Ma'am Here are a few things that you might update in the thread if you like.
For AI imo Lisp should be added in addition to Prolog. But almost any programming language can be used to code AI stuffs or Algorithms or even implementations.
For mathematical Problem solving : I think MATLAB, or GNU Octave or Mathematica should be listed before Haskell since they were primarily developed only for scientific computation.
Data Mining : Yes R is awesome. (I will soon make an introduction for this Language) BUt there are other tools which are better and the best this is that its opensource, Like RapidMiner or Weka (Made with Java), these are very very user friendly and easy to use. (I can vouch for Weka since I have worked with Weka)
Machine Learning : R, Java (Weka), Python (scikit-learn)
Natural Language Processing and Information Retrieval : Java (Stanford NLP or GATE or LingPipe), Python (NLTL) [Recommended since its highly customizable], Also there are libraries for NLP in almost every languages but many of them have wrappers of either Stanford NLP or NLTK etc. etc. after Java, and Python I recommend Prolog or Haskell.
Android Development is now not just restricted to Java but Python as well.
http://kivy.org/#home
I can give a lot of resources based on the topics above like DataSets, site links, tutorials, video guides or even Books, but only if someone shows real interest.
I hope this help