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Part I. Foundations: 1. Introduction 2. Matrices and complex numbers 3. Whole numbers 4. Graphs and curves 5. Representation of data 6. Probability and random numbers 7. Differential and difference equations Part II. Investigations: 8. Magic squares 9. GCDs, pseudoprimes and Miller's test 10. Graphics: curves and envelopes 11. Zigzags and fast curves 12. Sequences of real numbers 13. Newton-Raphson iteration and fractals 14. Permutations 15. Iterations for nonlinear equations 16. Matrices and solutions of linear systems 17. Functional interpolations and approximation 18. Ordinary differential equations Part III. Modelling: 19. Checkout queues: long or short 20. Fish farming 21. Epidemics 22. Dynamics of snowboating 23. Tides.