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Mathematics Quiz

Why is something true?

Answer five questions about Mathematics and get instant feedback.

Question 1

A part of a graph where every vertex can reach every other vertex

Answer options

  • Connected component
  • Eulerian cycle
  • Shortest path
  • Spanning tree

Key Idea

If you count connected components, you learn how many separate "islands" the graph has, and a single added edge can merge two components into one.

Question 2

What assigns a nonnegative size to each vector?

Answer options

  • A norm
  • A basis
  • A matrix
  • A derivative

Key Idea

Different norms can measure the same vector space in very different ways, for example the ℓ1\ell^1 norm sums coordinates while the ℓ2\ell^2 norm gives the usual Euclidean length.

Question 3

This image question appears in the interactive quiz.

Answer options

  • Matrix
  • Basis
  • Vector
  • Determinant

Key Idea

A matrix organizes numbers so rows and columns can represent transformations or data.

Question 4

This image question appears in the interactive quiz.

Answer options

  • Cycle
  • Tree
  • Matching
  • Path

Key Idea

A cycle is a route that returns to where it began without loose ends.

Question 5

What means an operation never leaves the set it is defined on?

Answer options

  • Closure
  • Identity
  • Distributivity
  • Commutativity

Key Idea

Closure is what makes a subset like 2Z2\mathbb{Z} a world of its own under addition, but it fails under division since 2/42/4 leaves the set.

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