MODULAR ARITHMETIC

The class meets twice a week for 1 hour each time. The meetings will take place every Tuesday and Thursday between July 5 and July 28, 2022, for a total of 8 sessions. We meet online, 5:30-6:30 pm Pacific Standard Time. All sessions are recorded and available for playback and download immediately after class. 

• 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:

• Mathew Crawford: Introduction to Number Theory, chapters 12-14

                 https://artofproblemsolving.com/store/item/intro-number-theory 

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

                 https://www.amazon.com/Mathematical-Circles-Russian-Experience-World/dp/0821804308 

• 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 consider signing-up on or before Saturday, June 25 to guarantee your spot in the class. 

Please contact me for payment information.