Introduction to Number Theory

Number theory is the study of the integers themselves — why primes behave the way they do, when congruences have solutions, and what structure hides inside seemingly simple questions about divisibility. You'll spend the semester proving things: weekly homework and a quiz push you through induction, the Euclidean algorithm, Fermat/Euler/Wilson, multiplicative functions, primitive roots, and quadratic reciprocity, with a midterm and final testing whether you can actually wield them. It's a proof-heavy bridge between the calculus-style math of your first two years and the algebra/cryptography courses ahead, and the techniques here are exactly what RSA and modern cryptosystems run on.