Hands on Mathematics for CS - News

8. Session: December 15th

Applet: Parse/Draw graph and calculate roots ( Session 5 )

• Christian Hümbert, Steffen Knapp

• Prove the sum rule for limits.
  
  • according to Polya
  • according to Leron (hierarchically)
  • according to the bridge construction paradigm [ Techreport (ps.gz) ]
  • according to LeAM calculus ( proof exercise ).
  
  

  Is it easy to follow the proof? If not, how would you improve the proof presentation? How would you integrate interactive elements? Prepare a presentation, but keep and deliver your "Schmierblätter" as well. Both will form a base for the next week's exercise on joint problem spaces . You are allowed to work in larger groups, but each sub group is supposed to present one proof. Compare all approaches and make notes of your discussion. Try the same approach for a different limit proof. Do you see any similarities? (*)

• Write an applet which presents a sequence and an epsilon environment graphically. The width of the epsilon environments can be changed by a slider. In addition, the user can choose freely an element x of the sequence. The element's mark should represent, whether the element is within an epsilon environment or not, or whether it is the first element in the epsilon environment. (***)
  

• Write an applet which presents a function, an epsilon and a delta environment graphically. The user can determine a point x_0 and change both environments widths by a slider preserving correctness. That is, determining one environment width leads to adaption of the other environment width. (***)