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)