We propose new sequential sorting operations by adapting techniques and methods used for designing parallel sorting algorithms. Although the norm is to parallelize a sequential algorithm to improve performance, we adapt a contrarian approach: we employ parallel computing techniques to speed up sequential sorting. Our methods can also work for multi-core sorting with minor adjustments that do not necessarily require full parallelization of the original sequential algorithm. The proposed approach leads to the development of asymptotically efficient deterministic and randomized sorting operations whose practical sequential and multi-core performance, as witnessed by an experimental study, matches or surpasses existing optimized sorting algorithm implementations. We utilize parallel sorting techniques such as deterministic regular sampling and random oversampling. We extend the notion of deterministic regular sampling into deterministic regular oversampling for sequential and multi-core sorting and demonstrate its potential. We then show how these techniques can be used for sequential sorting and also lead to better multi-core sorting algorithm performance as witnessed by the undertaken experimental study.