I really enjoyed the 'Four Algorithmic Journeys' Lecture series by Stepanov. (actually theres only 3 journeys) It is a combination of teaching your some basics

I really enjoyed the 'Four Algorithmic Journeys' Lecture series by Stepanov. (actually theres only 3 journeys) It is a combination of teaching your some basics of developing (generic) Algorithms, basic abstract algebra, and some (not always super accurate) history of mathematics. 1. The first journey starts with an ancient Egyptian multiplication algorithm. When we think about what is required for it to work, we are immediately lead to the axioms of a semi-group, and various examples are considered. 2. The second journey starts with division, and then Euclid GCD algorithm. We extend it to polynomials and beyond, and are led to the definition of a ring & euclidean domain. A surprising application to permutation algorithms is given as well! 3. The third journey is about the peano axioms and has a bit of logic and compatibility theory, then the peano axioms are weakened a bit to produce the notion of an iterator from programming. Abstract algebra really seems like a much more relevant 'mathematics of everyday programming' than the usual subject CS students take, which seem to appear in domain specific technical work. By contrast, abstract algebra is to some extent elementary arithmetic and algebra, but extended to non-numerical data, of the kind that appears all time in general-purpose computing. https://www.youtube.com/user/A9Videos/playlists https://www.youtube.com/user/A9Videos/playlists