G^N vs Probability for Computing

G^N is a special calculator not just a game: This math app animates iterations of one or compositions of two multi-valued maps for free groups of in principle arbitrary finite rank in the abelian and non-commutative cases respectively (in this version the rank is restricted to values in between 2 and 11). Well-known examples of such multi-valued maps are permutations, for example the flip (x_1,x_2)->(x_2,x_1), in G^N we just write (1,2)->(2,1) and instead of the inverse we convenient flip the number. A more involved type of such a multi-valued map is the n+1 cycle defined by (1,...,n)->(-2-3-...-n-1,3,4,...,n,1), a non-trivial theorem. For example if n=2 this map is the hexagon (1,2)->(-2-1,1), this map applied twice reads (1,2)->(2,-2-1) and the third iteration is the identity map (1,2)->(1,2).

Probability for Computing is an independent study app for learners who want focused practice in probability concepts used in computing, data, algorithms, systems, and technical interviews. Work through 160 questions across Fundamentals, Practical Skills, Common Pitfalls, and Advanced Concepts. Each question includes an explanation so you can understand the reasoning, not just memorize an answer. Features: - FSRS spaced-repetition intervals for long-term review - Weak-point heatmap to spot topics that need work - Daily challenge for steady practice - Mock exams for timed review - Offline practice for commutes, classrooms, and travel - No login required Use it as a companion for coursework, self-study, interview prep, or exam-style review when you need short, repeatable probability drills. Independent study app for Probability for Computing practice. Not affiliated with, endorsed by, or sponsored by any company, certification body, exam operator, or vendor. All trademarks belong to their respective owners. Practice offline, no login required.