"Hamamura Nagisa no Keisan Nooto" (Hamamura Nagisa's Calculation Notes) by Aoyagi Aito. A collection of cases that are solved using math. Math is the premise, the problem, the solution, and the punchline, in every chapter.
The premise is that a terrorist group has taken hostage of everyone in Japan. Specifically, a terrorist group run by mathematicians, who acted in protest of the government's curriculum changes that deprioritized math and science in favor of other subjects. This setting is surreal enough to be funny, and honestly these terrorists are quite lovable if they weren't killing people. One highlight of reading this novel to observe what happens when people became extremely passionate about math.
Of course, probably the most passionate of them all is our heroine, Hamamura Nagisa. She managed to counter all terrorists' math-based problems with her own mathematical solutions, while maintaining many cute traits common to heroines of this age group. Having a young girl as the main character also contributed to all the reader-friendly explanations for each math problem. This was a very carefully developed character.
Regarding the problems: simply discovering what kind of mathematical principle is behind each murder was a bit of a surprise, and the solution to those problems were often equally surprising. I am afraid there are no spoiler-free synopses possible. Let's just say that I never thought "division by zero" would be a key phrase in stopping a terrorist attack.
This first volume very much exceeded my expectations. It was really math through and through, but written in such a way that is approachable to both hardcore math majors and casual readers alike. Looking forward to volume 2.
Previous (2014-12-04): "No Game No Life" volume 6 by Kamiya Yuu
Next (2015-01-06): "Hamamura Nagisa no Keisan Nooto" volume 2 by Aoyagi Aito