Abstract: We present new exponential bounds for the Gaussian Q function (one- and two-dimensional) and its inverse, and for M-ary phase-shift-keying (MPSK), M-ary ...

Timothy Li is a consultant, accountant, and finance manager with an MBA from USC and over 15 years of corporate finance experience. Timothy has helped provide CEOs and CFOs with deep-dive analytics, ...

This post shows how to change what the Fn keys do in Windows 11/10. The Fn or the Function key is a meta-modifier key used to activate secondary functions or special features on certain keys. The ...

Math doesn’t have to be daunting, especially when your iPhone (or iPad) can do the heavy lifting. Tucked away inside iOS is a full-featured scientific calculator, ready to help you solve complex ...

Exponential growth compounds investment returns over time, enhancing long-term wealth. S&P 500's historic 10% annual return illustrates exponential growth's impact on investments. Staying invested in ...

AI encompasses machine learning, natural language processing, and computer vision. It enables systems to learn from data, make predictions, and automate tasks. Examples include: Predictive analytics ...

Graphs of exponential functions and logarithmic functions provide a visual insight into their properties, such as growth, decay, and the inverse relationship between them. Graphs of exponential ...

Exponential and logarithmic functions are mathematical concepts with wide-ranging applications. Exponential functions are commonly used to model phenomena such as population growth, the spread of ...

The original version of this story appeared in Quanta Magazine. Calculus is a powerful mathematical tool. But for hundreds of years after its invention in the 17th century, it stood on a shaky ...

In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

Along with the usual one-argument and two-argument exponential and logarithm functions, sqrt is considered to be an exponential function, because it raises a number to the power 1/2.