With the development of XML Web Services, the Internet could become an integral part of and the basis for teaching computer science and software engineering. The approach has been applied to a university course for students studying introduction to computer science from the point of view of software development in a stateless, Internet environment. The feedback obtained from the course attests to its success. This article is an attempt to focus attention on stateless programming and to give this paradigm its appropriate status in computer science studies. The course could provide an alternative to traditional patterns of computer science. The walk-through presented here is a way of demonstrating this new paradigm. The starting point for the course is the understanding of the Internet environment and the stateless HTTP request, followed by the use and development of XML Web Services integrated with XML and XML schemas, databases and SQL language.