Vassar Moodle

Numbers started life as adjectives. Three apples, seven mortgages, fifteen bicycle tires. Then, one day, long long ago, they became nouns and number theory was born. For thousands of years people from every corner of the world have been fascinated by numbers and the many secrets that they keep. Our collective knowledge of the subject grows at an accelerating clip, only outpaced by an ever greater view of the breadth of our ignorance. In this course, we will survey the periphery of the vast, deep, and ancient theory of numbers. Along the way we will learn how to read, write, analyze, and construct rigorous mathematical proofs. Some topics on our agenda include: primes, unique factorization, Diophantine equations, modular arithmetic, quadratic reciprocity, algebraic numbers, and arithmetic functions. No experience with number theory or proof writing will be assumed.