AIMS Maxwell 2021

Students each recall a representation of vectors that they have seen before and record it on an individual whiteboard. The instructor uses these responses to generate a whole class discussion that compares and contrasts the features of the representations. If appropriate for the class, the instructor introduces bra/ket notation as a new, but valuable representation.

What students learn There are many different representations of vectors, including:

• an algebraic name (preferably with an arrow over it);
• arrows in the plane or in space;
• rows or columns of numbers;
• a linear combination of basis vectors;
• a periodic function
  (This representation may be new to some students. Do not introduce it unless it is appropriate for the course.)
• an algebraic name inside a ket
  (This representation may be new to some students. Do not introduce it unless it is appropriate for the course.)