Hello All, My name is Joseph Obiajulu and I'm a junior studying mathematics and computer science at Princeton University. I was looking through the project ideas for potential GSoC projects on the Sage page, and I came across a project idea concerning "Native Julia solvers for ordinary differential equations." I have experience with differential equations from my math training, as well as exposure to different numerical computing methods and am starting to get my feet wet with coding in Julia, and so thought that I might be able to contribute to the project. I wanted to ask on this mailing list, especially to those who will mentor this project, where the best place to start would be (I have a few ideas, but I wanted to ask those who have put more thought into this question for advice). Also, I was wondering if this is a high-priority project, or if there is another project that the Julia community would rather have someone work on for the summer.
With that said, I also am thinking of proposing two of my own project ideas (of course, I would only end up pursuing one over the summer, but I figured it doesn't hurt to propose additional ideas). The first is working to expand Julia|Quantum>. I have a particular interest in quantum mechanics and especially quantum computing, and I thought a cool project would be to work on implementing some of the long term JuliaQuantum project goals (see these goals here <https://github.com/JuliaQuantum/Roadmap/blob/master/LongTerm.md>), as well as maybe implementing simple quantum computing algorithms, such as Shor's and Groover's. This idea is still very much in its infancy, so I'm curious to hear what people think of it. The second is a native julia implementation of holonomic functions <https://en.wikipedia.org/wiki/Holonomic_function>. Holonomic functions draw their strength from their closure properties, and often can simplify some calculations (or at least that's what I've read, I'm still looking into it). The following dissertation <http://www.risc.jku.at/publications/download/risc_3886/thesisKoutschan.pdf> would be something I would work through as I try to implement standard operations of holonomic functions (addition, multiplication, integration, derivatives, etc). This is more of a 'Blue Sky' project, but I find it particularly interesting, because it is probably the most "mathematically heavy" one of the three I've proposed, and I that's something that get's me excited, especially that it deals with analysis, which is my mathematical focus. I'm eagerly awaiting to hear from the Julia community! Thanks for the help, Joseph
