The article describes a new educational approach to support the movement from traditional educational process to research and/or engineering (design) activity in computer science/information technology, engineering, and applied mathematics.The approach was realized as faculty course for advanced senior undergraduate students(information technology).The basic educational flow is: applied problem, mathematical model, algorithm, software, computing the results, report.Twelve laboratory works support the flow above.In each work a combinatorial and/or multicriteria problem is (are) examined (e.g., multicriteria ranking, multiple choice problem, multicriteria assignment/allocation, clustering) including applied examples, algorithm(s), Matlab program(s).Thus students can obtain their skills in applied problems, models, and algorithms. In addition, each student can take into account his/her inclination, motivations, and personal goals. As a result, the student can select a part of the educational flow above to prepare a modified or new version of the part(i.e., applied problem, model, algorithm).Concurrently, students obtain a skills in composition of problems/models/algorithms to get a framework for a complex real world application. Motivated students have conducted advanced research projects and their articles were published.