One useful feature of the Python math module is quick access to mathematical constants. You can make Python more effective as ...

The Uttarakhand Board has released the Class 12 Maths Syllabus 2025-26. The exam will be conducted for 3 hours with a total ...

Abstract: In this paper, we consider a dynamical system whose trajectory is a result of minimizing a multiphase cost function. The multiphase cost function is assumed to be a weighted sum of specified ...

“Fundamentally, the issue that leads to Kerberoasting is bad passwords,” Tim Medin, the researcher who coined the term ...

Part 1 begins with an overview of properties of the real numbers and starts to introduce the notions of set theory. The absolute value and in particular inequalities are considered in great detail ...

A logarithm is the power which a certain number is raised to get another number. Before calculators and various types of complex computers were invented it was difficult for scientists and ...

We present a systematic derivation of three mathematical models of increasing complexity for optical design, based on Hamilton’s characteristic functions and conservation of luminous flux, and briefly ...

We all know that calculus courses such as 18.01 and 18.02 are univariate and vector calculus, respectively. Modern applications such as machine learning and large-scale optimization require the next ...

Index laws and the laws of logarithms are essential tools for simplifying and manipulating exponential and logarithmic functions. There is an inverse relationship between exponential and logarithmic ...

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 ...