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.