# How to add mathematical rigor to systems research?

My research focuses on wireless networking and designing various protocols. I primarily build systems. I, sometimes, analyze the performance of those systems, using techniques from probability, statistics, and algebra.

I want to improve my understanding of the mathematical underpinnings of my work. Specifically:

1. Derive and prove theorems on properties of a system and prove it;
2. Model a system.

This post differs from SE posts like this and this because I'm looking for concrete steps to incorporate math rigor into my systems research. I found the answers in those posts to be too abstract.

Other posts, such as this and this, provide concrete but scattered advice, suggesting:

1. take theory courses;
2. read math-heavy papers and learn.

For (1), what types of courses are likely to be useful? Is Great Theoretical Ideas In Computer Science a good source?

For (2), I find it difficult to lead from reading a proof to writing one of my own, or from reading about a model to creating my own model. Input is easy, output is still hard. Any good examples (papers, books, or online courses) to learn how to output theoretical results?

Besides these two lines of suggestions, any other specific suggestions on how to be a more mathematically fluent researcher for someone like me who is from systems background?

Some more context for the whole question: I'm working on my first theory-oriented paper and I have great difficulty in proving the optimality of my proposed protocol. Thus I'm asking to see if there is a general way to hone my proof skills in the short term and my general math skills in the long run.

• I think there are two questions here, one about how to learn theory (perhaps applied mathematics) and another about a specific paper. – mac389 Jun 23 '15 at 0:36
• Not enough for a full answer, but for your 2nd query, I've found that the book "How to Solve It" by George Pólya helped me to develop some of the types of skills you are interested in developing (I come from an electrical engineering background). – Mad Jack Jun 23 '15 at 0:55