Böcker utgivna av American Mathematical Society

Demonstrates that complex numbers and geometry can be blended together beautifully. This results in easy proofs and natural generalizations of many theorems in plane geometry, such as the Napoleon theorem, the Ptolemy-Euler theorem, the Simson theorem, and the Morley theorem.

Offers an introduction to algebraic number theory for readers with a moderate knowledge of elementary number theory and some familiarity with the terminology of abstract algebra. With its exceptionally clear prose, hundreds of exercises, and historical motivation, this is a textbook for a second undergraduate course in number theory.

Zeta and $L$-functions play a central role in number theory. They provide important information of arithmetic nature. This book, which grew out of the author's teaching over several years, explores the interaction between number theory and combinatorics using zeta and $L$-functions as a central theme.

Organised around carefully sequenced problems, Linear Algebra and Geometry will help students build both the tools and the habits that provide a solid basis for further study in mathematics. This volume uses elementary geometry to build the beautiful edifice of results and methods that make linear algebra such an important field.

Many laws of physics are formulated in terms of differential equations. This book puts together the three main aspects of the topic of partial differential equations, namely theory, phenomenology, and applications, from a contemporary point of view.

Pick up this book and dive into one of eight chapters relating mathematics to fiber arts! Amazing exposition transports any interested person on a mathematical exploration that is rigorous enough to capture the hearts of mathematicians.

Data science is a highly interdisciplinary field, incorporating ideas from applied mathematics, statistics, probability, and computer science, as well as many other areas. This book provides an introduction to the mathematical methods that form the foundations of machine learning and data science.

Offers a comprehensive history of the development of mathematics in the US and Canada. This first volume of a two-volume work takes the reader from the European encounters with North America in the fifteenth century up to the emergence of the United States as a world leader in mathematics in the 1930s.

Introduces a new notion of analytic space over a non-Archimedean field. The book includes a homotopic characterization of the analytic spaces associated with certain classes of algebraic varieties and an interpretation of Bruhat-Tits buildings in terms of these analytic spaces. The author also studies the connection with the earlier notion of a rigid analytic space.

Contains the proceedings of the conference String-Math 2016, held in June 2016 at College de France, Paris. The papers in this volume cover topics ranging from supersymmetric quantum field theories, topological strings, and conformal nets to moduli spaces of curves, representations, instantons, and harmonic maps, with applications to spectral theory and to the geometric Langlands program.

Provides an introduction to the representation theory of quivers and finite dimensional algebras. It gives a thorough and modern treatment of the algebraic approach based on Auslander-Reiten theory as well as the approach based on geometric invariant theory. The book is suitable for a graduate course in quiver representations and has numerous exercises and examples throughout.

Contains the proceedings of the conference on Manifolds, $K$-Theory, and Related Topics, held in June, 2014. The articles are a collection of research papers featuring recent advances in homotopy theory, $K$-theory, and their applications to manifolds. Topics covered include homotopy and manifold calculus, structured spectra, and their applications to group theory and the geometry of manifolds.

This book starts with simple arithmetic inequalities and builds to sophisticated inequality results such as the Cauchy-Schwarz and Chebyshev inequalities. Nothing beyond high school algebra is required of the student. The exposition is lean. Most of the learning occurs as the student engages in the problems posed in each chapter. And the learning is not "linear".

Provides an elementary introduction to geometric topology and its applications to chemistry, molecular biology, and cosmology. It does not assume any mathematical or scientific background, sophistication, or even motivation to study mathematics. It is meant to be fun and engaging while drawing students in to learn about fundamental topological and geometric ideas.

Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and this volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory.

In Really Big Numbers, mathematician and author, Richard Evan Schwartz, leads math lovers of all ages on an innovative and strikingly illustrated journey through the infinite number system. You Can Count on Monsters is a unique teaching tool that takes maths lovers on a journey designed to motivate kids to learn the fun of factoring and prime numbers.

This book, together with the companion volume, Fermat's Last Theorem: The Proof, presents in full detail the proof of Fermat's Last Theorem given by Wiles and Taylor. With these two books, the reader will be able to see the whole picture of the proof to appreciate one of the deepest achievements in the history of mathematics.

The fundamental idea of geometry is that of symmetry. With that principle as the starting point, this book presents a study of Euclidean geometry. It focuses on transformations of the plane. It contains hundreds of exercises. It is suitable for a one-semester undergraduate course on geometry.

The work of Joseph Fels Ritt and Ellis Kolchin in differential algebra paved the way for exciting new applications in constructive symbolic computation, differential Galois theory, the model theory of fields, and Diophantine geometry. This book assembles Kolchin's mathematical papers.

A comprehensive and up-to-date treatment of sieve methods. The theory of the sieve is developed thoroughly with complete and accessible proofs of the basic theorems. A wide range of applications are included, both to traditional questions, and to areas pr

Offers an introduction to large deviations. This book is divided into two parts: theory and applications. It presents basic large deviation theorems for i i d sequences, Markov sequences, and sequences with moderate dependence. It also includes an outline of general definitions and theorems.

Covers the classical theory of abstract Riemann surfaces. This book presents the requisite function theory and topology for Riemann surfaces. It also covers differentials and uniformization. For compact Riemann surfaces, it features topics such as divisors, Weierstrass points, and the Riemann-Roch theorem.

Operads are mathematical devices that describe algebraic structures of many varieties and in various categories. Operads are particularly important in categories with a good notion of 'homotopy', where they play a key role in organizing hierarchies of higher homotopies. This book offers an introduction describing the development of operad theory.

Research in string theory has generated a rich interaction with algebraic geometry, with exciting work that includes the Strominger-Yau-Zaslow conjecture. This monograph builds on lectures at the 2002 Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string theory and algebraic geometry.