Seminar

In this talk, we will discuss a ``new'' way to define an integral. Instead of using the standard definition of $\displaystyle \sum_{i=1}^{n} f(x_{i}) \hspace{3pt} \Delta x_{i}$, can we use an infinite product? How will this change the definition of an integral? Will this also change the definition of a derivative? Are there applications for these? This talk will examine the new mysteries of the so-called ``star-integral'' and ``star-derivative''.

The study of straightedge-and-compass geometric constructions goes back to ancient geometry. Many centuries later, the mathematicians became interested in straightedge-only constructions. Recall that a straightedge (a.k.a. a ruler without marks) is a device that can be used to connect any two points by a line but not to measure distances or draw parallel lines. Surprisingly, many things can be achieved with only a straightedge: for example, one can construct tangent lines to a given circle.

In this talk, we will discuss a ''new'' way to define an integral. Instead of using the standard definition of $\displaystyle \sum_{i=1}^{n} f(x_{i}) \hspace{3pt} \Delta x_{i}$, can we use an infinite product? How will this change the definition of an integral? Will this also change the definition of a derivative? This talk will examine the new mysteries of the so-called ''star-integral'' and ''star-derivative''.