Algebraic Geometry
What is the genus of a nonsingular cubic curve?
1
Is the right shift operator on sequences compact?
not compact
What does p squared equal modulo 24 for any prime greater than 3?
1
What is the formula for the number of derangements of n objects?
n factorial times sum from k equals 0 to n of negative 1 to the k over k factorial
What is the general solution to u sub x plus u sub y equals u?
e to the x times any function of y minus x
Is the curve y squared equals x to the fifth plus x singular or not?
nonsingular
True or false: every bounded linear operator on a complex Banach space has a nonempty spectrum
true
Are there infinitely many primes that are 1 modulo 4?
yes
What counts the number of ways to partition a set into k nonempty subsets?
stirling number of the second kind
What substitution solves dy dx equals y over x plus sine of y over x?
tangent of y over 2x equals c times x
What is the dimension of a projective variety in n dimensional projective space cut by two independent equations?
n minus 2
What is the dual space of ell one?
ell infinity
What is the value of the sum of mu of n divided by n over all positive integers in the limiting sense?
0
What is the value of the Ramsey number R 3 3?
6
What is the implicit solution form of the inviscid Burgers equation?
u equals f of xi where x equals xi plus t times f of xi
What is the formula for the genus of a smooth plane curve of degree d?
(d minus 1)(d minus 2) divided by 2
Are all Hilbert spaces reflexive?
yes
How does the sum of one over primes up to x grow asymptotically?
like log log x
What is the approximate value of the number of derangements of n?
n factorial divided by e
What is the solution to the heat equation with initial condition e to the negative x squared?
one over square root of 1 plus 4t times exponential of negative x squared over 1 plus 4t
A nonsingular cubic curve over the complex numbers is equivalent to what type of geometric object?
complex torus
What is the spectrum of the right shift operator on square summable sequences?
all complex numbers with absolute value less than or equal to 1
What theorem states that arithmetic progressions with coprime start and difference contain infinitely many primes?
dirichlet theorem
What theorem guarantees long arithmetic progressions in dense sets of integers?
szemeredi theorem
What is the status of the 3D Navier Stokes existence problem? (solved or unsolved)
unsolved