Experimentation in Mathematics: Computational Paths to Discovery

Jonathan Borwein, David Bailey, Roland Girgensohn1568811365, 9781568811369

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.