mathematics

 Tilted lanes captured in a human-crowd experiment. The lanes are formed by two groups of people moving in opposite directions. The inclination results from a `pass on the right’ traffic rule. Credit: K. Bacik. B. Bacik, T. RogersMathematical research from the University of Bath in the United Kingdom has shed new light on the formation and behavior of crowds.Have you ever pondered how people, without having a discussion or even giving it a second thought, instinctively form lanes when walking through a crowded area?A new…

In their paper, posted online in late November 2022, a key part of the proof involves showing that, for the most part, it doesn’t make sense to talk about whether a single die is strong or weak. Buffett’s dice, none of which is the strongest of the pack, are not that unusual: If you pick a die at random, the Polymath project showed, it’s likely to beat about half of the other dice and lose to the other half. “Almost every die is pretty average,” Gowers said.The project diverged from the AIM team’s original model in one…

Improve Article Save Article Like Article Improve Article Save Article Machine Learning is the field of study that gives computers the capability to learn without being explicitly programmed. Math is the core concept in machine learning which is used to express the idea within the machine learning model.Mathematics for Machine LearningIn this tutorial, we will look at different mathematics concepts and will learn about these modules from basic to advance with the help particular algorithm.Linear Algebra and…

Credit: Pixabay/CC0 Public Domain In recent years, 19 states in the U.S. have developed pathways for elementary teachers to become certified elementary mathematics specialists. In these certification and endorsement programs, educators gain a more in-depth knowledge of elementary mathematics content and the skills needed to become…

One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time.Since antiquity, artists and geometers have wondered how shapes can tile the entire plane without gaps or overlaps. And yet, “not a lot has been known until fairly recent times,” said Alex Iosevich, a mathematician at the University of Rochester.The most obvious tilings repeat: It’s easy to cover a floor with copies of squares, triangles or hexagons. In the 1960s, mathematicians found strange sets of tiles…

Mathematicians wanted to better understand these numbers that so closely resemble the most fundamental objects in number theory, the primes. It turned out that in 1899—a decade before Carmichael’s result—another mathematician, Alwin Korselt, had come up with an equivalent definition. He simply hadn’t known if there were any numbers that fit the bill.According to Korselt’s criterion, a number N is a Carmichael number if and only if it satisfies three properties. First, it must have more than one prime factor. Second, no…

Recently, I watched a fellow particle physicist talk about a calculation he had pushed to a new height of precision. His tool? A 1980s-era computer program called FORM.Particle physicists use some of the longest equations in all of science. To look for signs of new elementary particles in collisions at the Large Hadron Collider, for example, they draw thousands of pictures called Feynman diagrams that depict possible collision outcomes, each one encoding a complicated formula that can be millions of terms long. Summing…

For centuries, mathematicians have sought to understand and model the motion of fluids. The equations that describe how ripples crease the surface of a pond have also helped researchers to predict the weather, design better airplanes, and characterize how blood flows through the circulatory system. These equations are deceptively simple when written in the right mathematical language. However, their solutions are so complex that making sense of even basic questions about them can be prohibitively difficult.Perhaps the…

A mouse is running on a treadmill embedded in a virtual reality corridor. In its mind’s eye, it sees itself scurrying down a tunnel with a distinctive pattern of lights ahead. Through training, the mouse has learned that if it stops at the lights and holds that position for 1.5 seconds, it will receive a reward—a small drink of water. Then it can rush to another set of lights to receive another reward.This setup is the basis for research published in July in Cell Reports by the neuroscientists Elie Adam, Taylor Johns and…

A similar scenario played out in the 1990s, when a Tennessee naturalist named Lynn Faust read the confident published assertion of a scientist named Jon Copeland that there were no synchronous fireflies in North America. Faust knew then that what she had been watching for decades in the nearby woods was something remarkable.Faust invited Copeland and Moiseff, his collaborator, to see a species in the Great Smoky Mountains called Photinus carolinus. Clouds of the male fireflies fill forests and clearings, floating at about…