By Jeremy Gray

ISBN-10: 0817647724

ISBN-13: 9780817647728

ISBN-10: 0817647732

ISBN-13: 9780817647735

This ebook is a examine of the way a selected imaginative and prescient of the team spirit of arithmetic, referred to as geometric functionality idea, used to be created within the 19^{th} century. The vital concentration is at the convergence of 3 mathematical subject matters: the hypergeometric and comparable linear differential equations, team thought, and on-Euclidean geometry.

The textual content for this moment version has been tremendously multiplied and revised, and the prevailing appendices enriched with ancient money owed of the Riemann–Hilbert challenge, the uniformization theorem, Picard–Vessiot idea, and the hypergeometric equation in larger dimensions. The workouts were retained, making it attainable to take advantage of the ebook as a significant other to arithmetic classes on the graduate level.

"If you need to comprehend what mathematicians like Gauss, Euler and Dirichlet have been doing...this e-book will be for you. It fills in lots of historic gaps, in a narrative that's mostly unknown...This ebook is the results of paintings performed by means of a significant historian of mathematics...If you're intrigued by means of such subject matters studied years in the past yet now principally forgotten...then learn this book."--**The Mathematical Gazette** (on the second one edition)

"One one of the best books at the heritage of mathematics... Very stimulating studying for either historians of recent arithmetic and mathematicians as well."--**Mathematical Reviews** (on the 1st edition)

"The publication includes an grand wealth of fabric with regards to the algebra, geometry, and research of the 19th century.... Written with exact ancient point of view and transparent exposition, this e-book is actually not easy to place down."--**Zentralblatt fur Mathematik** (review of 1st edition)