## Running Sum of Randomly Generated Numbers

Integers from 1 to N are randomly generated . Each integer has an equal probability of being selected and unlimited repetition is permitted. A running sum is maintained. Given any integer k, such that 1 <= k <= n , what is...

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## Visualizing differential equations

Whenever I read a physics article, I try to visualize the quantities that the author is talking about.  I do this by ASSOCIATING the quantity with some REAL thing. Example – if the article talks about FREQUENCY, I think of...

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## Adventures in teaching–why 5th graders are smarter than grown-ups

A small bag is lying on the floor.  The room is big – with high ceilings. Yet, no one can jump over the bag. Why? I posed this to several grown-ups. No one got it. Next, I posed it to my 5th grade class. They spent exactly...

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## Principles versus Laws

People tend to use ‘laws’ interchangeably with ‘principles’. In reality, there is an important difference between the two – as described in this short post. Physics A law encompasses a specific area – e.g. mechanics...

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## “Deriving” into Pre Calculus, Course S68–S.I.G., University of Texas, Austin

Day 1 – Pre-Assessment Areas of interest, individualized personal objectives Five hardest questions in different areas of calculus Informal class discussion Day 2 – Graphing General equation of a line, Physical...

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## A probability problem – will these two friends ever meet?

Two friends decide to meet at a definite place between 9 AM and 10 AM. The first to arrive waits for his friend for 15 minutes and then leaves. If each of them arrives at an arbitrary moment between 9 and 10 AM, find the...

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## Modeling Traffic Flow

Traffic flow is not that different from the flow of anything else. Imagine heat flow along an iron rod or water flowing down a pipe. If you observe the traffic (on a highway) from a far enough distance, the mass of cars would...

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Uncategorized

## Complex Transformations – The Complex Logarithmic Function

The real logarithmic function has two interesting properties: The Flattening property:  – a product is flattened into a sum The Linearizing property: –> Linearized an exponential (growth) function These...

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## N Points on a unit sphere

Problem Statement Consider n points lying on the Unit Sphere (the image shows a unit circle instead of a sphere). Show that the sum of the squares of the lengths of all segments determined by the n points is less than...

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## Mathematics as a hobby (math as a hobby) ? Yes – Really!

Even if you do not consider math to be a hobby, this article may provide an understanding of why a lot of people do. Not being a math-aficionado, my wife thought it a bit strange that I enjoyed solving math problems for fun (I...

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