We investigate several formal systems influential in computer science, and also some of their applications (e.g. inspiring and providing the foundation for a computer programming style, or providing the basis for solving important practical problems like communications protocols, compiling, systems analysis, graphics ...) In more detail, we study: propositional and predicate logic and applications like the Prolog language and circuit design; formal languages and automata theory (FLAT) and applications like scanners and parsers, using the C Language; lambda calculus and the Scheme language with an AI application; matrices and the Matlab language, with applications in robotics or graphics.