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124 results

The torsion component of the Picard scheme

2026OtherBogdan Zavyalov

Every finite flat commutative group scheme over a noetherian local ring is the torsion component of the Picard scheme of a smooth projective scheme with 3-dimensional fibers, built as a quotient of a complete intersection. An application: Hodge numbers that jump in a smooth projective family.

500

Векторные представления текстов и графов

2026LectureКонстантин Вячеславович Воронцов

Векторные представления текстов и графов. Лекция курса «Машинное обучение» К. В. Воронцова. Векторные представления графов.

220

Алгебра 2, Листок 1

2026Problem sheetAlexey Ilyin

Задачные листки к курсам алгебры. Институт и учебное заведение в исходных публикациях не указаны, поэтому здесь не названы.

170

Basic Operations on Matrices

2026TheorySergey

Addition, scalar multiplication, transposition and multiplication of matrices, along with subtraction, powers, and trace.

150

Determinant

2026TheorySergey

The determinant of a square matrix — its meaning, minors and cofactors, Laplace expansion, and computation methods.

190

Linear Operator

2026TheorySergey

A linear operator and its matrix, the action x' = Ax, similar matrices, and the formula B = C⁻¹AC.

150

Топология–1. Лекция 5

2026LectureKonstantin Loginov

150

Топология–1. Лекция 6

2026LectureKonstantin Loginov

120

Fun example: empty colimit does not commute with empty limit

2026NotesBogdan Zavyalov

Why the definition of a filtered category insists on non-emptiness: the empty colimit fails to commute with the empty limit, and that is the only failure.

310

Table of Derivatives

2026ReferenceSergey

Reference table of the derivatives of the elementary functions: power, exponential, logarithmic, trigonometric and their inverses.

240

Table of Basic Integrals

2026ReferenceSergey

Reference table of the basic indefinite integrals of the elementary functions: power, exponential, logarithmic and trigonometric.

270

IMO 2009

2026Problem sheet

50th International Mathematical Olympiad. Bremen, Germany, 2009.

340

IMO 2010

2026Problem sheet

51st International Mathematical Olympiad, 2010.

320

IMO 2011

2026Problem sheet

52nd International Mathematical Olympiad. Amsterdam, 2011.

360

IMO 2012

2026Problem sheet

53rd International Mathematical Olympiad. Mar del Plata, Argentina, 2012.

290

IMO 2014

2026Problem sheet

55th International Mathematical Olympiad. Cape Town, South Africa, 2014.

330

IMO 2019

2026Problem sheet

60th International Mathematical Olympiad, 2019.

390

Анализ-1, Листок 4

2026Problem sheetAlexander Kalmynin

270

Теория вероятностей, Листок 1

2026Problem sheetСтанислав Шапошников

Задачный листок к курсу теории вероятностей. Институт и учебное заведение в исходных публикациях не указаны, поэтому здесь не названы.

270

Vector calculus. Surface integrals of the first kind

2026Problem sheetSergey

Integration with respect to surface area: the area element for an explicit and a parametric surface, pieces of planes, the sphere in spherical coordinates.

340