1Define and work rigorously with real numbers, sequences, and series, determining convergence.

2Analyze continuous functions, understand differentiability, and apply Riemann integration.

3State and use core theorems such as Cauchy Criterion, Bolzano–Weierstrass, Intermediate Value, Extreme Value, Mean Value, and Fundamental Theorem of Calculus.

4Understand precise mathematical notions and theorems, and construct clear, logically valid proofs using standard methods.