CS 310 · Year 3 · Semester 1 · 3 credits · Computer Science

Numerical Methods & Scientific Computing

Bridging mathematical rigour and machine precision to build robust, high-performance actuarial algorithms.

Season 1 · 8 episodes

The Architecture of Precision: Building Titan

When a catastrophic numerical bug threatens to bankrupt Apex Mutual during a high-stakes Solvency II audit, lead computational actuary Julian Vance must rebuild the firm's multi-billion-dollar valuation and capital engine from foundational scientific computing principles.

Protagonist · Dr. Julian Vance, Lead Computational Actuary at Apex Mutual Reinsurance, caught between legacy black-box spreadsheets and aggressive regulatory solvency deadlines.

Setting · Apex Mutual's Quantitative Analytics Floor in London and the European Solvency Supervisory Board review chambers in Zurich.

Stakes · A failure in numerical stability or a timeout during the supervisory stress tests will trigger an automatic 35 percent regulatory capital surcharge, destroying Apex Mutual's credit rating and voiding twelve billion dollars in active reinsurance treaties.

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Episodes

Season finale: Julian deploys the fully refactored, stable, and vectorised Titan engine minutes before the regulatory deadline, executing a nested stochastic valuation of ten million policy records in two minutes with zero floating-point drift and provable error bounds.

From the lecturer: Welcome to CS 310. Actuarial theory often assumes infinite precision and closed-form tractability, but production pricing models, Solvency II internal capital models, and IFRS 17 liability engines run on silicon. In this course, you will learn to build scientific software that is mathematically sound, numerically stable, and computationally fast. To get the most from these films, keep an interactive Python/C++ environment alongside your physical derivation notebook. As we introduce an algorithm, pause the film to trace the matrix dimensions and error propagation terms by hand before looking at the implementation. While this course does not map to a single preliminary exam, the computational techniques you master here directly power the practical modeling workflows required in advanced exams (such as SOA FAM/ASTAM/ALTAM and CAS Exam 7/8/9) and quantitative enterprise risk management. Track every floating-point edge case, measure wall-clock execution times against theoretical asymptotic complexities, and insist on error-controlled numerical convergence at every step.

Cold open

At four in the morning, Apex Mutual's production reserving engine halts with a floating-point division by zero error, reporting a negative variance on a four-billion-dollar casualty portfolio.

preparing lecture…

Transcript

At four in the morning, Apex Mutual's production reserving engine halts with a floating-point division by zero error, reporting a negative variance on a four-billion-dollar casualty portfolio.

Explain the IEEE 754 standard for double-precision floating-point numbers and define machine epsilon.
Derive the relative condition number of a mathematical problem and distinguish ill-conditioned problems from unstable algorithms.
Diagnose catastrophic cancellation in actuarial calculations and rewrite expressions algebraically to preserve precision.
Select optimal step sizes in numerical differentiation to balance truncation error and floating-point roundoff error.