This is a collection of cute puzzles of the form “Show that if a function satisfies the following constraints, it must be . . . ” Please add further examples to this collection! Apart from the one about factorial, they all come from the delightful booklet by Terence Tao [1] but go back to Math Olympiads and similar events. Please add further examples of this kind, either directly or by sending ...

Motivated by recent works on “Higgsless theories,” I discuss an SU(2)0 × SU(2) × U(1) gauge theory with arbitrary bifundamental (or custodial SU(2) preserving) symmetry breaking between the gauge subgroups and with ordinary matter transforming only under the U(1) and SU(2)0. When the couplings, gj, of the other SU(2)s are very large, this reproduces the standard model at the tree level. I calcu...

Mathematical documents are not only hard but fun to write, they are equally hard but fun to read. Unfortunately, the “fun” part comes only in, when one has mastered the art of using mathematical vernacular and grasped all relevant context dimensions. Even though this seems an immanent issue for mathematical authors only, it is also for mathematical readers. In this paper, we argue for the need ...

The fraction of unattached (fun) nanosized 222Rn short-lived decay products in indoor air has been measured in different environments and the following ranges obtained: 0.03-0.25 in kindergartens, 0.03-0.18 in schools, 0.08-0.20 in wineries, and 0.12-0.68 in a karst cave. The dependence of fun on the environmental conditions (air temperature, relative humidity and pressure), as well as on the w...

The FASD study gathered 1330 answers about fun and software development from open source developers as well as 114 answers from programmers working in commercial software projects. The analysis of these data proves that fun plays an important role when software developers decide to get engaged in an open source project. Moreover, the comparison of the answers gives evidence for the hypothesis t...

We onsider a fundamental problem in omputational learning theory: learning an arbitrary Boolean fun tion that depends on an unknown set of k out of n Boolean variables. We give an algorithm for learning su h fun tions from uniform random examples that runs in time roughly (n k ) ! !+1 ; where ! < 2:376 is the matrix multipli ation exponent. We thus obtain the rst polynomial fa tor improvement o...

We performed populations synthesis calculations of single stars and binaries and show that binary evolution is extremely important for Galactic astronomy. We review several binary evolution models and conclude that they give quite different results. These differences can be understood from the assumptions related to how mass is transfered in the binary systems. Most important are 1) the fractio...

We report our experience of including the implementation of a player of a computer game as a programming project in a CS2 course focusing in data structures and algorithms. Every semester, an instructor designs the rules of a game, prepares its visualization, and implements an elementary player with a very simple strategy. The game is then delivered to students who, as a first step in order to ...

Tony Hoare has always been a leader in writing down and proving properties of programs. To prove properties of programs automatically, the most widely used technology today is by far the ubiquitous type checker. Alas, static type systems inevitably exclude some good programs and allow some bad ones. This dilemma motivates us to describe some fun we’ve been having with Haskell, by making the typ...