Hands on Mathematics for CS - Exercises

5. Session: November 24th

Inductive proof in Omdoc:

• Michael Dietrich, Dominik Jednoralski (postponed)

• Steffen Heil, Verena Kremer, Daniel Schmitt

• Suleman Parvez Butt, M Kamran Azam

Exercises:

Erroneous examples: Read the following proofs and build in some errors. Make up questions, in which the user might be asked, whether a step is correct or not. In the letter case the user has to express where the error is. Use multiple choice questions for providing several (made up) reasons. (*)

• Proof of Bernoulli's inequality
• Proof for the inequality for the arithmetic and the geometric mean.
• Babylonic root extraction (Babylonisches Wurzelziehen)

• f(x)=(x-1)(x-2)-2)/x
• f(x)=1/2 cos(13*Pi*x)
• f(x)=1/2 cos(13*Pi*x)+1/4 cos(13^2*Pi*x)
  
  

• Compare your solution approach with computer-based techniques (nested intarvals, Newton, fix point etc.) (**)
  

• Write an applet which parses and plots functions, where functions are conveyed as parameter. For this you might use the Mathematical Visualization Toolkit . Feel free to choose any other java library if you consider it superior. But it should be freeware.
  

  Then after plotting, the user should be able to mark specific points and assign them a meaning. In this case the user should be able to mark roots. (Later, we will also want to mark extrema, stationary points or saddle points.) After marking roots, the applet should verify user's input. Employ any of the mentioned techniques.
  

  Generally speaking, this applet should form a base for more applet exercises in the near future, where we will get in touch with discussion of functions in more detail. (***)