Challenging problems and research have been considered as vital components of Aerospace Engineering curricula. Some Engineering, Computer Science, and Math Courses in American colleges have been analyzed to find positive factors that would be helpful in mutually beneficial cooperation between colleges and industry. The analysis of traditional and modern applications of the course concepts [design of a hypersonic vehicle, nonequilibrium thermodynamics, anisotropic media and liquid crystals, properties of Martian atmospheric gases, non-monotone aerodynamic coefficients of simple-shape bodies, etc.] and ways of collaboration between industry and universities have been discussed. Students' "mistakes" have been reviewed allowing to generate new research ideas and numerical algorithms, as well as to discover new physical phenomena. Challenge in the classroom allows motivating students in the analysis of modern engineering concepts, developing strong background and research skills, finding unique solutions of new problems, and preparing students for success and surviving in industrial environment.