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### Neuroscientist’s create mathematical model for how the brain keeps a beat

For the musically fortunate, keeping a beat is as natural as breathing. But for those without the talent, the notion of producing and keeping a beat may seem an impossibility.

On Thursday this week, researchers announced a mathematical model that describes a potential mechanism by which the brain may keep a musical beat. The paper, published in PLOS Computational Biology, is a joint effort between Amitabha Bose of New Jersey Institute of Technology; as well as Aine Byrne and John Rinzel of New York University.

### Understanding the physics of a pendulum

You've probably seen a pendulum swing, but have you ever thought about why it is that a pendulum swings at all? Further, why is it that a pendulum only swings for some period of time becoming motionless? It turns out, a simple pendulum is a great means through which we can develop intuition about the conservation of energy and the relationship between gravitational potential energy and kinetic energy -- not to mention oscillations.

### How high up is outer space?

The Kármán line is the altitude of the boundary between earth’s atmosphere and outer space. This $100$  km or $328, 084$ ft. The value comes from Fédération Aéronautique Internationale, and it’s the same value that NASA uses to define the boundary between our planet’s atmosphere and outer space.

If you’re like me, the highest you've ever been from sea level is around $30,000$ ft to $40,000$ ft, which is the range of altitudes at which most commercial airliners cruise at.

### Human Beings and the Next Revolution: Automation

“Can you believe people actually used to work?”

Some day in the not-too-distance future, people will say words like these.

There is a moment in humanity’s future that is approaching. And in this moment in time, people will no longer have careers or work full-time jobs.

### What's the difference between simple and elementary regions?

Simple regions are a topic that comes up in vector calculus.

First, let's understand the difference between x-simple and y-simple regions. Visually, the Type 1 region seen here is an example of a y-simple region and the Type 2 region is an example of an x-simple region. See any textbook on vector calculus for a formal definition.

### Complex numbers: the relationship between rectangular form, exponential form, angular notation

Learning complex analysis can be a bit daunting. Not only is this topic filled with abstract ideas, there are a number of equivalent ways of talking about the same idea. For example, there are at least three different forms one can use to represent a complex number. In this video, I explain these different forms, the relationships, and when to use each.

### Calculus explained in a way that anyone can understand

Calculus is an essential mathematical tool used by scientists in many fields -- from physics to artificial intelligence. So, what is it?

Calculus is the study of change.