MODULAR ARITHMETIC

This class meets once a week for one hour each time. Tentative schedule: Tuesdays, 3:30 - 4:30 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 good 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 an excellent class for anyone interested in expanding their understanding of number theory. Participants interested in math competitions will find the class extremely helpful. Students in grades 6 and up are encouraged to sign-up.
• 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 Tuesday, August 25, 2020 to guarantee your spot in the class. 

I accept personal checks or electronic payments through Paypal or Zelle.

I offer a 20% discount for siblings for this class.