IMO 2001
Problem sheet
International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.
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IMO 2002
Problem sheet
International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.
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IMO 2003
Problem sheet
International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.
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IMO 2004
Problem sheet
International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.
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IMO 2006
Problem sheet
International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.
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Matrices
Theory
A matrix, its notation, and the main types: row, column, echelon, square, diagonal, identity, symmetric - defined and shown with worked examples.
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Systems of Linear Equations
Theory
Linear systems in matrix form, the Kronecker–Capelli theorem, homogeneous systems, and the fundamental system of solutions.
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Properties of Matrix Operations
Theory
The basic properties of addition, scalar multiplication, transposition, and multiplication of matrices, with justifications.
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Inverse Matrices
Theory
Nonsingular matrices, the invertibility criterion, the adjugate-matrix formula, and the Gauss–Jordan method.
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Векторные представления текстов и графов
Lecture
Векторные представления текстов и графов. Лекция курса «Машинное обучение» К. В. Воронцова. Векторные представления графов.
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Алгебра 2, Листок 1
Problem sheet
Задачные листки к курсам алгебры. Институт и учебное заведение в исходных публикациях не указаны, поэтому здесь не названы.
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Fun example: empty colimit does not commute with empty limit
Notes
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.
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Table of Basic Integrals
Reference
Reference table of the basic indefinite integrals of the elementary functions: power, exponential, logarithmic and trigonometric.
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Table of Derivatives
Reference
Reference table of the derivatives of the elementary functions: power, exponential, logarithmic, trigonometric and their inverses.
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Basic Operations on Matrices
Theory
Addition, scalar multiplication, transposition and multiplication of matrices, along with subtraction, powers, and trace.
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Determinant
Theory
The determinant of a square matrix — its meaning, minors and cofactors, Laplace expansion, and computation methods.
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Charge Collection After Heavy-Ion Strikes: A Material Parameter Sweep in a 2001 TCAD Solver
Notes
A pilot study mapping ion-induced charge collection against bandgap and carrier mobility, and what it revealed about the cost of getting the time integration wrong
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