Experimentation in Mathematics: Computational Paths to Discovery 1st Edition by Jonathan M. Borwein (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Great book. Prompt delivery.

⭐The book is an advanced text in computational maths. It requires a solid undergraduate background in real analysis. Typically, you’d have this if you are a maths major. Or possibly a theoretical physics major. The level of rigour is unlike most undergrad texts on numerical analyis. The authors strive to demonstrate that even in pure maths, it can be fruitful to have a computer perform computations. The chapters show that often when there are what appear to be pure maths derivations, a context might appear where you can, or perhaps need to, crunch some numbers.There are many problems; some quite challenging. Not all the computations are numerical. Several involve symbolic algebra. The text leaves it to you to use whatever maths packages you prefer.

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