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.)
Write one representation of a vector. The class as a whole should try to generate as many representations as possible.
 Keywords
 Vectors graphing visualization Matrix BraKet
 Learning Outcomes
