ABSTRACT
The relative intensity distributions of isotopologs in mass spectrometry, the number of entropic microstates, and the number of species in enzymes with several interacting active sites follow the binomial theorem. Exponentials and their inverse functions, the logarithms, are ubiquitous in nature. Logarithms are particularly useful to linearize and thus compress large value ranges. Differential equations contain both a function and one or more of its derivatives. The highest derivative determines the order of the differential equation. Expansion into partial fractions is useful to simplify a rational function before integrating it. Vectors can be translated without changing their properties, which is useful to illustrate vector addition and subtraction. The Fourier transform is an extension of the Fourier series concept to include non-periodic functions. The deconvolution of the observed diffraction pattern separates the symmetry aspect from the unit cell content.
