[ipnon]

Elements of Programming seems to be approaching the limits of advanced programming techniques. It has the reputation of being mathematically rigorous. What else can you study at that point regarding the mathematics of programming? My concern is that software engineering will be slow to graduate into a science, and we will be stuck as merely an artform for the foreseeable future.

[mpiedrav]

Perhaps Knuth's "The Art of Computer Programming" and Sedgewick's (Knuth's student) "An Introduction to the Analysis of Algorithms".

Also, Ben-Ari's "Mathematical Logic for Computer Science" and Pierce's "Software Foundations".

[ipnon]

This is my first time hearing of any of these authors besides Knuth, thanks.

[streetcat1]

You might also want to check out

David Gries, the science of programming:

https://www.springer.com/gp/book/9780387964805

[RossBencina]

Another aspect of the mathematics of programming is the Categorical perspective. For a taste, I've been enjoying following along at home with MIT's course 18.S097: Programming with Categories:

http://brendanfong.com/programmingcats.html