Archives for Physics, Math - Page 3
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…
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…
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…
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…
Joint Event Probabilities
See also ‘Single Event Probabilities’ The probability of a 'joint' event - drawing a white ball followed by two black balls (from a jar containing 7 white and 5 black…
Open sets and limit points
A set $A$ is open iff for every point $a\in A$, there exists a $\delta$ such that the neighborhood $\left(a-\delta,a+\delta\right)$ surrounding $a$ is completely contained within (is a subset of)…
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 ; She still feels…
centripetal versus centrifugal force
Centrifugal force is observed by the rotating bucket of water – pulling it towards the ; The bucket of water is in a noninertial frame ,what we (in our own…
Comparing temperatures in centigradeS
Is 20 C twice as hot as 10 C? No - because the centigrade scale does not start at if we used a meter scale that started at meters, what…
The Monty hall problem, Quantum Games
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 –…