FPMI Courses

Published

18 October 2026

Published courses

Foundations of Probability and Measure Theory

Classic Informatics Mathematics NES CSE-sp

The β€œtypewriter sequence”: a bump of width \(2^{-k}\) and height \(2^k\) sweeps across \([0,1]\). The sequence converges to zero in measure but diverges at every point, so it does not converge almost everywhere. Nor does it converge in \(L^1\), since \(\|f_n\|_1 = 1\) while \(\|0\|_1 = 0\). The subsequence highlighted in red, however, does converge almost everywhere.

Part I. Foundations of Probability

Part II. Measure Theory

Probability Theory

Classic NCS/CSE Informatics CSE-sp Mathematics NES AMI base

The law of the iterated logarithm, the central limit theorem, and the law of large numbers on a single chart: 100 simulated trajectories of \[ \frac{1}{\sqrt{2n \ln \ln n}}S_n. \] Almost surely the limit superior of each is \(1\) and the limit inferior is \(-1\). The histogram on the left shows that, for each fixed \(n\), the distribution itself is well approximated by a normal distribution and shrinks toward zero.

Part 1

Part 2

Mathematical Statistics

Classic NCS/CSE Informatics CSE-sp Mathematics NES AMI base

The geometry of testing a composite hypothesis in a linear Gaussian model: the observation vector, its least-squares estimate, and its constrained (conditional) version β€” as points and lines in space

Part I

Part II

Random Processes

Classic NCS/CSE Informatics Mathematics NES

Brownian motion: the LΓ©vy-Ciesielski construction. Schauder polygons with random coefficients converge to Brownian paths

Curriculum

A reference map of courses by semester for the programs β€œApplied Mathematics and Informatics” (Classic) and β€œInformatics and Computer Engineering: Natural and Computer Sciences” (NCS/CSE). It does not include foreign languages, physical education, history and philosophy courses, departmental courses or research work. Courses already published on the site are shown in bold. The set of courses and their placement may vary by year of admission and by program; the site does not replace the official curriculum.

🟒 β€” full course published Β· 🟑 β€” course passport published Β· βšͺ β€” course not yet represented in the catalog.

Semester I

Semester II

Semester III

Semester IV

Semester V

Semester VI

For some other programs (MMTU, AI360), individual courses of the probability block may be scheduled in a different semester than shown here β€” see the full breakdown in _internal/fpmi-curriculum-report.md.