Math 2406: Abstract Vector Spaces

Lecture 2 Plan  (Thursday, August 23, 2007).

“Writing Proofs” by Chris Heil, pp. 3-4.

Apostol 1.6-1.13.

           

Review questions:

1. Why do we have to prove the k = 1 case separately in proof by induction?
2. Can you write a true statement like the triangle inequality, but with three vectors?
3. How is a span different from a linearly independent set?


Homework 1 due Thursday, August 30, 2007 at 5 p.m. in Skiles 238A door box.

1. Apostol 0.13, Exercise 1b.

2. Prove by contradiction: There are no two consecutive integers which are both prime, and both larger than 2.

3. Apostol 1.4, Exercise 10.

4. Apostol 1.8, Exercise 25.

5. Apostol 1.11, Exercise 17.