Hands on Mathematics for CS - News

12. Session: January 26th

Deriving new inequalities ( Session 10 )

• Christian Hümbert, Steffen Knapp
• Maciej Mrowiec, Khoa Chu

• Sebastian Germesin, Stefan Nesbigall
• Hideo Sato, Björn Gehl

The lexicon enables the user to search for mathematical items such as definitions or theorems. Moreover it provides a list of items the particular mathematical item depends on. We call this list conceptual dependency.

• Identify recursively for both books, 'Analysis Individuell' and 'LeAM calculus' the "full-depth" conceptual dependency of the definition for limits (sequences and functions) and of the definition for continuity. Present both dependencies graphically and compare them. Fathom whether there are any dependencies missing according to your comprehension. (*)
  

• A conceptual dependency graph can be used in exercises as well. Suppose you have such a full graph and you drop some edges. Then you can ask a learner to determine all dependencies, such that all conceptual dependencies are represented correctly. Likewise, you may leave some nodes blank asking the learner to name the blank concept node. Additionally you may add some false nodes or edges constructing an erroneous example.
  

  Provide three interesting examples for conceptual dependency graphs using the LeAM content. Form reasonable exercise by suggesting blank nodes, deleting edges or adding false nodes or edges. (**)
  

• Design and write an applet for the presentation of mathematical concept dependencies. The input is a graph structure, where nodes represent concepts and edges their dependencies. Additionally, nodes are colored according to the user's mastery level. Employ the free software jGraph for your implementation. The graph can be expanded either completely or incrmentally by clicking on nodes. Extract the dependency of the continuity definition as input for testing. You get a bonus point if you provide the exercise functionality described in the previous exercise. (***)