Financial Informatics is the development and evaluation of applications, tools, processes, and structures which manage financial data or support the investment process.
Open Source Tools
Here are some open source tools which can be used to learn about financial software development. Some of these tools can be used to construct production systems, others might be better as tools for learning about a specific area. This list is neither complete, nor a recommendation to use this software.
The R Language is an open source statistcal computing package. It is widely used with big data. MATLAB® is the leading commmerical product in this space.
Enthought provides a packaged distribution of Python for scientific calculations called Canopy in both a free and commercial version. IPython is an interactive Python notebook similar in function to MATLAB®. Pandas is an open source Python data analysis package which has some traction within the financial community. It makes use of NumPy and SciPy two other Python packages which offer scientific and numerical computing features to the Python language.
Quantlib is an excellent library for quantitative financial calculations. QuantlibXL is an Excel addin which I use in my Financial Informatics class as a way to make use of Quantlib without needing to do C++ programming.
QuickFIX/J is an open source FIX engine. A FIX Engine manages communication between a client and a server application using the FIX protocol. QuickFIX/J is used in the open source trading system Marketcetera as well as other production systems and comes with a simple client/server application called Banzai which can be used to learn about the FIX protocol and FIX application development.
Esper is an open source complex event processing package. Complex event processing is not a concept limited to the Financial domain, but much of the data in the financial environment is streaming past quite quickly so tools designed to filter and act on that data are very useful to have. There are several commercial products in this space.