Линейная алгебра, Листок 1. Линейные пространства
2026Problem sheetTaras Panov
Задачные листки к курсу линейной алгебры. Институт и учебное заведение в исходных публикациях не указаны, поэтому здесь не названы.
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210
Search results for “линейная алгебра”
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37 results
Линейная алгебра, Листок 2. Аффинные пространства
2026Problem sheetTaras Panov
Задачные листки к курсу линейной алгебры. Институт и учебное заведение в исходных публикациях не указаны, поэтому здесь не названы.
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290
Linear algebra and analytic geometry. Vector algebra
2026Problem sheetSergey
Vectors in coordinates: dividing a segment, midpoints of sides, the angle between vectors, the cross product and the scalar triple product.
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180
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.
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310
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.
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520
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.
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470
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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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.
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Topology 2. Lecture 3
2026LectureФёдор Вылегжанин
Singular homology — standard simplices and the inclusions of facets, singular simplices and chains, the differential; zeroth homology and path components, the homology of a point, reduced homology; chain maps and maps of homology, functoriality, the chain map induced by a continuous map; chain homotopies and the prism; the homotopy invariance theorem with a full proof via the prism operator; subcomplexes, quotient complexes and the homology of a pair.
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550
Topology 2. Problem sheet 1
2026Problem sheetФёдор Вылегжанин
Problems for the course "Topology 2" (F. E. Vylegzhanin, Independent University of Moscow, autumn 2026), sheet 1 of 9 September 2026 — simplicial homology and chain complexes. Zeroth homology and connected components; homology of a disjoint union and of a wedge; triangulations of the circle, the sphere and the Möbius band; the join and the product of simplicial complexes; the Euler characteristic and the Morse inequalities; the number of vertices of a triangulated surface; operations on chain complexes; exact sequences; the Smith normal form and the splitting of a complex.
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450
Linear Dependence and Independence of Rows
2026TheorySergey
Linear dependence and independence of the rows of a matrix, the criterion via a linear combination, and the connection to rank.
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560
Basis, Dimension, and Span
2026TheorySergey
Linear dependence of vectors, basis and coordinates, dimension, subspaces, and linear span.
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220
Линейные пространства
2026LectureTaras Panov
Линейные пространства над произвольным полем, подпространства, линейная зависимость, базис и размерность, сумма и пересечение подпространств, замена базиса.
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530
Линейные модели регрессии
2026LectureКонстантин Вячеславович Воронцов
Линейные модели регрессии. Лекция курса «Машинное обучение» К. В. Воронцова. Задача регрессии, многомерная линейная регрессия.
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120