Works to read here added this month

Reference table of indefinite integrals of products of exponentials with sine and cosine.

Reference table of indefinite integrals of expressions containing square roots and other radicals.

Reference table of indefinite integrals of rational functions, including quadratic denominators and partial-fraction forms.

Reference table of indefinite integrals of expressions containing the natural logarithm.

Reference table of indefinite integrals of the hyperbolic sine, cosine, tangent and cotangent.

Reference table of indefinite integrals of the exponential function and its products with powers of x.

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

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

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.

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.

A complete local ring with a finitely generated maximal ideal is Noetherian. Drop completeness and it fails: an ultraproduct construction gives a non-Noetherian local ring whose maximal ideal is principal.

Линейные пространства над произвольным полем, подпространства, линейная зависимость, базис и размерность, сумма и пересечение подпространств, замена базиса.

Аффинные пространства и подпространства, аффинные системы координат и формулы их замены, прямые и плоскости в аффинных пространствах.

Евклидовы и эрмитовы пространства, скалярное произведение, неравенство Коши–Буняковского и неравенство треугольника, ортогональные системы векторов.