Geometry

One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years.

In his classic work of geometry, Euclid focused on the properties of flat surfaces.

In his work on rings of operators in Hilbert space, John von Neumann discovered a new mathematical structure that resembled the lattice system Ln.

The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory.

Fields Medal-winning mathematician John Milnor's classic treatment of singular points of complex hypersurfacesOne of the greatest mathematicians of the twentieth century, John Milnor has made fundamental discoveries in diverse areas of mathematics, from topology and dynamical systems to algebraic K-theory.

Locally symmetric spaces are generalizations of spaces of constant curvature.

This collection of papers constitutes a wide-ranging survey of recent developments in differential geometry and its interactions with other fields, especially partial differential equations and mathematical physics.

A classic treatment of flows on homogeneous spaces from the acclaimed Annals of Mathematics Studies seriesPrinceton University Press is proud to have published the Annals of Mathematics Studies since 1940.

A classic treatment of the Atiyah-Singer index theorem from the acclaimed Annals of Mathematics Studies seriesPrinceton University Press is proud to have published the Annals of Mathematics Studies since 1940.

Riemann introduced the concept of a "e;local system"e; on P1-{a finite set of points} nearly 140 years ago.

The need for an axiomatic treatment of homology and cohomology theory has long been felt by topologists.

Kenneth Brakke studies in general dimensions a dynamic system of surfaces of no inertial mass driven by the force of surface tension and opposed by a frictional force proportional to velocity.

In 1920, Pierre Fatou expressed the conjecture that--except for special cases--all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration.

One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems.

Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade.

The original goal that ultimately led to this volume was the construction of "e;motivic cohomology theory,"e; whose existence was conjectured by A.

This book proves an analogue of William Thurston's celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it.

Among the many differences between classical and p-adic objects, those related to differential equations occupy a special place.

This book studies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over Q.

Resolution of singularities is a powerful and frequently used tool in algebraic geometry.

For hundreds of years, the study of elliptic curves has played a central role in mathematics.

Between the seventeenth and nineteenth centuries Japan was totally isolated from the West by imperial decree.

A foundational account of a new construction in the p-adic Langlands correspondenceMotivated by the p-adic Langlands program, this book constructs stacks that algebraize Mazur's formal deformation rings of local Galois representations.

New mathematical research in arithmetic dynamicsIn The Arithmetic of Polynomial Dynamical Pairs, Charles Favre and Thomas Gauthier present new mathematical research in the field of arithmetic dynamics.

A fascinating exploration of the pentagon and its role in various culturesThe pentagon and its close cousin, the pentagram, have inspired individuals for the last two and half millennia, from mathematicians and philosophers to artists and naturalists.

This book is the first to present a new area of mathematical research that combines topology, geometry, and logic.

This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology.

These notes describe a general procedure for calculating the Betti numbers of the projective quotient varieties that geometric invariant theory associates to reductive group actions on nonsingular complex projective varieties.

Essential mathematical insights into one of the most important and challenging open problems in general relativity-the stability of black holesOne of the major outstanding questions about black holes is whether they remain stable when subject to small perturbations.

Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry.

Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples.

This book presents the complete proof of the Bloch-Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry.

This book studies the interplay between the geometry and topology of locally symmetric spaces, and the arithmetic aspects of the special values of L-functions.

An advanced treatment of surgery theory for graduate students and researchersSurgery theory, a subfield of geometric topology, is the study of the classifications of manifolds.

A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K.

An exploration of mathematical style through 99 different proofs of the same theoremThis book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem.

By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical foundation for several exciting recent developments.

An interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentiethThe Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s.

An inviting, intuitive, and visual exploration of differential geometry and formsVisual Differential Geometry and Forms fulfills two principal goals.

This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology.

John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P.

How mathematics helped build the world's most important buildings from early Egypt to the presentFrom the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings.

An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group.

This book gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology.

This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography.

William Thurston (1946-2012) was one of the great mathematicians of the twentieth century.

A milestone in the geometric understanding of algebraization theorems that also provides an introduction to Arakelov geometryMotivated by questions of transcendental number theory, arithmetic, and Diophantine geometry, this book provides a thorough study of a new kind of mathematical objectformal-analytic arithmetic surfaces.

Bachelorarbeit aus dem Jahr 2021 im Fachbereich Mathematik - Geometrie, Note: 1,7, Technische Universität Carolo-Wilhelmina zu Braunschweig (Didaktik der Mathematik und Elementarmathematik), Sprache: Deutsch, Abstract: Die allgemeine Innenwinkelsumme regelmäßiger Sternfiguren stellt in der Mathematik die Summe der Innenwinkel in ihren Spitzen dar, die bereits untersucht und bewiesen wurde.

Bachelorarbeit aus dem Jahr 2022 im Fachbereich Mathematik - Geometrie, Note: 2,1, Universität Hildesheim (Stiftung), Sprache: Deutsch, Abstract: Die Arbeit beschäftigt sich mit drei Kreissätzen aus der Geometrie, mit denen sich die Winkel von Figuren wie Dreiecken undVierecken innerhalb von Kreisen berechnen lassen.

Unterrichtsentwurf aus dem Jahr 2021 im Fachbereich Mathematik - Geometrie, , Sprache: Deutsch, Abstract: Dies ist ein Unterrichtsentwurf, der 2021 zum Ende der Probezeit auch praktisch durchgeführt wurde.