During the summers (1951–1954) that I was a graduate student in “pure mathematics,” I worked in the Systems Engineering Section of the Glenn L. Martin Company. I began to notice the applicability of supposedly pure topics like prime number theory and finite field theory to problems in communications. My first major applied effort involved developing the theory of “Shift Register Sequences.” (My book with this title will soon see its third edition, with a third publisher.) Much of my work has been in response to practical questions I was asked, for which I had the necessary mathematical tools. These topics have included comma-free codes, Costas arrays, Tuscan squares, Golomb rulers, zero-sidelobe radar, etc. My shift register work has had the broadest impact: to cell phone signals, the GPS system, error-correcting codes, radar, cryptography, etc. I am fortunate to have lived long enough to get some recognition for my work.