## The Twin Paradox – Once and for All

Check out also – Problems In Advanced Math and Physics and Rare Finds in Special and General Relativity Every science buff has heard of the Twin Paradox. Movies have been made, books have been written, plots and sub-plots all...

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## The magic of Complex numbers

Check out also – Problems In Advanced Math and Physics and Rare Finds in Special and General Relativity Why are complex numbers so useful in the natural sciences? Analyticity (harder to do without complex numbers) Analytic...

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## pigeonhole principle problem solving

Suppose 82 students are enrolled in a college – offering only 4 courses. Suppose that each course has 3 sections – and a student can choose any one of three sections. Show that at least TWO students have to share a...

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## Remove a countable set of points from an open set

Let A be an open set. Show that if a finite number of points are removed from A, the remaining set is still open. Is the same true if a countable number of points are removed? Solution If we order the points removed from A, x1...

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## Single Event Probabilities

Binomial Random Variable – and Probability of SINGLE event happening more than once (multiple heads in a coin-toss etc.) Whenever you have a variable that can take on two possible values (flip of a coin for example), you...

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## Joint Event Probabilities

See also ‘Single Event Probabilities’ The probability of a ‘joint’ event – e.g. drawing a white ball followed by two black balls (from a jar containing 7 white and 5 black balls) can be calculated using...

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## Open sets and limit points

A set is open iff for every point , there exists a such that the neighborhood surrounding is completely contained within (is a subset of) . A point is a limit point of a set iff given any , all neighborhoods intersect the...

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## What about accelerating frames of reference?

If a woman is standing in an elevator, she feels a force of gravity pushing her against the floor. As the elevator accelerates upwards, this force increases.  She still feels as if a ‘gravitational’ force has increased...

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## centripetal versus centrifugal force

Centrifugal force is observed by the rotating bucket of water – pulling it towards the center.  The bucket of water  is in a noninertial frame  ,what we (in our own inertial frame) observe is the centripetal...

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## Comparing temperatures in centigradeS

Is 20 C twice as hot as 10 C? No – because the centigrade scale does not start at 0.For e.g.- if we used a meter scale that started at 1.0 meters, what can you say about comparing 1.1 to 1.2? Can you say that 1.2 is TWICE...

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