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Browse Classroom Capsules and Notes

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Displaying 11 - 20 of 1209

This capsule introduces a straightfoward way of calculating partial fraction decomposition for functions of specific forms by long division. The obtained partial fractions can be easily...

Based on a closed form and recurrence relation of Catalan numbers, the authors proves their parity and primality.

This article generalizes a problem of dogs fetching a ball in the water and presents it as a problem of calculus of variation.

This capsule investigates the sequences that converge to Euler's constant. By utilizing the geometric description of the terms, the author can obtain a rate of convergence comparable to...

This capsule introduces a way of producing the Möbius function in Number Theory through the algebra of formal series. The author hopes that this exposition can lobby more mathematicians...

This capsule applied the concept of cross ratio in complex analysis to derive the Pythagorean Theorem. It appears to be the first in the literature to use this approach to prove the famous...

A technique is introduced for the purpose of finding the relative maximum values of the probability density function. The crux is to find the critical numbers of the exponential of the...

Based on the notion of "arithmetic triangles," arithmetic quadrilaterals are defined. It was proved by using an elliptic curve argument that no such quadrilateral can be inscribed on...

This capsule discusses an alternative way of examining the Fibonacci sequence. As a result, a class of generalized  Fibonacci sequences of numbers can be defined.

An example in business calculus is used to show a short-cut to compute the discrepancy between the difference of values and the differential for certain class of functions.

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