Selecting a truly RANDOM Sample If you choose every person who passes you on the sidewalk, that would not be a random sample, since you would miss out the people moving in vehicles. If you, likewise, stop every car on the...

# Category - Math

Number theory, complex variables (applications), fourier analysis and applications.

Also see my – Problem Books for Pure Math, Physics and Mathematical Physics If you are looking for some of the most important, yet elegant math proofs, look no further than these two books. The first one – Proofs from the...

Under Construction Check out also Advanced Problem Books in Math and Physics and Rare Finds in Relativity Two prisoners have been accused of the same crime and are kept in separate rooms for questioning. If both confess to the...

I had a lot of trouble distinguishing between continuous and differentiable and analytic functions… Analytic An analytic function is a function that is smooth (in the sense that it is continuous and infinitely times...

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...

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...