Mathematics

Hi, this a part of my work in the course “Measure theory and integration” at the University of Calgary. I discuss the concept of Hausdorff dimension and its application to fractals. You can download the pdf file here

Conversion between objects I would like to begin this article with a question. Is there a way to turn bread into sugar? The answer from biology is yes. $$\textrm{Bread} \xrightarrow{\text{chewing}} \textrm{Smaller pieces of bread}$$ $$\textrm{Smaller pieces of bread} \xrightarrow{\text{enzyme}} \textrm{Sugar}$$ The question of whether or not there is a way is different from the question of whether or not the way is practical. A practicality question may ask whether or not a person can do this....

A wavefunction is a mathematical object which represents a quantum state. Many would have been introduced to wavefunctions from Schrödinger’s cat or the double-slit experiment. However, there is a more straightforward way to present the concept of wavefunction without resorting to the complex historical development of physics. Often, the wavefunction is introduced by not knowing exactly where a particle is or its state. This is inaccurate because wavefunction is about something other than the lack of knowledge but the nature of quantum state and measurement....