When math powers algorithms it’s entertaining

I think that I already wrote previously that a couple of years ago I bought the Elements of Programming book by Alexander Stepanov and Paul McJones. The issue was that the book content was hard for me to grasp at the time. I can hardly say that I now understand it better, but now I got where the rationale for that book came from and why it was written the way it was. It turns out the Alexander Stepanov as a mathematician was influenced deeply by Abstract Algebra, Group Theory and Number Theory. The elements of these fields of mathematics can be traced in the Elements of Programming clearly. For example, chapter 5 is called Ordered Algebraic Structures and it mentions among other things semigroup, monoid and group, which are elements in Group Theory. Overall, the book is structured somewhat like Euclid’s Elements, since the book starts from definitions, that are later used to build gradually upon in other chapters of the book.

Which brings me to the main topic of this post. By the way, the post is about a different book Alexander Stepanov wrote with Daniel Rose and that book was created by refining the notes for the Four Algorithmic Journeys course that Stepanov taught in 2012 at A9 company (subsidiary of Amazon). The course is available in YouTube and it consists of three parts each having a number of videos and the Epilogue part.

I highly recommend to watch it to anyone who is curious about programming, mathematics and science in general. The course is entertaining and it talks about how programming, or more exactly algorithms that are used in programming, are based on algorithms that were already known thousands of years ago in Egypt, Babylon etc. Alexander Stepanov has a peculiar way of lecturing and I find this way of presentation funny. The slides for the course and the notes that were aggregated in the Three Algorithmic Journeys book draft are freely available at Alexander Stepanov’s site.

So the book which I want to mention is From Mathematics to Generic Programming which was published in 2014 and is a reworked version of the Three Algorithmic Journeys draft. This is how Daniel Rose describes this in the Authors’ Note of the book.

The book you are about to read is based on notes from an “Algorithmic Journeys” course taught by Alex Stepanov at A9.com during 2012. But as Alex and I worked together to transform the material into book form, we realized that there was a stronger story we could tell, one that centered on generic programming and its mathematical foundations. This led to a major reorganization of the topics, and removal of the entire section on set theory and logic, which did not seem to be part of the same story. At the same time, we added and removed details to create a more coherent reading experience and to make the material more accessible to less mathematically advanced readers.

My verdict

As authors mentioned the book is geared towards Generic Programming, but I recommend to read both of them in parallel, since each one complements the other. I think that the Three Algorithmic Journeys is even better than the From Mathematics to Generic Programming (FM2GP). First, it’s free and second, ironically, it’s more generic than the FM2GP book.

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