Archives for Math
Some great graduate math problems
Prof. Steeb - collection of problems Berkeley Problems in Mathematics
Graph of Dirichlet Function
I often wondered what the graph of this weird function would look like…A function that equates to 1 for all rational x and equates to 0 for all irrational…
The Historical Context of Data, Using Data for Decision Making
This is still in draft mode The Historical Context of Data Collected Unless we look at the ‘context’ of the data that we collect, we may be missing the big…
Statistical Fallacies
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…
Some Cool Proofs (Books and Resources) in Math
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…
Nash equilibrium, Prisoner dilemma
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…
Continuous (Smooth) vs Differentiable versus Analytic
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…
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…