Decidability and complexity issues as well as mathematical and discrete models and algorithms are ubiquitous in computer science, such as formal semantics for modeling systems, behavior of large software components, community detection through graph algorithms, mathematics for discrete/continuous optimization, and scientific computing in a broad sense. We provide algorithms to optimize computer systems, for decision making, to increase the reliability of computing software and/or to assess the security of cryptographic primitives and prepare the quantum era. Most of them suffer from the curse of dimensionality and our goal is to push forward the current barriers.