MATH 101 · Year 1 · Semester 1 · 4 credits · Mathematics & Statistics

Calculus I

Mastering continuous change: the calculus engine behind interest forces, loss distributions, and financial risk models.

Season 1 · 8 episodes

The Century Ledger

When junior actuarial analyst Maya Lin discovers a billion-pound legacy annuity fund nearing regulatory insolvency due to corrupted discrete approximations, she must rebuild the entire valuation model from continuous first principles before the Prudential Regulation Authority shuts the firm down.

Protagonist · Maya Lin, a first-year quantitative actuarial analyst at Meridian Life and Longevity Re

Setting · Meridian Life headquarters, London; the legacy valuation division overseeing the troubled Century Fund

Stakes · A miscalculation of more than two percent will trigger a mandatory capital add-on of four hundred million pounds, bankrupting Meridian's annuity subsidiary and invalidating thousands of pensioner guarantees.

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Episodes

Season finale: Maya derives and numerically integrates Thiele's differential equation across the entire Century Fund cohort, delivering an unassailable closed-form continuous reserve valuation that passes the regulatory stress audit with ninety million pounds in surplus.

From the lecturer: Welcome to MATH 101. Calculus is the universal grammar of quantitative modeling, and in this course, we treat every limit, derivative, and integral as a living actuarial object. You are not merely manipulating symbols; you are measuring instantaneous rates of claim arrivals, calculating the present value of continuous cash flows, and integrating continuous probability density functions. To get the most out of these film lessons, never watch passively. Keep an unlined notebook and pen beside you. When I pose a guiding question or present an integral, pause the video and work the algebra yourself before watching the derivation unfold. While MATH 101 does not map to a single professional exam code, it forms the non-negotiable mathematical bedrock for SOA Exam P, CAS Exam MAS-I, and life contingencies in Exams FAM and ALTAM. Your mastery of improper integrals like the integral of e to the minus delta t dt, integration by parts, and Taylor series approximations will directly determine your speed and confidence in later actuarial exams and machine learning theory. Let us build your foundational calculus fluency with absolute rigour and intuitive clarity.

Cold open

At six in the morning on a rainy Tuesday, Maya's terminal flashes a critical alert. The Century Fund, holding forty-five thousand legacy whole-life contracts, shows an instantaneous solvency ratio of zero divided by zero because the valuation software attempted to step time forward by zero seconds.

preparing lecture…

Transcript

Evaluate two-sided and one-sided limits algebraically using standard limit laws and factorization.
Define continuity at a point and classify removable, jump, and essential discontinuities in piecewise actuarial models.
Derive the continuous compounding limit leading from nominal interest rates to the constant force of interest.
Apply the Intermediate Value Theorem (IVT) to establish the existence of internal rates of return and breakeven policy durations.