Math Competition – Number Theory

This class will introduce students to number theory. Number theory is the study of integers and the relationships between them. It is a very popular subject in competitive mathematics (AMC 10/12, Mu Alpha Theta, etc.) as it allows many arithmetic problems to be solved much more quickly. We will begin with fundamental concepts like prime numbers, divisors, and factorizations, and then move onto more advanced problems dealing with base numbers, modular arithmetic, and linear congruences. In order to accurately represent a competition environment, every lesson will be heavily focused on challenging problems for the corresponding topics, and at least two such problems will be assigned for homework. Solutions will be provided shortly before the following class so that students have time to solve the problems on their own. A pre-test will be administered to gauge how prepared students are for the class.

Curriculum

Lesson 1: Integers – The Basics
Lesson 2: Primes and Composites
Lesson 3: Multiples and Divisors
Lesson 4: Prime Factorization
Lesson 5: Divisor Problems
Lesson 6: Special Numbers
Lesson 7: Algebra with Integers
Lesson 8: Base Numbers
Lesson 9: Base Number Arithmetic
Lesson 10: Units Digits
Lesson 11: Decimals and Fractions
Lesson 12: Intro to Modular Arithmetic
Lesson 13: Divisibility Rules
Lesson 14: Linear Congruences
Lesson 15: Number Sense

Teacher: Mr. Costa (see teacher’sBIO)

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