A kaleidoscopic excursion into numerical calculations of differential equations -- 1. Introduction -- 2. Logistic equation -- 3. Harmonic oscillator -- 4. Wave equations -- 5. Epilogue -- An introduction to the Finite Element Method -- 1. Introduction -- 2. An elementary example -- 3. The 2-dimensional Poisson equation -- 4. Final remarks -- Coupling of sound and structural vibrations -- 1. Introduction -- 2. Governing equations and analysis -- 3. Numerical results and discussion -- Mathematical modeling and dimensional analysis -- 1. Introduction -- 2. Mathematical Modeling -- 3. Dimensional Analysis -- 4. Four-wheel steering -- About difference equations, algebras and discrete events -- 1. Difference equations -- 2. Changing the algebra -- 3 Example on production -- 4. Some graph theory and the spectral theory of matrices -- 5. A stochastic extension -- 6. Counter versus dater description -- 7. The Z-transform -- 8. Conclusions -- Acoustical detection of obstructions in a pipe with a temperature gradient -- 1. Introduction -- 2. The problem -- 3. The model -- 4. Solution -- 5. Results -- 6. Conclusions -- Interior point approach to linear programming: theory, algorithms and parametric analysis -- 1. Introduction -- 2. Central approach to the theory of LP -- 3. A polynomial-time path-following algorithm -- 4. Parametric analysis -- Some reflections on Newton's Method -- 1. Introduction and motivation -- 2. Rational Newton Flows -- 3. Structural Stability -- 4. Newton Graphs -- 5. Characterization of Newton Graphs -- 6. Open problems -- Recurrence and induction in Computer Science -- 1. Introduction -- 2. Strings of Symbols -- 3. Gray codes and recursiveness -- 4. Recursive algorithms.