By Samuel Belko, published on November 7, 2023.
There are many math books out there, but some of them are truly impressive works. In this post, I would like to share a list of those that I personally admire for their consistency, attention to detail, surprising remarks and overall clarity of thought.
I noticed that usually textbooks in 3th, 4th or later editions are pretty good candidates for being outstanding theory expositions.
My list is of course biased by my own interests. I don't claim to have read every book cover to cover, but with each one I spend enough many hours to know it definitely should be mentioned here.
There are some good candidates that I omit for now, but I might add them later once I have a more complete impression of them.
A list of outstanding theory books:
Convex Optimization. Stephen Boyd and Lieven Vandenberghe. 2004.
Probability theory–a comprehensive course. Achim Klenke. Third Edition. 2020.
Combinatorial optimization. Polyhedra and efficiency. Alexander Schrijver. 2003
Integer programming. Michele Conforti, Gérard Cornuéjols, Giacomo Zambelli. 2014.
Some interesting & non-standard problems can be found in:
Mathematical tapas. Vol. 1 (for undergraduates). Jean-Baptiste Hiriart-Urruty. 2016.
Mathematical tapas. Vol. 2 (from undergraduate to graduate level) Jean-Baptiste Hiriart-Urruty. 2017.