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Sussman Gerald Jay: Functional
Differential Geometry

Functional Differential Geometry

Mathematics of Networks: Modulus Theory and Convex Optimization is a book that seeks to answer the question: "What can be learned by adapting the theory of p-modulus (and related continuum analysis concepts) to discrete graphs?"

Modulus Theory and Convex Optimization

Mathematics of Networks

Cambridge Mathematical Library

The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This book, reissued with a new Foreword, presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more modern developments. It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic. After an informal preparatory chapter, the book follows an historical path, beginning with the work of Abel and Gauss on elliptic integrals and elliptic functions. This is followed by chapters on theta functions, modular groups and modular functions, the quintic, the imaginary quadratic field, and on elliptic curves. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics, with many exercises with hints scattered throughout the text.

Function Theory, Geometry, Arithmetic

Elliptic Curves

Series In Algebraic And Differential Geometry

This book serves as an accessible introduction to schemes, coherent sheaves, and their cohomology, designed for readers with only a foundational knowledge of commutative algebra. Developed from years of teaching experience, the author has carefully crafted the text to be self-contained, covering all the essential concepts necessary for a solid understanding of algebraic geometry.Many readers will find it invaluable for grasping the subject, appreciating its clear explanations and lack of prerequisites. In addition to laying a strong foundation, the book provides ample background for those seeking to explore more advanced topics in the field.

Algebraic Geometry: Schemes, Coherent Sheaves And Cohomology

Cambridge Studies in Advanced Mathematics

This up-to-date introduction to type theory and homotopy type theory will be essential reading for advanced undergraduate and graduate students interested in the foundations and formalization of mathematics. The book begins with a thorough and self-contained introduction to dependent type theory. No prior knowledge of type theory is required. The second part gradually introduces the key concepts of homotopy type theory: equivalences, the fundamental theorem of identity types, truncation levels, and the univalence axiom. This prepares the reader to study a variety of subjects from a univalent point of view, including sets, groups, combinatorics, and well-founded trees. The final part introduces the idea of higher inductive type by discussing the circle and its universal cover. Each part is structured into bite-size chapters, each the length of a lecture, and over 200 exercises provide ample practice material.

Introduction to Homotopy Type Theory

Trends in Mathematics

This volume collects papers based on lectures given at the XLI Workshop on Geometric Methods in Physics, held in Białystok, Poland in July 2024 as well as extended abstracts of minicourses presented during the XIII&nbsp;School on Geometry and Physics. These chapters provide readers an overview of cutting-edge research in&nbsp;quantum field theories, infinite-dimensional groups, integrable systems, noncommutative geometry, and a wide&nbsp;variety of other areas. Specific topics include: • Graded structures • Lie algebra structures • Quasicrystals • Sigma models • Barycentric algebras • Nijenhuis geometry Geometric Methods in Physics XLI will be a valuable resource for mathematicians and physicists interested in&nbsp;recent developments at the intersection of these areas.

Workshop, Białystok, Poland, 2024

Geometric Methods in Physics XLI

The Mathematics of Origami

Science Networks. Historical Studies

This unique reference work systematically presents and studies mathematical terms, sourcing literature from antiquity until the 20th century.
The book provides detailed and reliable information on the origins and developments of more than 1,000 mathematical terms from all branches of mathematics. The dictionary is based on extensive research of the primary literature, cites from original sources, provides historical illustrations, discusses synonyms and competing terms, and quotes critical or approving comments on newly created terms. Each entry is self-contained and includes a bibliography. All major mathematical fields are represented, ranging from geometry and arithmetic to, for example, calculus, topology, and category theory.
This set comprises both volumes I and II, covering the letters from A through Z.

Volumes I and II

A Historical Dictionary of Mathematical Terms

The book is a comprehensive compilation of diverse articles delving into various intriguing topics within the realm of geometry. Each article is refereed by prominent researchers in the field. The book contains research articles offering valuable insights and original results, making it a valuable resource for researchers in the field, as well as survey articles that review current developments and list open problems.

Celebrating the 65th Birthday of Athanase Papadopoulos

Essays on Geometry

New Mathematical Monographs

Abstract polytopes are partially ordered sets that satisfy some key aspects of the face lattices of convex polytopes. They are chiral if they have maximal symmetry by combinatorial rotations, but none by combinatorial reflections. Aimed at graduate students and researchers in combinatorics, group theory or Euclidean geometry, this text gives a self-contained introduction to abstract polytopes and specialises in chiral abstract polytopes. The first three chapters are introductory and mostly contain basic concepts and results. The fourth chapter talks about ways to obtain chiral abstract polytopes from other abstract polytopes, while the fifth discusses families of chiral polytopes grouped by common properties such as their rank, their small size or their geometric origin. Finally, the last chapter relates chiral polytopes with geometric objects in Euclidean spaces. This material is complemented by a number of examples, exercises and figures, and a list of 75 open problems to inspire further research.

Abstract Chiral Polytopes

This book consists of a collection of articles dedicated to Valentin Poénaru, on topology and geometry in a broad sense. Poénaru is one of the leading mathematicians whose work had an essential impact on the development of topology in France over the last forty years of the twentieth century. The special topics addressed in this volume include hyperbolic geometry, 3-manifolds, complex and symplectic geometry, differential topology, combinatorial group theory, piecewise-linear topology, algebraic geometry, knots and links, homotopy theory, braid groups, phylogenetics, the history of geometry, and the philosophy of mathematics. This collection of articles, written by well-known researchers, provides a lively insight into a number of current research topics in geometry and topology.

Dedicated to Valentin Poénaru

Essays on Topology

Volume II: J-Z

Chapman & Hall/CRC Monographs and Research Notes in Mathematics

This book focuses on spectral theory for linear operators involving bounded or unbounded demicompact linear operators acting on Banach spaces.

Demicompactness and Perturbation Theory

Spectral Theory for Linear Operators

Functional Differential Geometry

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