Mathematics
Number theory, algebra, analysis, combinatorics
Adjoint Action of SO(4) on Its Lie Algebra - Equivariant Cohomology and Closed Invariant Submanifolds
hardConsider the adjoint action of SO(4) on its Lie algebra \mathfrak{so}(4). Determine the nonempty closed invariant submanifolds and compute the total r...
Find the Pattern: Given the Sequence of Numbers 6, 7, ?, 3, 5, 7, 8, 9, 1, 8
mediumFind the pattern: Given the sequence of numbers 6, 7, ?, 3, 5, 7, 8, 9, 1, 8, what number should replace the question mark? The numbers share a common...
James Is a Famous Spy and a Math Genius - Notebook of 100 Pages
hardJames is a famous spy and a math genius. He is spying on an enemy base and has lost all his tools, having only a notebook of 100 pages. He can fold th...
What Is the Cardinality of the Set of Continuous Functions Where f(f(x)) = exp(x)?
hardWhat is the cardinality of the set of continuous functions f: \mathbb{R} \to \mathbb{R} such that f(f(x)) = e^x for all x?