Experimentation in Mathematics : Computational Paths to Discovery

"Sometimes mathematicians like to believe that theorems spring full- fledged from their brains, given birth solely by the power of naked mind. Borwein, Bailey, and Girgensohn take a different approach, using computer programs like Maple and Mathematica to explore hypothesis and generate ideas. Their approach is still rigorous, however, because the insight gained from computer experimentation is then incorporated into a rigorous proof. Topics are drawn primarily from analysis and number theory, including sequences and series, fourier series, zeta functions, partitions and powers, and primes and polynomials. Advanced undergraduate students with solid experience in these areas, or beginning graduate students should find this book accessible; in either case, no programming knowledge is assumed. The first volume of this work is Mathematics by Experiment: Plausible Reasoning in the 21st Century; each of the two can stand on its own." -- Publisher New mathematical insights and rigorous results are often gained through extensive experimentation using numerical examples or graphical images and analyzing them. Today computer experiments are an integral part of doing mathematics. This allows for a more systematic approach to conducting and replicating experiments. The authors address the role of experimental research in the statement of new hypotheses and the discovery of new results that chart the road to future developments. Following the lead of Mathematics by Experiment: Plausible Reasoning in the 21st Century this book gives numerous additional case studies of experimental mathematics in action, ranging from sequences, series, products, integrals, Fourier series, zeta functions, partitions, primes and polynomials. Some advanced numerical techniques are also presented. To get a taste of the material presented in both books view the condensed version. Several years ago I was invited to contemplate being marooned on the proverbial desert island.