• i. Floating Point: IEEE doubles, epsilons, catastrophic cancellation, stable formulas, Kahan summation and long double portability.
• ii. Big Integers and Fractions: avoiding big numbers, __int128 I/O, a base-$10^9$ big integer with long division, exact fractions, Stern–Brocot and Farey.
• iii. Root Finding and Integration: Newton (safeguarded, integer roots, doubling everywhere), all real polynomial roots, adaptive Simpson, Newton–Schulz.
• iv. Linear Programming: standard forms, duality and total unimodularity, two-phase simplex with Bland’s rule, Seidel’s 2D LP.