Throughout history, epidemics have had a profound impact on human health, economies, and social structures. From the plague of the Middle Ages to modern pandemics like COVID-19, the ability to predict disease spread has become an essential tool for public health and policy decisions. Today, mathematical modeling allows scientists not only to analyze how infections propagate but also to assess…

Modern life is structured in such a way that nearly every action we take—whether negotiating, choosing a route, making a purchase, or competing in sports—can be understood as participation in a kind of “game.” In this game, there are rules, participants, objectives, and, most importantly, outcomes that depend not only on our decisions but also on the decisions of others.…

The mathematics of motion plays a central role in understanding how objects move through space and time. With its tools, it is possible to predict trajectories, calculate velocity and acceleration, and analyze the dynamics of complex systems. Kinematics, a branch of mechanics, uses the concepts of vectors, magnitude, direction, and projection to describe motion precisely without considering the forces causing…

Plane geometry forms the foundation of modern mathematical and visual analysis, and understanding transformations in the plane is a key skill for students, professionals, and anyone working in graphics or design. Transformations allow us to study how shapes change under various operations, identify symmetry, preserve proportions, and apply matrix methods for computations. They have applications not only in pure mathematics…

Probability is a cornerstone of mathematics, governing everything from simple games of chance to complex statistical models in science, finance, and engineering. A foundational aspect of probability theory is combinatorics, the mathematics of counting arrangements, selections, and sequences. Without a solid understanding of combinatorial principles, it is difficult to quantify likelihoods accurately or reason about uncertainty in real-world situations. Combinatorics…

Pascal’s Triangle is one of the most celebrated constructs in mathematics. On the surface, it appears to be simply a triangular arrangement of numbers, where each number is the sum of the two numbers directly above it. Yet, this simple structure conceals a multitude of hidden patterns and relationships that have fascinated mathematicians for centuries. Beyond the basic arithmetic properties,…

In mathematics, physics, engineering, and the applied sciences, formulas are often seen as universal and objective expressions of truth. Students learn to memorize them, manipulate them, and substitute values into them in order to produce numerical answers. Yet the reliability of these results depends not only on remembering a formula correctly, but also on understanding the system of units and…

Many students experience mathematics as a series of disconnected lessons: geometry one month, algebra the next, calculus in another year. Formulas appear, are memorized for an exam, and then are often forgotten. Yet, mathematics is not a scattered field of isolated rules. It is an interconnected system built around patterns that appear repeatedly across different topics. When students learn to…