Geometry

This book follows the Erlangen program to develop hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe.

Trigonometry has always been the black sheep of mathematics. It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by tedious computation. In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosine, and their trigonometric relatives, he brings the subject to life in a compelling blend of history, biography, and mathematics. He presents both a survey of the main elements of trigonometry and a unique account of its vital contribution to science and social development. Woven together in a tapestry of entertaining stories, scientific curiosities, and educational insights, the book more than lives up to the title Trigonometric Delights.

The aim of Spectral Geometry of Partial Differential Operators is to provide a basic and self-contained introduction to the ideas underpinning spectral geometric inequalities arising in the theory of partial differential equations.

This open access book gives a systematic introduction into the Spectral Theory of Differential Operators on metric graphs. Main focus is on the fundamental relations between the spectrum and the geometry of the underlying graph.

An overview of the mechanisms and evolution of Spatial Cognition, integrating evidence from psychology, neuroscience, cognitive science, and Computational Geometry. The volume is also relevant to the epistemology of spatial knowledge in the philosophy of mind.