Why are complex numbers so useful in the natural sciences? Analyticity (harder to do without complex numbers) Analytic functions can be expanded in Taylor series in their region of analyticity. Which means that, in that region...

# Category - Physics, Math

Interesting Physics and Math Stuff

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...

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...

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...

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...

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...

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...

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...

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...

The original problem Three doors, a prize behind only one door (say, a new car). Other two doors are each hiding a goat. Contestant has to pick a door – and hope that she wins the car. At just this stage, the chance of...