Lecture 2

Learning objectives

After this class, you should be able to:

1. Define the problems of intersecting lines and intersecting Vs (or zigs).
2. Formulate the maximum number of regions for the above problems as recurrences.
3. Determine closed form expressions for the solutions of the above recurrences, and prove their correctness using induction.
4. Given a variant of the above problems, derive a recurrence for the maximum number of regions, and determine a closed form solution to it.

Reading assignment

1. Sec 1.2.
2. Sec 2.1.

Exercises and review questions

• Questions on current lecture's material
  1. Exercises 1.6, 1.14 (also derive a closed for expression for the number of cheese cubes, P(n)).

• Questions on next lecture's material
  1. Prove by induction that the sum of the first n positive integers is n(n+1)/2.