Hands on Mathematics for CS - Exercises

2. Session: November 3rd

• Noreen Nasar, M. Sarmad Hussain: Relations
• Noreen Nasar, M. Sarmad Hussain: Functions
• Suleman Parvez Butt, M Kamran Azam: Relations
• Suleman Parvez Butt, M Kamran Azam: Functions
• Stefan Nesbigall, Sebastian Germesin: Functions

Exercises:

In this exercise session we will cover simple induction proofs . Try to follow and to integrate Polya's phases . Do you think proving resembles to a search process (try and error)?

1. Modelling exercises by state diagrams:

• Process the exercise: The sum of odd numbers. Draw a state diagram representing the structure/flow of the exercise (interaction steps, feedback, etc.). (*)
  

• Devise a state diagram representing the structure/flow (interaction steps, feedback, etc.) for the exercise: The sum of cubic numbers. Try to follow and to include Polya's phases .(*)
  

• Devise a state diagram representing the structure/flow (interaction steps, feedback, etc.) for the theorem: Bernoulli's inequality . The proof is already given. Try to follow and to include Polya's phases .(*)
  

• Devise a state diagram representing the structure/flow (interaction steps, feedback, etc.) for the theorem: Inequality for the arithmetic and the geometric mean . The proof is already given. Try to follow and to include Polya's phases .(*)