Kategoria BISAC: Mathematics >> Geometry - General

Konrad Schobel aims to lay the foundations for a consequent algebraic geometric treatment of variable Separation, which is one of the oldest and most powerful methods to construct exact solutions for the fundamental equations in classical and quantum physics. The present work reveals a surprising algebraic geometric structure behind the famous list of separation coordinates, bringing together a great range of mathematics and mathematical physics, from the late 19th century theory of separation of variables to modern moduli space theory, Stasheff polytopes and operads.

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Berthold Heinrich stellt die mathematischen und zeichnerischen Grundlagen fur die Darstellung von Objekten im Raum auf kariertem Papier vor. Dabei prasentiert er auch die Nutzung von Software. In der Schule wird oft kariertes Papier als Raster zur Darstellung von Flachen und Korpern genutzt. Allerdings werden, selbst in einigen Druckwerken, z.B. die entstehenden Ellipsen und Winkelbogen ungenau gezeichnet oder eine Kugelkontur falsch als Kreis dargestellt. Im vorliegenden Essential werden die korrekten Verfahren sowohl theoretisch als auch an konkreten Beispielen vorgestellt und konnen...

Leonid Ryvkin gives a motivated and self-sustained introduction to n-plectic geometry with a special focus on symmetries. The relevant algebraic structures from scratch are developed. The author generalizes known symplectic notions, notably observables and symmetries, to the n-plectic case, culminating in solving the existence question for co-moment maps for general pre-n-plectic manifolds. Finally partial results scattered along the literature are derived from our general result.

The third edition of this monograph provides a systematic treatment of topological quantum field theories in three dimensions, inspired by the discovery of the Jones polynomial of knots, the Witten-Chern-Simons field theory, and the theory of quantum groups. The author, one of the leading experts in the subject, gives a rigorous and self-contained exposition of fundamental algebraic and topological concepts that emerged in this theory.

This book offers a new interpretation of Hermann von Helmholtz s work on the epistemology of geometry. A detailed analysis of the philosophical arguments of Helmholtz s Erhaltung der Kraft shows that he took physical theories to be constrained by a regulative ideal. They must render nature completely comprehensible, which implies that all physical magnitudes must be relations among empirically given phenomena. This conviction eventually forced Helmholtz to explain how geometry itself could be so construed. Hyder shows how Helmholtz answered this question by drawing on the theory...

Geometric group theory is the study of the interplay between groups and the spaces they act on, and has its roots in the works of Henri Poincare, Felix Klein, J.H.C. Whitehead, and Max Dehn. Office Hours with a Geometric Group Theorist brings together leading experts who provide one-on-one instruction on key topics in this exciting and relatively new field of mathematics. It's like having office hours with your most trusted math professors.

An essential primer for undergraduates making the leap to graduate work, the book begins with free groups--actions of free groups on...