Евклидовы пространства
2026LectureTaras Panov
Евклидовы и эрмитовы пространства, скалярное произведение, неравенство Коши–Буняковского и неравенство треугольника, ортогональные системы векторов.
1
190
Search results for “линейная регрессия”
47 results
Algebra 1. Lecture 1
2026LectureАртём Авилов
What algebra studies — algebraic structures. Groups (definition, examples, additive notation, uniqueness of the identity and of inverses), rings (variants of the axioms, rings with and without identity), fields and division rings, vector spaces and modules, algebras over a field. The symmetric group — permutations, non-commutativity, two-row notation, cycles and transpositions, decomposition into transpositions, disjoint permutations commute, decomposition into disjoint cycles and its uniqueness, powers, inversions, parity and the sign of a permutation, multiplying by a transposition changes the sign.
0
310
Topology 2. Lecture 1
2026LectureФёдор Вылегжанин
Why homology is needed — the fundamental group as a functor, homotopy groups, bordism and its combinatorial approximation; chain complexes and their homology; abstract simplicial complexes, geometric realisation and triangulations; the complex of simplicial chains, the proof of , the simplicial homology of a segment, of two points and of the boundary of a triangle; reduced homology.
1
470
Topology 2. Lecture 2
2026LectureФёдор Вылегжанин
Where simplicial homology shows up in real life — topological data analysis. The union of balls around a point cloud, persistence modules and their decomposition into a sum of interval modules over a field (the structure theorem and the algorithm), the barcode; the Vietoris–Rips and Čech complexes; the stability theorem for barcodes, the Hausdorff, Gromov–Hausdorff and Wasserstein distances; open covers and their nerves, Leray covers and the nerve theorem, the category of covers, paracompactness, Lebesgue covering dimension, Čech homology and cohomology.
1
520
Vector calculus. Line integrals of the first kind
2026Problem sheetSergey
Integration with respect to arc length: parametrising a curve, the length element , arc length, curves in polar coordinates, the mass and centre of mass of a wire, symmetry instead of computation.
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530
Базис, координаты и проекция вектора
2026TheorySergey
Разложение вектора по базису на плоскости и в пространстве, ортонормированный базис и декартова система координат, координаты вектора и линейные операции над ними, проекция вектора на ось, её линейность и проекция на вектор.
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60
Linear (Vector) Space
2026TheorySergey
The axioms of a linear (vector) space, examples and counterexamples.
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160
Systems of Linear Equations
2026TheorySergey
Linear systems in matrix form, the Kronecker–Capelli theorem, homogeneous systems, and the fundamental system of solutions.
0
210
Алгебра 1. Лекция 4. Формальные степенные ряды и производящие функции
2026LectureAlexey Ilyin
В этой лекции рассматриваются формальные степенные ряды как алгебраический объект. Вводятся операции сложения, умножения, а также аналоги производной и интеграла. Ключевая идея лекции — применение этого аппарата для решения линейно-рекуррентных соотношений с помощью производящих функций, что демонстрируется на классическом примере чисел Фибоначчи.
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240
Machine Learning. Additional Lecture 1. The Theory of Overfitting
2026LectureКонстантин Вячеславович Воронцов
The combinatorial theory of overfitting: the probability of overfitting and why the Vapnik–Chervonenkis bounds are loose; experiments with overfitting — a monotone chain of algorithms, the effect of splitting and connectivity of the family on the probability of overfitting and on the complete cross-validation estimate, overfitting of chains, the exact formula for the probability of overfitting when choosing between two algorithms; the splitting–connectivity graph of a family of algorithms, examples for linear classifiers, a monotone chain and a two-dimensional net; generating and forbidden sets, upper connectivity and inferiority of an algorithm; the splitting–connectivity upper bound, the idea of its proof and its properties.
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220
Machine Learning 1. Bayesian Classification Theory
2026LectureКонстантин Вячеславович Воронцов
The probabilistic formulation of classification: prior and posterior class probabilities, class likelihood functions, the maximum a posteriori principle; the optimal Bayes classifier and losses from errors; empirical estimation of prior probabilities and class densities; the naive Bayes classifier, features with exponential-family densities and the linear naive Bayes classifier; a survey of Bayesian classifiers: the Parzen window method, the quadratic discriminant, Fisher's linear discriminant, Gaussian mixtures with diagonal covariance matrices, and the radial basis function network.
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180
Topology 2. Problem sheet 2
2026Problem sheetФёдор Вылегжанин
Problems for the course "Topology 2" (F. E. Vylegzhanin, Independent University of Moscow, autumn 2026), sheet 2 of 16 September 2026 — singular homology and chain homotopies. A chain map from simplicial to singular chains; retractions and direct summands; the Hurewicz homomorphism from the fundamental group to the first homology; finite CW complexes and homology classes; homology of a union of a chain of spaces; homology of a simplex and of its skeleton; simplicial maps; the chain homotopy equivalence between a complex and its homology; chain homotopy as an equivalence relation; the five lemma.
1
400
Аффинные пространства
2026LectureTaras Panov
Аффинные пространства и подпространства, аффинные системы координат и формулы их замены, прямые и плоскости в аффинных пространствах.
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460