1 Numbers everywhere Selected topics in numerical analysis.- 1.1 Numerical evaluation.- 1.2 Equation solving.- 1.3 Random numbers and Monte Carlo.- 2 Exploratory computation Collected intra- and interdisciplinary projects.- 2.1 Mathematical problems.- 2.2 Nature-motivated models.- 2.3 Projects from biology.- 2.4 Projects from physics and chemistry.- 3 The lure of large numbers Projects in number theory.- 3.1 Large-integer arithmetic.- 3.2 Prime numbers.- 3.3 Fast algorithms.- 3.4 Factoring.- 4 The FFT forest-The ubiquitous FFT and its relatives.- 4.1 Discrete Fourier transform.- 4.2 FFT algorithms.- 4.3 Real-valued transforms.- 4.4 Number-theoretic transforms.- 5 Wavelets Young arrivals in the transform family.- 5.1 Chords, notes, and little waves.- 5.2 Discrete wavelet bases.- 5.3 Discrete wavelet transform.- 6 Complexity reigns Chaos & fractals & such.- 6.1 Chaos.- 6.2 Fractals.- 7 Signals from the real world Projects in signal processing.- 7.1 Data compression.- 7.2 Sound.- 7.3 Images.- Appendix Support code for the book Projects.- References.