This talk will be a tutorial on the Orthogonal Frequency Division Multiplexing (OFDM) Modulations and variants employed in 4G/5G and how they are parameterized via the forward/inverse Fast Fourier Transforms (FFT/IFFT). The talk will discuss the complex baseband formulation of the underlying digital modulations used via a brief introduction to quadrature amplitude modulation, its complex baseband representation, and subsequent extension into OFDM. The talk will address the FFT/IFFT properties employed in the conceptual formulation of the scheme and will motivate how thinking about the FFT/IFFT in a linear-algebraic sense can add insight into the complicated-looking structure of the FFT/IFFT and other transforms used in engineering sciences.