Burke's career began at I.P. Sharp Associates, where he worked on financial systems, and continued with several other roles in finance including independent consulting. In 1994, he joined Jsoftware and began work on J's programming environment as well as libraries written in J. Burke is now an equal partner in Jsoftware with Eric Iverson and Roger Hui. In 2009 Kx Systems hired Burke, who had been living in Asia since 2001, as head of its new Asia Pacific office.
- "APL and J", a series in Vector journal (pdf)
- "Programming in J/Windows" at APL94.
- "J for the APL Programmer", with Roger Hui
- "J4 and OOP"
- "Memory Mapped Files in J"