equations, Gauss's method for determining the date of Easter, divisibility rules
Linear congruences and modular inverses
Systems of linear congruences and the Chinese Remainder Theorem
Applications to cryptography: knapsack and exponential ciphers (if time permits)

Instructor's notes (no textbooks are required)
Prerequisites: strong algebra 1 background and a solid understanding of basic number theory (divisibility and properties, prime numbers and prime factorization, divisors and multiples, gcd's and lcm's, etc)

Supplemental reading material:

Dmitri Fomin, Sergey Genkin, Ilia Itenberg, Mathematical Circles (Russian Experience), chapters 3 and 10

This is a highly recommended class for anyone interested in expanding their understanding of number theory. Students aiming to participate in math competitions will find the class extremely helpful.
Students in grades 7 and up are encouraged to sign-up. Younger students require advance instructor approval. The class is geared towards beginners or students with little experience of modular arithmetic.
Space is limited, but a minimum number of participants is required to run the class. In the event the class is canceled due to low enrollment, your payment will be refunded in full within 24 hours.

Please contact me for payment information.