Bøger udgivet af American Mathematical Society

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.

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.

Presents rigorous mathematical techniques for the analysis of boundary value problems for ODEs arising in applications. The emphasis is on proving existence of solutions, but there is also a substantial chapter on uniqueness and multiplicity questions and several chapters which deal with the asymptotic behaviour of solutions with respect to either the independent variable or some parameter.

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.

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.

Representation theory plays important roles in geometry, algebra, analysis, and mathematical physics. This book presents an introduction to the representation theory of finite groups from an algebraic point of view, regarding representations as modules over the group algebra. It is suitable for a year-long graduate course.

Focuses on the fundamentals of a theory, which is an analog of affine algebraic geometry for partial differential equations. This work describes applications of Secondary Calculus ranging from algebraic geometry to field theory, classical and quantum, including areas such as characteristic classes, differential invariants and variational calculus.

Treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry. This book covers a wide range of topics of modern coordinate-free differential geometry.

Information geometry provides the mathematical sciences with a fresh framework of analysis. This book presents a comprehensive introduction to the mathematical foundation of information geometry. It provides an overview of many areas of applications, such as statistics, linear systems, information theory, quantum mechanics, and convex analysis.

Among nonlinear PDEs, dispersive and wave equations form an important class of equations, including the nonlinear Schrodinger equation, nonlinear wave equation, Korteweg de Vries equation, and the wave maps equation. This book offers an introduction to the methods and results used in the modern analysis of the Cauchy problem for such equations.

An introduction to stochastic processes studying certain elementary continuous-time processes. It includes a description of the Poisson process and related processes with independent increments as well as a brief look at Markov processes with a finite number of jumps.

Deals with the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, this book moves to less trivial results, both classical and contemporary. It demonstrates the advantage of purely geometric methods of studying conics.

Mathematicians are expected to publish their work: in journals, conference proceedings, and books. It is vital to advancing their careers. This is a guidebook to publishing mathematics. It describes both the general setting of mathematical publishing and the specifics about the various publishing situations mathematicians may encounter.

Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. It is suitable for those working in algebraic geometry.

The Ausdehnungslehre of 1862 is Grassmann's mature presentation of his extension theory. The work captured his mathematical achievements. This book includes development of the inner product and its relation to the concept of angle, the 'theory of functions' from the point of view of extension theory, and his contribution to the Pfaff problem.

Presents research on understanding, teaching, and learning mathematics at the post-secondary level. This book offers some preliminary results on student learning using technology when lessons are delivered via the Internet.

Based on courses given by the author at MIT and at Rome University in spring 1997, this book presents an introduction to algebraic aspects of conformal field theory. It includes material on the foundations of a rapidly growing area of algebraic conformal theory.

Presents the basics of linear algebra, with an emphasis on nonstandard and interesting proofs. This book features about 230 problems with solutions. It is suitable as a supplementary text for an undergraduate or graduate algebra course.

Includes a treatment of exponential, logarithmic, and trigonometric functions, progressions, and induction method, as well as an extensive introduction to differential and integral calculus.

Suitable for both students and teachers who love mathematics and want to study its various branches beyond the limits of school curriculum. This book contains vast theoretical and problem material in main areas of what authors consider to be 'extracurricular mathematics'.

A guide to the qualitative theory of foliations. It features topics including: analysis on foliated spaces, characteristic classes of foliations and foliated manifolds. It is suitable as a supplementary text for a topics course at the advanced graduate level.

Presents the translation from the Japanese textbook for the grade 10 course, 'Basic Mathematics'. This book covers algebra (including quadratic functions, equations, and inequalities), trigonometric functions, and plane coordinate geometry.