Advanced Mathematics quiz

More questions about Advanced Mathematics

These visible examples show the question style. LearnClash turns the full topic into ranked duels and spaced repetition.

1. 1 Easy

   Which conjecture says positive integers reach 1 via even n/2 and odd 3n+1?

   Answer: Collatz conjecture

   Why: Famed mathematician Paul Erdős remarked about the simple-sounding Collatz conjecture that mathematics may not be ready for such problems.

2. 2 Medium

   What is the cardinality of real numbers?

   Answer: Uncountable

   Why: Cantor's diagonal argument shows that no list of them can ever be complete, however cleverly the list is arranged.

3. 3 Hard

   Which algebraic structure is associative, has an identity, but no inverses?

   Answer: Monoid

   Why: Add inverses and it becomes a group, while dropping the identity element leaves a semigroup behind.

4. 4 Easy

   Which matrix value tests invertibility as the product of all eigenvalues?

   Answer: Determinant

   Why: If a matrix's determinant equals zero, the matrix collapses space into lower dimensions, making it non-invertible.

5. 5 Medium

   What distribution in statistics models the frequency of events over time?

   Answer: Poisson distribution

   Why: Ladislaus Bortkiewicz made it famous in 1898 by fitting it to yearly horse kick deaths in 14 Prussian cavalry corps over 20 years.

6. 6 Hard

   In the Monty Hall problem, what is the probability of winning by switching?

   Answer: $\frac{2}{3}$

   Why: Your first pick is wrong two times in three, and the host opening a door does not change that, it just concentrates the odds elsewhere.