Advanced Calculus I

This is where calculus gets rebuilt from the ground up: instead of computing derivatives and integrals, you prove why they exist, starting from the least upper bound property of the reals and working through epsilon-delta arguments, Cauchy sequences, and uniform convergence. Expect weekly problem sets out of Abbott or Rudin where most of your time goes into writing careful proofs rather than crunching numbers, plus quizzes and two midterms that test whether you can actually construct an argument under time pressure. It's the gateway to real mathematics at Bilkent, and the foundations you build here, completeness, continuity, convergence, are what every later course in analysis, topology, and probability quietly assumes you know cold.