Works to read here

188 results

Метод опорных векторов

2026LectureКонстантин Вячеславович Воронцов

Метод опорных векторов. Лекция курса «Машинное обучение» К. В. Воронцова. Оптимальная разделяющая гиперплоскость. Понятие зазора между классами (margin).

Метрические методы классификации и регрессии

2026LectureКонстантин Вячеславович Воронцов

Метрические методы классификации и регрессии. Лекция курса «Машинное обучение» К. В. Воронцова. Гипотезы компактности и непрерывности.

Нейронные сети: градиентные методы оптимизации

2026LectureКонстантин Вячеславович Воронцов

Нейронные сети: градиентные методы оптимизации. Лекция курса «Машинное обучение» К. В. Воронцова. Биологический нейрон, модель МакКаллока-Питтса как линейный классификатор. Функции активации.

Стохастический градиент и линейный классификатор

2026LectureКонстантин Вячеславович Воронцов

Стохастический градиент и линейный классификатор. Лекция курса «Машинное обучение» К. В. Воронцова. Метод стохастического градиента SG.

Основные понятия и примеры прикладных задач

2026LectureКонстантин Вячеславович Воронцов

Основные понятия и примеры прикладных задач. Лекция курса «Машинное обучение» К. В. Воронцова. Постановка задач обучения по прецедентам. Объекты и признаки. Типы шкал: бинарные, номинальные, порядковые, количественные.

The Steinberg Representation

2026TheorySean Cotner

An introduction to the Steinberg representation of a finite group of Lie type — its alternating-sum construction from parabolic inductions, worked out explicitly for SL_2.

Some examples of algebraic groups

2026TheorySean Cotner

Two pathological phenomena for algebraic groups over general bases — a group degenerating between the multiplicative and additive group across a DVR, and a non-affine identity component — built as centralizers in SL_n.

Finite flat commutative group schemes embed locally into abelian schemes

2026TheorySean Cotner

A proof of Raynaud's theorem: every finite flat commutative group scheme over a locally noetherian base embeds, Zariski-locally, as a closed subgroup of an abelian scheme.

An example of a non-reduced Picard scheme

2026TheorySean Cotner

An example, due to Serre, of a smooth projective surface in positive characteristic whose Picard scheme fails to be reduced, worked out via the two governing dimension inequalities.

A curiosity: “supersmooth” varieties

2026TheorySean Cotner

A rigidity condition on schemes, strictly stronger than smoothness, introduced with examples and a look at where it fails to be geometric — no known application, just a curiosity.

Quadratic Forms

2026TheorySergey

Quadratic forms and their matrix, definiteness, Sylvester's criterion, and canonical form.

Change of Basis

2026TheorySergey

The change-of-basis matrix, recomputing a vector's coordinates and an operator's matrix, and the orthonormal case.

Eigenvectors and Eigenvalues

2026TheorySergey

Eigenvectors and eigenvalues, the characteristic equation, eigenspaces, and diagonalization of matrices.

Linear Operator

2026TheorySergey

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

Basis, Dimension, and Span

2026TheorySergey

Linear dependence of vectors, basis and coordinates, dimension, subspaces, and linear span.

Linear (Vector) Space

2026TheorySergey

The axioms of a linear (vector) space, examples and counterexamples.

Cramer's Rule and Gaussian Elimination

2026TheorySergey

Two methods for solving a SLAE — Cramer's rule via determinants and the universal Gaussian elimination method, with examples.

Systems of Linear Equations

2026TheorySergey

Linear systems in matrix form, the Kronecker–Capelli theorem, homogeneous systems, and the fundamental system of solutions.

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.

Matrix Rank

2026TheorySergey

Minors and the rank of a matrix, invariance of rank under elementary transformations, and a practical method for computing it.