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Browse Classroom Capsules and Notes

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A discrete analog of integration by parts

This article uses four different methods to evaluate a type of Poisson integral: Riemann sums, functional equation, parametric differentiation, and infinite series.

An inductive proof is presented for the bounds of the remainder of Taylor expansion. This result, with Darboux's theorem, implies the classical formula for the remainder.

Using just very basic knowledge of finite fields and the inclusion-exclusion formula, the authors show how one can see the shape of Gauss` formula for the number of irreducible polynomials of...

The authors study the upper bound for the expected differences between order statistics of a distribution.

A Fibonacci identity is depicted visually.

The authors explain certain inequalities visually.

A covering system is a system of \(k\) arithmetic progressions whose union includes all integers. This paper presents upper bounds on the number of consecutive integers which need to be checked...

In this note an elementary proof of Stirling's asymptotic formula for \(n!\) is given.

The number of black squares in a crossword puzzle, and the number of marks needed to bound the black squares allows one to determine the number of words the puzzle contains.

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