### The mathematical purity test

#### The basics

- Have you ever been excited about math?
- Had an exciting dream about math?
- Made a mathematical calculation?
- Manipulated the numerator of an equation?
- Manipulated the denominator of an equation?
- On your first problem set?
- Worked on a problem set past 3:00 a.m.?
- Worked on a problem set all night?
- Had a hard problem?
- Worked on a problem continuously for more than 30 minutes?
- Worked on a problem continuously for more than four hours?
- Done more than one problem set on the same night (i.e. both started and finished them)?
- Done more than three problem sets on the same night?
- Taken a math course for a full year?
- Taken two different math courses at the same time?
- Done at least one problem set a week for more than four months?
- Done at least one problem set a night for more than one month (weekends excluded)?
- Done a problem set alone?
- Done a problem set in a group of three or more?
- Done a problem set in a group of 15 or more?
- Was it mixed company?
- Have you ever inadvertently walked in upon people doing a problem set?
- And joined in afterwards?
- Have you ever used food doing a problem set?
- Did you eat it all?
- Have you ever had a domesticated pet or animal walk over you while you were doing a problem set?
- Done a problem set in a public place where you might be discovered?
- Been discovered while doing a problem set?

#### Kinky stuff

- Have you ever applied your math to a hard science?
- Applied your math to a soft science?
- Done an integration by parts?
- Done two integration by parts in a single problem?
- Bounded the domain and range of your function?
- Used the domination test for improper integrals?
- Done Newton's Method?
- Done the Method of Frobenius?
- Used the Sandwich Theorem?
- Used the Mean Value Theorem?
- Used the Dominated Convergence Theorem?
- Used the Hairy Ball Theorem?
- Used a Gaussian surface?
- Used a Lipschitz condition?
- Used a foreign object on a math problem (eg: calculator)?
- Used a program to improve your mathematical technique (eg: MACSYMA)?
- Not used brackets when you should have?
- Integrated a function over its full period?
- Factored a polynomial under the order of 17?
- Done a calculation in three-dimensional space?
- Done a calculation in n-dimensional space?
- Done a change of bases?
- Done a change of bases specifically in order to magnify your vector?
- Worked through four complete bases in a single night (eg: using the Graham-Schmidt method)?
- Inserted a number into an equation?
- Calculated the residue of a pole?
- Scored perfectly on a test?
- Swallowed everything your professor gave you?
- Used explicit notation in your problem set?
- Purposefully omitted important steps in your problem set?
- Padded your own problem set?
- Been blown away on a test?
- Blown away your professor on a test?
- Have you ever multiplied 23 by 3?
- Have you ever used a unit?
- ...But were disappointed to find your unit was idempotent?
- ...But relieved to find your unit wasn't nilpotent?
- Have you ever calculated the size of your unit ball using a Weiner measure?
- Have you ever bounded your Bessel function so that the membrane did not shoot to infinity?
- Have you ever understood the following quote:
The relationship between Z

^{0}to C_{0}, B_{0}, and H_{0}is an example of a general principle which we have encountered: the kernel of the adjoint of a linear transformation is both the annihilator space of the image of the transformation and also the dual space of the quotient of the space of which the image is a subspace by the image subspace."--Sternberg & Bamberg's A "Course" in Mathematics for Students of Physics, vol. 2