Learning Mathematics Through Modelling and Simulation: An Investigative Approach

Contents: Preface. 1. Monte Carlo Methods: Estimating π. 2. Exploring Probability through Simulation. 3. Graph Theory: Seven Bridges Problem and the Tower of Hanoi. 4. The Mathematics of Ciphers: Public Key Encryption and RSA. 5. Exploring Fractals. 6. The Newton‒Raphson Method and Fractals. 7. Experiments in Symmetry: Frieze and Wallpaper Patterns. 8. Applications of Matrices. Bibliography.

Learning Mathematics through Modelling and Simulation: An Investigative Approach, offers the readers a hands-on experience of discovering the beautiful aspects of mathematics through the use of technology. Three powerful tools falling into the categories of spreadsheet programs (Microsoft Excel), dynamic geometry software (GeoGebra) and computer algebra systems (Mathematica), are introduced. They are applied in the book to enable the readers to independently explore, visualise, conjecture, reason and solve problems.

The book highlights the role of mathematical software in enabling explorations leading to a deeper insight into the problems. Technology is used to generate phenomena and acquire data from which questions naturally arise and create a demand for appropriate theory.

Readers are introduced to the applications of Calculus, Probability, Number Theory, Linear Algebra and Discrete Mathematics. Each chapter includes a set of exercises, called Investigations, that prompt analytical thinking, encourage exploration of a concept, or test the readers’ ability to apply the concept to a realistic problem situation.